From ab35bbc2bd08d216468e3e44a81f228593d54629 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 9 Dec 2014 11:29:16 +0300 Subject: [PATCH 01/46] Update variable step-size SSPLMM. --- src/pyclaw/sharpclaw/solver.py | 60 ++++++++++++++++++++++++---------- 1 file changed, 43 insertions(+), 17 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 66cc35652..5fafdb178 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -156,8 +156,8 @@ def before_step(solver,solution) _cfl_default = { 'SSP104': [2.45, 2.5], - 'SSPMS32': [0.16, 0.2], - 'SSPMS43': [0.14, 0.16] + 'SSPMS32': [0.24, 0.25], + 'SSPMS43': [0.15, 1./6.] } # ======================================================================== @@ -194,6 +194,7 @@ def __init__(self,riemann_solver=None,claw_package=None): # Used only if time integrator is a multistep method self.step_index = 1 + self.sspcoeff0 = None self.alpha = None self.beta = None @@ -310,56 +311,77 @@ def step(self,solution): elif self.time_integrator == 'SSPMS32': - # Store initial solution if self.step_index == 1: - for i in range(2): - self._registers[-2+i].dt = self.dt + # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() + self._registers[-1].dq = self.dq(state) + self._registers[-1].dt = self.dt + self._registers[-1].dtFE = self.dt * self.cfl_max / self.cfl.get_cached_max() + # initialize dt and dtFE history + for i in range(2): + self._registers[-3+i].dt = 0. + self._registers[-3+i].dtFE = 0. if self.step_index < 3: # Use Euler method for starting values - deltaq = self.dq(state) + deltaq = self._registers[-1].dq state.q += deltaq + self.sspcoeff0 = self._sspcoeff['Euler'] + self.step_index += 1 - + if self.step_index == 3: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + else: omega = (self._registers[-2].dt + self._registers[-1].dt)/self.dt # ssp coefficient r = (omega-1.)/omega - # method coefficients + # method coefficients delta = 1./omega**2 beta = (omega+1.)/omega - deltaq = self.dq(state) + + deltaq = self._registers[-1].dq state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q - # Update stored solutions + # Update stored information for i in range(2): self._registers[-3+i].q = self._registers[-2+i].q.copy() self._registers[-3+i].dt = self._registers[-2+i].dt + self._registers[-3+i].dtFE = self._registers[-2+i].dtFE self._registers[-1].q = state.q.copy() self._registers[-1].dt = self.dt + self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number + self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() elif self.time_integrator == 'SSPMS43': - # Store initial solution if self.step_index == 1: - for i in range(3): - self._registers[-3+i].dt = self.dt + # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() + self._registers[-1].dq = self.dq(state) + self._registers[-1].dt = self.dt + self._registers[-1].dtFE = self.dt * self.cfl_max / self.cfl.get_cached_max() + # initialize dt and dtFE history + for i in range(3): + self._registers[-4+i].dt = 0. + self._registers[-4+i].dtFE = 0. if self.step_index < 4: # Use SSP22 method for starting values import copy s1 = copy.deepcopy(state) - deltaq=self.dq(state) + deltaq = self._registers[-1].dq s1.q = state.q + deltaq s1.t = state.t + self.dt deltaq = self.dq(s1) state.q = 0.5*(state.q + s1.q + deltaq) + self.sspcoeff0 = 1. # SSP coefficient for SSP22 self.step_index += 1 - + if self.step_index == 4: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + else: H = self._registers[-3].dt + self._registers[-2].dt + self._registers[-1].dt omega3 = H/self.dt @@ -370,17 +392,21 @@ def step(self,solution): delta0 = (4*omega4 - omega3**2)/omega3**3 beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - deltaq = self.dq(state) + + deltaq = self._registers[-1].dq deltaqm4 = self.dq(self._registers[-4]) state.q = beta3*(r*state.q + deltaq) + \ - (r*beta0+delta0)*self._registers[-4].q + beta0*deltaqm4 + (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 # Update stored solutions for i in range(3): self._registers[-4+i].q = self._registers[-3+i].q.copy() self._registers[-4+i].dt = self._registers[-3+i].dt + self._registers[-4+i].dtFE = self._registers[-3+i].dtFE self._registers[-1].q = state.q.copy() self._registers[-1].dt = self.dt + self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number + self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() elif self.time_integrator == 'LMM': From ffed0f7e939fee3ffe5a055871499b2e8134b9f4 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 9 Dec 2014 11:32:25 +0300 Subject: [PATCH 02/46] Make a function to accept/reject step and update code for new step-size calculatiob. --- src/pyclaw/sharpclaw/solver.py | 80 +++++++++++++++++++++++----------- 1 file changed, 54 insertions(+), 26 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 5fafdb178..614e7328e 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -586,39 +586,67 @@ def _allocate_registers(self,solution): self._registers.append(copy.deepcopy(state)) - def get_cfl_max(self): - """ - Set maximum CFL number for current step depending on time integrator + def accept_reject_step(self,cfl): + r""" + Decide whether to accept or not the current step. + For Runge-Kutta methods the step is accepted if cfl <= cfl_max. + For SSPMS32 the choice of step-size guarantees the cfl condition is satisfied. + For SSPMS43 additional checks on previous forward Euler step-sizes are required. """ - if self.time_integrator[:-2] == 'SSPMS' and self.step_index >= len(self._registers): - s = len(self._registers)-2 - H = self._registers[-2].dt - for i in range(s): - H += self._registers[-3-i].dt - r = (H - s*self._registers[-1].dt)/H # ssp coefficient at the current step - sigma = r/self._sspcoeff[self.time_integrator] + accept_step = True + + if self.time_integrator == 'SSPMS43': + if self.step_index < len(self._registers): + # condition for starting solutions + rho = 3./5. + if self.step_index == 1: + self._registers[-1].dtFE = self.dt * self.cfl_max / cfl + if cfl > self.cfl_max or self.dt > rho * self._registers[-1].dtFE: + accept_step = False + else: + # condition for solution calculated by SSPMS43 + rhoFE = 9./10. + dtFE = self._registers[-1].dtFE + dtFEm1 = self._registers[-2].dtFE + if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: + accept_step = False + + elif self.time_integrator == 'SSPMS32' and self.step_index >= len(self._registers): + pass + else: - sigma = 1.0 + # check cfl condition for Runge-Kutta methods + if cfl > self.cfl_max: + accept_step = False - return sigma * self.cfl_max + return accept_step - def get_dt_new(self): - """ - Set time-step for next step depending on time integrator + + def get_dt_new(self,cfl,accept_step): + r""" + Set time-step for next step depending on the time integrator """ - # desired time-step - dt_des = self.dt * self.cfl_desired / self.cfl.get_cached_max() - - if self.time_integrator[:-2] == 'SSPMS' and self.step_index >= len(self._registers): - s = len(self._registers)-2 - H = self._registers[-1].dt - for i in range(s): - H += self._registers[-2-i].dt - sigma = H / (self._sspcoeff[self.time_integrator]*H + s*dt_des) + if accept_step: + if self.time_integrator[:-2] == 'SSPMS' and self.step_index >= len(self._registers): + s = len(self._registers) + p = int(self.time_integrator[-2]) + mu = min([self._registers[-1-i].dtFE for i in range(s)]) + H = sum([self._registers[-1-i].dt for i in range(s-1)]) + self.dt = H * mu / (H + (p-2)*mu) + else: + self.dt = self.dt * self.cfl_desired / cfl else: - sigma = 1.0 + self.logger.debug("Step rejected.") + if self.time_integrator == 'SSPMS43': + if self.step_index < len(self._registers): + rho = 3./5. + self.dt = min(rho * self._registers[-1].dtFE, self.dt * self.cfl_desired / cfl) + else: + self.dt /= 2. + else: + self.dt = self.dt * self.cfl_desired / cfl - return sigma * dt_des + return min(self.dt_max,self.dt) From f59a1b99a720ff3d7de77caa4f9387b8b90dc4fc Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 9 Dec 2014 11:35:36 +0300 Subject: [PATCH 03/46] Update pyclaw solver to match with changes in sharpclaw solver. --- src/pyclaw/solver.py | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 5187b4f45..610bd3bbf 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -505,10 +505,6 @@ def _bc_upper(self, bc_type, state, dim, t, array, idim, name): def get_cfl_max(self): return self.cfl_max - def get_dt_new(self): - cfl = self.cfl.get_cached_max() - return min(self.dt_max,self.dt * self.cfl_desired / cfl) - def evolve_to_time(self,solution,tend=None): r""" Evolve solution from solution.t to tend. If tend is not specified, @@ -571,13 +567,15 @@ def evolve_to_time(self,solution,tend=None): if self.dt_variable: q_backup = state.q.copy('F') told = solution.t + if self.time_integrator[:-2] == 'SSPMS': + step_index_old = self.step_index self.step(solution) # Check to make sure that the Courant number was not too large cfl = self.cfl.get_cached_max() - cfl_max = self.get_cfl_max() - if cfl <= cfl_max: + accept_step = self.accept_reject_step(cfl) + if accept_step: # Accept this step self.status['cflmax'] = max(cfl, self.status['cflmax']) if self.dt_variable==True: @@ -594,12 +592,15 @@ def evolve_to_time(self,solution,tend=None): # Increment number of time steps completed num_steps += 1 self.status['numsteps'] += 1 + else: # Reject this step self.logger.debug("Rejecting time step, CFL number too large") if self.dt_variable: state.q = q_backup solution.t = told + if self.time_integrator[:-2] == 'SSPMS': + self.step_index = step_index_old else: # Give up, we cannot adapt, abort self.status['cflmax'] = \ @@ -609,7 +610,7 @@ def evolve_to_time(self,solution,tend=None): # Choose new time step if self.dt_variable: if cfl > 0.0: - self.dt = self.get_dt_new() + self.dt = self.get_dt_new(cfl,accept_step) self.status['dtmin'] = min(self.dt, self.status['dtmin']) self.status['dtmax'] = max(self.dt, self.status['dtmax']) else: From ab16359185aca6b29361cad1de6651c2e3a2a63f Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 9 Dec 2014 11:37:51 +0300 Subject: [PATCH 04/46] Edit how cfl number is updated, so cfl at each step relates with current solution. --- src/pyclaw/cfl.py | 3 +-- src/pyclaw/sharpclaw/solver.py | 1 + 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/src/pyclaw/cfl.py b/src/pyclaw/cfl.py index 2e0207039..5c19a2761 100644 --- a/src/pyclaw/cfl.py +++ b/src/pyclaw/cfl.py @@ -23,5 +23,4 @@ def set_local_max(self,new_local_max): self._global_max = new_local_max def update_global_max(self,new_local_max): - self._global_max = new_local_max - + self._global_max = max(self._global_max,new_local_max) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 614e7328e..63d61f50a 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -266,6 +266,7 @@ def step(self,solution): `solver.time_integrator`. """ state = solution.states[0] + self.cfl.set_local_max(0.) self.before_step(self,state) From 493c141fd70ac62afcd5de87f77ca43f92e5f5b8 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Thu, 11 Dec 2014 18:39:11 +0300 Subject: [PATCH 05/46] Reset local cfl at the beggining of step in classic. --- src/pyclaw/classic/solver.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/pyclaw/classic/solver.py b/src/pyclaw/classic/solver.py index 46e286985..9ffd1432c 100644 --- a/src/pyclaw/classic/solver.py +++ b/src/pyclaw/classic/solver.py @@ -126,6 +126,8 @@ def step(self,solution): :Output: - (bool) - True if full step succeeded, False otherwise """ + + self.cfl.set_local_max(0.) if self.before_step is not None: self.before_step(self,solution.states[0]) From 6d5b5fdf25009f09711a7a71eff58cd15616331c Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Thu, 11 Dec 2014 18:42:26 +0300 Subject: [PATCH 06/46] Add functions for accept/reject step and new step-size choice for classic. Remove step_index reset to sharpclaw solver. --- src/pyclaw/solver.py | 16 +++++++++------- 1 file changed, 9 insertions(+), 7 deletions(-) diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 610bd3bbf..a139dfaef 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -502,9 +502,15 @@ def _bc_upper(self, bc_type, state, dim, t, array, idim, name): # ======================================================================== # Evolution routines # ======================================================================== - def get_cfl_max(self): - return self.cfl_max - + def accept_reject_step(self,cfl): + accept_step = True + if cfl > self.cfl_max: + accept_step = False + return accept_step + + def get_dt_new(self,cfl,accept_step): + return min(self.dt_max,self.dt * self.cfl_desired / cfl) + def evolve_to_time(self,solution,tend=None): r""" Evolve solution from solution.t to tend. If tend is not specified, @@ -567,8 +573,6 @@ def evolve_to_time(self,solution,tend=None): if self.dt_variable: q_backup = state.q.copy('F') told = solution.t - if self.time_integrator[:-2] == 'SSPMS': - step_index_old = self.step_index self.step(solution) @@ -599,8 +603,6 @@ def evolve_to_time(self,solution,tend=None): if self.dt_variable: state.q = q_backup solution.t = told - if self.time_integrator[:-2] == 'SSPMS': - self.step_index = step_index_old else: # Give up, we cannot adapt, abort self.status['cflmax'] = \ From 732d99a0f41f9db1431ecda5b77a5e713e6eef95 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Thu, 11 Dec 2014 18:45:46 +0300 Subject: [PATCH 07/46] Major edits/corrections in accept/reject step and new step-size setup. step_index is updated only when step is accepted. --- src/pyclaw/sharpclaw/solver.py | 100 +++++++++++++++------------------ 1 file changed, 46 insertions(+), 54 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 63d61f50a..bce6d8ebb 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -193,7 +193,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.c = None # Used only if time integrator is a multistep method - self.step_index = 1 + self.step_index = 0 self.sspcoeff0 = None self.alpha = None self.beta = None @@ -291,11 +291,9 @@ def step(self,solution): deltaq=self.dq(self._registers[0]) state.q = 1./3.*state.q + 2./3.*(self._registers[0].q+deltaq) - elif self.time_integrator=='SSP104': state.q = self.ssp104(state) - elif self.time_integrator=='RK': # General RK with specified coefficients # self._registers[i].q actually stores dt*f(y_i) @@ -310,9 +308,8 @@ def step(self,solution): for j in range(num_stages): state.q += self.b[j]*self._registers[j].q - elif self.time_integrator == 'SSPMS32': - if self.step_index == 1: + if self.step_index <= 1: # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() self._registers[-1].dq = self.dq(state) @@ -322,17 +319,11 @@ def step(self,solution): for i in range(2): self._registers[-3+i].dt = 0. self._registers[-3+i].dtFE = 0. - if self.step_index < 3: # Use Euler method for starting values deltaq = self._registers[-1].dq state.q += deltaq self.sspcoeff0 = self._sspcoeff['Euler'] - - self.step_index += 1 - if self.step_index == 3: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] - else: omega = (self._registers[-2].dt + self._registers[-1].dt)/self.dt # ssp coefficient @@ -354,9 +345,8 @@ def step(self,solution): self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - elif self.time_integrator == 'SSPMS43': - if self.step_index == 1: + if self.step_index <= 1: # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() self._registers[-1].dq = self.dq(state) @@ -366,7 +356,6 @@ def step(self,solution): for i in range(3): self._registers[-4+i].dt = 0. self._registers[-4+i].dtFE = 0. - if self.step_index < 4: # Use SSP22 method for starting values import copy @@ -378,11 +367,6 @@ def step(self,solution): deltaq = self.dq(s1) state.q = 0.5*(state.q + s1.q + deltaq) self.sspcoeff0 = 1. # SSP coefficient for SSP22 - - self.step_index += 1 - if self.step_index == 4: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] - else: H = self._registers[-3].dt + self._registers[-2].dt + self._registers[-1].dt omega3 = H/self.dt @@ -409,7 +393,6 @@ def step(self,solution): self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - elif self.time_integrator == 'LMM': num_steps = len(self.alpha) @@ -424,6 +407,7 @@ def step(self,solution): self._registers[-num_steps+self.step_index].q = state.q.copy() self._registers[-num_steps+self.step_index].dq = self.dq(state) self.step_index += 1 + else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self._registers[-1].dq @@ -435,7 +419,6 @@ def step(self,solution): self._registers[-1].q = state.q.copy() self._registers[-1].dq = self.dq(state) - else: raise Exception('Unrecognized time integrator') except CFLError: @@ -596,56 +579,65 @@ def accept_reject_step(self,cfl): """ accept_step = True - if self.time_integrator == 'SSPMS43': + # check cfl condition for SSP LMM methods + if self.time_integrator[:-2] == 'SSPMS': + # condition for starting RK methods if self.step_index < len(self._registers): - # condition for starting solutions - rho = 3./5. - if self.step_index == 1: + # first step is always rejected because CFL condition is violated in dq() + if self.step_index == 0: self._registers[-1].dtFE = self.dt * self.cfl_max / cfl - if cfl > self.cfl_max or self.dt > rho * self._registers[-1].dtFE: + self.step_index += 1 + if cfl > self.cfl_max: accept_step = False - else: - # condition for solution calculated by SSPMS43 + # additional condition for SSPMS43 + if self.time_integrator == 'SSPMS43' and self.dt > 3./5. * self._registers[-1].dtFE: + accept_step = False + # only need to check conditions for SSPMS43 for the steps LMM is active + elif self.time_integrator == 'SSPMS43': rhoFE = 9./10. dtFE = self._registers[-1].dtFE dtFEm1 = self._registers[-2].dtFE if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False - - elif self.time_integrator == 'SSPMS32' and self.step_index >= len(self._registers): - pass - - else: - # check cfl condition for Runge-Kutta methods - if cfl > self.cfl_max: - accept_step = False + # check cfl condition for Runge-Kutta methods + elif cfl > self.cfl_max: + accept_step = False return accept_step def get_dt_new(self,cfl,accept_step): r""" - Set time-step for next step depending on the time integrator + Set time-step for next step depending on the time integrator and whether or not the step is accepted """ - if accept_step: - if self.time_integrator[:-2] == 'SSPMS' and self.step_index >= len(self._registers): - s = len(self._registers) - p = int(self.time_integrator[-2]) - mu = min([self._registers[-1-i].dtFE for i in range(s)]) - H = sum([self._registers[-1-i].dt for i in range(s-1)]) - self.dt = H * mu / (H + (p-2)*mu) - else: - self.dt = self.dt * self.cfl_desired / cfl - else: - self.logger.debug("Step rejected.") - if self.time_integrator == 'SSPMS43': - if self.step_index < len(self._registers): - rho = 3./5. - self.dt = min(rho * self._registers[-1].dtFE, self.dt * self.cfl_desired / cfl) + if self.time_integrator[:-2] == 'SSPMS': + # step-size update for SSP LMM methods + if accept_step == True: + if self.step_index == len(self._registers): + s = len(self._registers) + p = int(self.time_integrator[-2]) + mu = min([self._registers[-1-i].dtFE for i in range(s)]) + H = sum([self._registers[-1-i].dt for i in range(s-1)]) + self.dt = H * mu / (H + (p-2)*mu) else: + # step-size update for starting methods + self.dt = self.dt * self.cfl_desired / cfl + self.step_index += 1 + if self.step_index == 4: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + elif accept_step == False: + if self.step_index < len(self._registers): + self.dt = self.dt * self.cfl_desired / cfl + # additional conditions for SSPMS43 + if self.time_integrator == 'SSPMS43': + self.dt = min(3./5. * self._registers[-1].dtFE, self.dt) + elif self.time_integrator == 'SSPMS43': + # cruel step-size reduction if step-size assumptions for SSPMS43 are violated + # no such assumptions are needed for SSPMS32 self.dt /= 2. - else: - self.dt = self.dt * self.cfl_desired / cfl + else: + # step-size update for Runge-Kutta methods + self.dt = self.dt * self.cfl_desired / cfl return min(self.dt_max,self.dt) From 046e929a2faa4b2a96f736cd4b9a59863c404943 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Thu, 11 Dec 2014 20:02:21 +0300 Subject: [PATCH 08/46] Correct step-size update at the last RK step. --- src/pyclaw/sharpclaw/solver.py | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index bce6d8ebb..b681e3318 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -592,6 +592,9 @@ def accept_reject_step(self,cfl): # additional condition for SSPMS43 if self.time_integrator == 'SSPMS43' and self.dt > 3./5. * self._registers[-1].dtFE: accept_step = False + # apply LMM at the next step if last RK step is accepted + if accept_step == True and self.step_index == len(self._registers)-1: + self.step_index += 1 # only need to check conditions for SSPMS43 for the steps LMM is active elif self.time_integrator == 'SSPMS43': rhoFE = 9./10. @@ -612,7 +615,7 @@ def get_dt_new(self,cfl,accept_step): """ if self.time_integrator[:-2] == 'SSPMS': # step-size update for SSP LMM methods - if accept_step == True: + if accept_step: if self.step_index == len(self._registers): s = len(self._registers) p = int(self.time_integrator[-2]) @@ -623,9 +626,9 @@ def get_dt_new(self,cfl,accept_step): # step-size update for starting methods self.dt = self.dt * self.cfl_desired / cfl self.step_index += 1 - if self.step_index == 4: + if self.step_index == len(self._registers)-1: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - elif accept_step == False: + else: if self.step_index < len(self._registers): self.dt = self.dt * self.cfl_desired / cfl # additional conditions for SSPMS43 From 9f6571d9d94cbcce34ec9b2108c88c54a67587cf Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Mon, 15 Dec 2014 08:50:43 +0300 Subject: [PATCH 09/46] Improve the way information from previous steps is updated. --- src/pyclaw/sharpclaw/solver.py | 27 +++++++++------------------ 1 file changed, 9 insertions(+), 18 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index b681e3318..39562de5e 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -311,14 +311,10 @@ def step(self,solution): elif self.time_integrator == 'SSPMS32': if self.step_index <= 1: # Store initial solution, function evaluation, dt and forward Euler dt - self._registers[-1].q = state.q.copy() self._registers[-1].dq = self.dq(state) + self._registers[-1].q = state.q.copy() self._registers[-1].dt = self.dt self._registers[-1].dtFE = self.dt * self.cfl_max / self.cfl.get_cached_max() - # initialize dt and dtFE history - for i in range(2): - self._registers[-3+i].dt = 0. - self._registers[-3+i].dtFE = 0. if self.step_index < 3: # Use Euler method for starting values deltaq = self._registers[-1].dq @@ -336,10 +332,9 @@ def step(self,solution): state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q # Update stored information - for i in range(2): - self._registers[-3+i].q = self._registers[-2+i].q.copy() - self._registers[-3+i].dt = self._registers[-2+i].dt - self._registers[-3+i].dtFE = self._registers[-2+i].dtFE + register = type(state) + self._registers.append(register(state.patch,state.num_eqn,state.num_aux)) + self._registers = self._registers[1:] self._registers[-1].q = state.q.copy() self._registers[-1].dt = self.dt self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number @@ -352,10 +347,6 @@ def step(self,solution): self._registers[-1].dq = self.dq(state) self._registers[-1].dt = self.dt self._registers[-1].dtFE = self.dt * self.cfl_max / self.cfl.get_cached_max() - # initialize dt and dtFE history - for i in range(3): - self._registers[-4+i].dt = 0. - self._registers[-4+i].dtFE = 0. if self.step_index < 4: # Use SSP22 method for starting values import copy @@ -383,11 +374,10 @@ def step(self,solution): state.q = beta3*(r*state.q + deltaq) + \ (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 - # Update stored solutions - for i in range(3): - self._registers[-4+i].q = self._registers[-3+i].q.copy() - self._registers[-4+i].dt = self._registers[-3+i].dt - self._registers[-4+i].dtFE = self._registers[-3+i].dtFE + # Update stored information + register = type(state) + self._registers.append(register(state.patch,state.num_eqn,state.num_aux)) + self._registers = self._registers[1:] self._registers[-1].q = state.q.copy() self._registers[-1].dt = self.dt self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number @@ -536,6 +526,7 @@ def _set_fortran_parameters(self,state,clawparams,workspace,reconstruct): reconstruct.alloc_recon_workspace(maxnx,self.num_ghost,state.num_eqn,self.num_waves, clawparams.lim_type,clawparams.char_decomp) + def _allocate_registers(self,solution): r""" Instantiate State objects for Runge--Kutta stages and Linear Multistep method steps. From 93ab5dd953a9c46455b65b578f660f4c31b62b2b Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Mon, 15 Dec 2014 10:50:14 +0300 Subject: [PATCH 10/46] Make LMM tests pass. Also: - Change LMM names from 'MS' to 'LMM' - Make step rejection work correctly for LMMs - Allow use of grid norms in util.check_diff() by passing delta --- .../test_acoustics.py | 12 +- .../acoustics_2d_homogeneous/acoustics_2d.py | 7 +- .../test_2d_acoustics.py | 5 +- .../verify_sharpclaw_lmm.txt | 200 +++++++++--------- .../acoustics_2d_interface.py | 2 +- .../test_acoustics_2d_variable.py | 2 +- examples/advection_1d/test_advection.py | 4 +- src/pyclaw/sharpclaw/solver.py | 48 ++--- src/pyclaw/solver.py | 12 +- src/pyclaw/util.py | 10 +- 10 files changed, 158 insertions(+), 144 deletions(-) diff --git a/examples/acoustics_1d_homogeneous/test_acoustics.py b/examples/acoustics_1d_homogeneous/test_acoustics.py index 1f500f67c..515044e55 100644 --- a/examples/acoustics_1d_homogeneous/test_acoustics.py +++ b/examples/acoustics_1d_homogeneous/test_acoustics.py @@ -28,23 +28,23 @@ def acoustics_verify(claw): from clawpack.pyclaw.util import gen_variants - classic_tests = gen_variants(acoustics_1d.setup, verify_expected(0.00104856594174), + classic_tests = gen_variants(acoustics_1d.setup, verify_expected(0.001049), kernel_languages=('Python','Fortran'), solver_type='classic', disable_output=True) - ptwise_tests = gen_variants(acoustics_1d.setup, verify_expected(0.00104856594174), + ptwise_tests = gen_variants(acoustics_1d.setup, verify_expected(0.001049), kernel_languages=('Fortran',), ptwise=True, solver_type='classic', disable_output=True) - sharp_tests_rk = gen_variants(acoustics_1d.setup, verify_expected(0.000298879563857), + sharp_tests_rk = gen_variants(acoustics_1d.setup, verify_expected(0.000299), kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSP104', disable_output=True) - sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00227996627104), + sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00125), kernel_languages=('Python','Fortran'), solver_type='sharpclaw', - time_integrator='SSPMS32', disable_output=True) + time_integrator='SSPLMM32', disable_output=True) - weno_tests = gen_variants(acoustics_1d.setup, verify_expected(0.000153070447918), + weno_tests = gen_variants(acoustics_1d.setup, verify_expected(0.000153), kernel_languages=('Fortran',), solver_type='sharpclaw', time_integrator='SSP104', weno_order=17, disable_output=True) diff --git a/examples/acoustics_2d_homogeneous/acoustics_2d.py b/examples/acoustics_2d_homogeneous/acoustics_2d.py index f98dc605a..6124c2a12 100755 --- a/examples/acoustics_2d_homogeneous/acoustics_2d.py +++ b/examples/acoustics_2d_homogeneous/acoustics_2d.py @@ -43,9 +43,10 @@ def setup(kernel_language='Fortran', use_petsc=False, outdir='./_output', if solver.time_integrator=='SSP104': solver.cfl_max = 0.5 solver.cfl_desired = 0.45 - elif solver.time_integrator=='SSPMS32': - solver.cfl_max = 0.2 - solver.cfl_desired = 0.16 + elif solver.time_integrator=='SSPLMM32': + solver.lim_type = 1 + solver.cfl_max = 0.25 + solver.cfl_desired = 0.24 else: raise Exception('CFL desired and CFL max have not been provided for the particular time integrator.') diff --git a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py index d3c3ac251..fb578c512 100644 --- a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py +++ b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py @@ -16,7 +16,8 @@ def verify(claw): test_pressure = test_q[0,:,:] thisdir = os.path.dirname(__file__) expected_pressure = np.loadtxt(os.path.join(thisdir,data_filename)) - return check_diff(expected_pressure, test_pressure, reltol=1e-3) + return check_diff(expected_pressure, test_pressure, reltol=1e-3, + delta=claw.solution.grid.delta) else: return return verify @@ -36,7 +37,7 @@ def verify(claw): sharp_tests_lmm = gen_variants(acoustics_2d.setup, verify_data('verify_sharpclaw_lmm.txt'), kernel_languages=('Fortran',), solver_type='sharpclaw', - time_integrator='SSPMS32', disable_output=True) + time_integrator='SSPLMM32', disable_output=True) from itertools import chain for test in chain(classic_tests, ptwise_tests, sharp_tests_rk, sharp_tests_lmm): diff --git a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt index 65afb820b..e21bc0b6b 100644 --- a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt +++ b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt @@ -1,100 +1,100 @@ -9.231119437693868183e-24 -1.663522542629988372e-23 -6.093854755896507327e-23 1.268304538034542429e-22 3.442078696919200020e-22 -8.165086829115567750e-22 -1.891859192003515688e-21 4.947612919540062114e-21 1.244991286636758939e-20 -1.869997026620309521e-20 -5.314394799308197212e-20 2.894946399649543628e-19 2.471223803353294565e-18 1.661551112118917712e-17 1.076361510524772535e-16 6.592343676224618478e-16 3.801383552788822493e-15 2.061589935638272693e-14 1.050812530935308834e-13 5.031217039885908519e-13 2.261816911067158777e-12 9.544198635613678515e-12 3.779353989075422513e-11 1.404136822416146254e-10 4.893536233693357295e-10 1.599254035279989592e-09 4.898510097397338969e-09 1.405148713582248677e-08 3.771263188058152656e-08 9.463317737719833436e-08 2.220209795728026722e-07 4.876453438044300986e-07 1.005484917575609680e-06 1.953295291688379407e-06 3.587673529311953745e-06 6.250134730325662227e-06 1.035785331017817741e-05 1.637574350715632600e-05 2.476871697441546339e-05 3.593367337280689876e-05 5.011625255054555269e-05 6.732510073191434285e-05 8.725337332299301575e-05 1.092297920592529367e-04 1.322097343416809092e-04 1.548183697096536054e-04 1.755361673974696732e-04 1.927952398276206803e-04 2.051934519266125048e-04 2.116743225201552696e-04 2.116743225201552696e-04 2.051934519266125048e-04 1.927952398276206803e-04 1.755361673974696732e-04 1.548183697096536867e-04 1.322097343416808821e-04 1.092297920592529367e-04 8.725337332299297510e-05 6.732510073191434285e-05 5.011625255054554591e-05 3.593367337280691231e-05 2.476871697441547016e-05 1.637574350715632261e-05 1.035785331017817741e-05 6.250134730325659686e-06 3.587673529311952474e-06 1.953295291688377289e-06 1.005484917575608198e-06 4.876453438044288281e-07 2.220209795728019575e-07 9.463317737719792408e-08 3.771263188058134127e-08 1.405148713582241729e-08 4.898510097397313326e-09 1.599254035279982561e-09 4.893536233693339718e-10 1.404136822416142118e-10 3.779353989075413466e-11 9.544198635613660743e-12 2.261816911067155950e-12 5.031217039885904480e-13 1.050812530935308077e-13 2.061589935638272378e-14 3.801383552788820916e-15 6.592343676224617492e-16 1.076361510524772535e-16 1.661551112118917712e-17 2.471223803353295335e-18 2.894946399649545073e-19 -5.314394799308197212e-20 -1.869997026620309521e-20 1.244991286636758487e-20 4.947612919540063619e-21 -1.891859192003514560e-21 -8.165086829115563989e-22 3.442078696919199080e-22 1.268304538034542194e-22 -6.093854755896503801e-23 -1.663522542629988666e-23 9.231119437693869652e-24 --1.663522542629988372e-23 -6.897218129220874566e-23 1.414225242599584776e-22 3.972463419764661334e-22 -9.628241304471548218e-22 -2.173255869367201352e-21 6.159531717822605583e-21 1.408686706048940720e-20 -2.610454776839951381e-20 -5.987611760317355405e-20 4.311927966514470000e-19 3.506499277161588535e-18 2.511706081495857299e-17 1.690900262217314629e-16 1.074596745610647901e-15 6.437134422314383524e-15 3.630472257734208692e-14 1.926353145593442842e-13 9.610164123734157467e-13 4.505210532446860926e-12 1.983820394835149193e-11 8.202542868464184202e-11 3.183758171544381866e-10 1.159772895536598877e-09 3.963885555517697395e-09 1.270565092395971755e-08 3.816921133414469092e-08 1.073692413960607617e-07 2.825508871584507349e-07 6.952842633049299769e-07 1.600634135225895453e-06 3.453613798628312238e-06 7.005246719062155312e-06 1.340584041044501447e-05 2.428592492934549115e-05 4.177510623552754896e-05 6.842065583394459137e-05 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3.183758171544375662e-10 8.202542868464169985e-11 1.983820394835147254e-11 4.505210532446856887e-12 9.610164123734151409e-13 1.926353145593442085e-13 3.630472257734208692e-14 6.437134422314383524e-15 1.074596745610648098e-15 1.690900262217315122e-16 2.511706081495857299e-17 3.506499277161590075e-18 4.311927966514470963e-19 -5.987611760317354201e-20 -2.610454776839953187e-20 1.408686706048940720e-20 6.159531717822607088e-21 -2.173255869367200976e-21 -9.628241304471548218e-22 3.972463419764660864e-22 1.414225242599585011e-22 -6.897218129220873390e-23 -1.663522542629989253e-23 --6.093854755896507327e-23 1.414225242599584776e-22 4.013102203858478117e-22 -1.013072278124398056e-21 -2.165175553603995408e-21 6.732823274280724988e-21 1.389852617625868630e-20 -3.039664408139589896e-20 -5.673373455648695333e-20 5.382515301521706081e-19 4.289455503876089953e-18 3.122023818139002600e-17 2.155111595475404595e-16 1.407197459777525578e-15 8.666031440885989271e-15 5.028033272098199122e-14 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7.243591855625602781e-19 4.330836462578561028e-18 2.481694480519269807e-17 1.362115288811106738e-16 7.156169910920266889e-16 3.596199380655385299e-15 1.727359562442570343e-14 7.924349225995462250e-14 3.469298013924171495e-13 1.448321427843020419e-12 5.760756208830955996e-12 2.181396555981919938e-11 7.857611419654273492e-11 2.690463109359319283e-10 8.750919617706526539e-10 2.702225878939697075e-09 7.918384677778785830e-09 2.201266609849151481e-08 5.804788470488548688e-08 1.452212650312650538e-07 3.447968537569643703e-07 7.774253307374684357e-07 1.666112863134581668e-06 3.397794504061926863e-06 6.602802987053709142e-06 1.224521852983377251e-05 2.170896854679861998e-05 3.685661925563098673e-05 6.003392289659555023e-05 9.399361571439020517e-05 1.417129958841647401e-04 2.061266934058331841e-04 2.897485003769223423e-04 3.943102687877786936e-04 5.203290183402979607e-04 6.669282439004262314e-04 8.314051881077027129e-04 1.009375604952518490e-03 1.191599591563148944e-03 1.368426400401131149e-03 1.531999712391240434e-03 1.672883192970426106e-03 1.783360574284515668e-03 1.857946041840690060e-03 1.894856732132488633e-03 1.900083333023770346e-03 1.857256200586212408e-03 1.782937868087727633e-03 1.669799935927392467e-03 1.529096667559472515e-03 1.365039653189198876e-03 1.187923857588264959e-03 1.007374355750299995e-03 8.313545840904171692e-04 6.677198080252990092e-04 5.216277329510815401e-04 3.958460242506494395e-04 2.913401870726598387e-04 2.075788759463460939e-04 1.428780509008422534e-04 9.478190641158906835e-05 6.043890301171931393e-05 3.693547232410701565e-05 2.155829130649722733e-05 1.196919528824581019e-05 6.289888859998507049e-06 3.109007224961511309e-06 1.433451366583101392e-06 6.092838391371227392e-07 2.344455560647064991e-07 7.908071903649345330e-08 2.176379684684452546e-08 3.703106045429395770e-09 -7.236048263659848163e-10 -8.561277510299456653e-10 -4.795493940107543950e-10 -1.762861024608451231e-10 -3.720208972702089443e-11 2.988314917147430488e-12 6.156086348535031417e-12 3.290722156839735520e-12 9.555622363129486648e-13 6.647801672487237258e-14 -9.335648374218029605e-14 -5.343838818912347980e-14 -1.601961345316746524e-14 -4.231299991737438680e-16 1.761499057980406529e-15 8.678966337985889769e-16 1.806100200299646710e-16 -4.956881031753963994e-17 -3.340313567869619680e-17 -1.018688427818092924e-17 8.618643968000507202e-20 1.419164731093504726e-18 diff --git a/examples/acoustics_2d_variable/acoustics_2d_interface.py b/examples/acoustics_2d_variable/acoustics_2d_interface.py index 84223ebdc..6184bd8af 100755 --- a/examples/acoustics_2d_variable/acoustics_2d_interface.py +++ b/examples/acoustics_2d_variable/acoustics_2d_interface.py @@ -40,7 +40,7 @@ def setup(kernel_language='Fortran', use_petsc=False, outdir='./_output', elif solver_type=='sharpclaw': solver=pyclaw.SharpClawSolver2D(riemann.vc_acoustics_2D) solver.time_integrator=time_integrator - if time_integrator=='SSPMS32': + if time_integrator=='SSPLMM32': solver.cfl_max = 0.25 solver.cfl_desired = 0.24 diff --git a/examples/acoustics_2d_variable/test_acoustics_2d_variable.py b/examples/acoustics_2d_variable/test_acoustics_2d_variable.py index 487e05edd..82d97bd92 100644 --- a/examples/acoustics_2d_variable/test_acoustics_2d_variable.py +++ b/examples/acoustics_2d_variable/test_acoustics_2d_variable.py @@ -41,7 +41,7 @@ def verify_acoustics(controller, solver_type='classic'): sharp_tests_lmm = gen_variants(acoustics_2d_interface.setup, verify_func, lim_type=1, solver_type='sharpclaw', - time_integrator='SSPMS32', + time_integrator='SSPLMM32', disable_output=True, num_cells=(50, 50)) diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index ff25b503b..3e88dbe54 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,9 +32,9 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(3.39682948116e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(1.8937e-05), kernel_languages=('Python','Fortran'), - solver_type='sharpclaw',time_integrator='SSPMS32', outdir=None) + solver_type='sharpclaw',time_integrator='SSPLMM43', outdir=None) weno_tests = gen_variants(advection_1d.setup, verify_expected(7.489618e-06), kernel_languages=('Fortran',), solver_type='sharpclaw', diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 39562de5e..6716159a2 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -69,9 +69,9 @@ def before_step(solver,solution) 'Euler' : 1st-order Forward Euler integration 'SSP33' : 3rd-order strong stability preserving method of Shu & Osher 'SSP104' : 4th-order strong stability preserving method Ketcheson - 'SSPMS32': 2nd-order strong stability preserving 3-step linear multistep method, + 'SSPLMM32': 2nd-order strong stability preserving 3-step linear multistep method, using Euler for starting values - 'SSPMS43': 3rd-order strong stability preserving 4-step linear multistep method + 'SSPLMM43': 3rd-order strong stability preserving 4-step linear multistep method using SSPRK22 for starting values 'RK' : Arbitrary Runge-Kutta method, specified by setting `solver.a` and `solver.b` to the Butcher arrays of the method. @@ -148,16 +148,16 @@ def before_step(solver,solution) 'Euler' : 1.0, 'SSP33': 1.0, 'SSP104' : 6.0, - 'SSPMS32' : 0.5, - 'SSPMS43' : 1./3., + 'SSPLMM32' : 0.5, + 'SSPLMM43' : 1./3., 'RK': None, 'LMM': None } _cfl_default = { 'SSP104': [2.45, 2.5], - 'SSPMS32': [0.24, 0.25], - 'SSPMS43': [0.15, 1./6.] + 'SSPLMM32': [0.24, 0.25], + 'SSPLMM43': [0.15, 1./6.] } # ======================================================================== @@ -308,7 +308,7 @@ def step(self,solution): for j in range(num_stages): state.q += self.b[j]*self._registers[j].q - elif self.time_integrator == 'SSPMS32': + elif self.time_integrator == 'SSPLMM32': if self.step_index <= 1: # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].dq = self.dq(state) @@ -340,7 +340,7 @@ def step(self,solution): self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - elif self.time_integrator == 'SSPMS43': + elif self.time_integrator == 'SSPLMM43': if self.step_index <= 1: # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() @@ -544,13 +544,13 @@ def _allocate_registers(self,solution): elif self.time_integrator == 'SSP33': nregisters=1 elif self.time_integrator == 'SSP104': nregisters=2 elif self.time_integrator == 'RK': nregisters=len(self.b)+1 - elif self.time_integrator == 'SSPMS32': nregisters=3 - elif self.time_integrator == 'SSPMS43': nregisters=4 + elif self.time_integrator == 'SSPLMM32': nregisters=3 + elif self.time_integrator == 'SSPLMM43': nregisters=4 elif self.time_integrator == 'LMM': nregisters=len(self.alpha) self.dt_variable = False else: - raise Exception('Unrecognized time intergrator') + raise Exception('Unrecognized time integrator: '+self.time_integrator) state = solution.states[0] # use the same class constructor as the solution for the Runge Kutta stages @@ -565,13 +565,13 @@ def accept_reject_step(self,cfl): r""" Decide whether to accept or not the current step. For Runge-Kutta methods the step is accepted if cfl <= cfl_max. - For SSPMS32 the choice of step-size guarantees the cfl condition is satisfied. - For SSPMS43 additional checks on previous forward Euler step-sizes are required. + For SSPLMM32 the choice of step-size guarantees the cfl condition is satisfied. + For SSPLMM43 additional checks on previous forward Euler step-sizes are required. """ accept_step = True # check cfl condition for SSP LMM methods - if self.time_integrator[:-2] == 'SSPMS': + if self.time_integrator[:-2] == 'SSPLMM': # condition for starting RK methods if self.step_index < len(self._registers): # first step is always rejected because CFL condition is violated in dq() @@ -580,14 +580,14 @@ def accept_reject_step(self,cfl): self.step_index += 1 if cfl > self.cfl_max: accept_step = False - # additional condition for SSPMS43 - if self.time_integrator == 'SSPMS43' and self.dt > 3./5. * self._registers[-1].dtFE: + # additional condition for SSPLMM43 + if self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self._registers[-1].dtFE: accept_step = False # apply LMM at the next step if last RK step is accepted if accept_step == True and self.step_index == len(self._registers)-1: self.step_index += 1 - # only need to check conditions for SSPMS43 for the steps LMM is active - elif self.time_integrator == 'SSPMS43': + # only need to check conditions for SSPLMM43 for the steps LMM is active + elif self.time_integrator == 'SSPLMM43': rhoFE = 9./10. dtFE = self._registers[-1].dtFE dtFEm1 = self._registers[-2].dtFE @@ -604,7 +604,7 @@ def get_dt_new(self,cfl,accept_step): r""" Set time-step for next step depending on the time integrator and whether or not the step is accepted """ - if self.time_integrator[:-2] == 'SSPMS': + if self.time_integrator[:-2] == 'SSPLMM': # step-size update for SSP LMM methods if accept_step: if self.step_index == len(self._registers): @@ -622,12 +622,12 @@ def get_dt_new(self,cfl,accept_step): else: if self.step_index < len(self._registers): self.dt = self.dt * self.cfl_desired / cfl - # additional conditions for SSPMS43 - if self.time_integrator == 'SSPMS43': + # additional conditions for SSPLMM43 + if self.time_integrator == 'SSPLMM43': self.dt = min(3./5. * self._registers[-1].dtFE, self.dt) - elif self.time_integrator == 'SSPMS43': - # cruel step-size reduction if step-size assumptions for SSPMS43 are violated - # no such assumptions are needed for SSPMS32 + elif self.time_integrator == 'SSPLMM43': + # cruel step-size reduction if step-size assumptions for SSPLMM43 are violated + # no such assumptions are needed for SSPLMM32 self.dt /= 2. else: # step-size update for Runge-Kutta methods diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index a139dfaef..398c1475e 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -571,7 +571,11 @@ def evolve_to_time(self,solution,tend=None): # Keep a backup in case we need to retake a time step if self.dt_variable: - q_backup = state.q.copy('F') + if 'LMM' in getattr(self,'time_integrator',''): + import copy + backup = copy.deepcopy(self._registers[0]) + else: + q_backup = state.q.copy('F') told = solution.t self.step(solution) @@ -601,7 +605,11 @@ def evolve_to_time(self,solution,tend=None): # Reject this step self.logger.debug("Rejecting time step, CFL number too large") if self.dt_variable: - state.q = q_backup + if 'LMM' in getattr(self,'time_integrator',''): + self._registers.insert(0,backup) + self._registers = self._registers[:-1] + else: + state.q = q_backup solution.t = told else: # Give up, we cannot adapt, abort diff --git a/src/pyclaw/util.py b/src/pyclaw/util.py index 5ab342d75..4c6ee986f 100755 --- a/src/pyclaw/util.py +++ b/src/pyclaw/util.py @@ -264,9 +264,13 @@ def check_diff(expected, test, **kwargs): This function expects either the keyword argument 'abstol' or 'reltol'. """ - err_norm = np.linalg.norm(expected - test) - expected_norm = np.linalg.norm(expected) - test_norm = np.linalg.norm(test) + if kwargs.has_key('delta'): + d = np.prod(kwargs['delta']) + else: + d = 1.0 + err_norm = d*np.linalg.norm(expected - test) + expected_norm = d*np.linalg.norm(expected) + test_norm = d*np.linalg.norm(test) if 'abstol' in kwargs: if err_norm < kwargs['abstol']: return None else: return (expected_norm, test_norm, err_norm, From e97bcfef1951331d6f626cf7534eec6e43feb317 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Mon, 15 Dec 2014 11:17:33 +0300 Subject: [PATCH 11/46] Update regression data for WC blast test. Due to step rejection occurring since we now check the CFL number for all RK stages. --- .../euler_1d/blast_regression_density.txt | 1600 ++++++++--------- 1 file changed, 800 insertions(+), 800 deletions(-) diff --git a/examples/euler_1d/blast_regression_density.txt b/examples/euler_1d/blast_regression_density.txt index 4e65a0f10..27018e2d3 100644 --- a/examples/euler_1d/blast_regression_density.txt +++ b/examples/euler_1d/blast_regression_density.txt @@ -1,800 +1,800 @@ -1.495593759843748261e-01 -1.495607794456512707e-01 -1.495635876166322431e-01 -1.495677964675333205e-01 -1.495734000931148722e-01 -1.495803908754305411e-01 -1.495887596674518316e-01 -1.495984959792487634e-01 -1.496095881517695569e-01 -1.496220235073579541e-01 -1.496357884731323029e-01 -1.496508686816981348e-01 -1.496672490614545659e-01 -1.496849139342814605e-01 -1.497038471404001925e-01 -1.497240322078918773e-01 -1.497454525777710543e-01 -1.497680918853355747e-01 -1.497919342862590042e-01 -1.498169648034096968e-01 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+3.085565247090079621e-01 +3.085633576428368219e-01 +3.085696145293979065e-01 +3.085753798824207861e-01 +3.085807338109072262e-01 +3.085857496837500213e-01 +3.085904929621138826e-01 +3.085950208179024101e-01 +3.085993822934819386e-01 +3.086036099048375947e-01 +3.086077075741359144e-01 +3.086116713952148372e-01 +3.086154928902560268e-01 +3.086191601320974476e-01 +3.086226593063510770e-01 +3.086259767241004703e-01 +3.086291005271082355e-01 +3.086320223341084690e-01 +3.086347383302109892e-01 +3.086372499274214753e-01 +3.086395639381581124e-01 +3.086416923036455762e-01 +3.086436514465573655e-01 +3.086454614576792932e-01 +3.086471450954658136e-01 +3.086487265328291540e-01 +3.086502299457715148e-01 +3.086516776131138506e-01 +3.086530879869838762e-01 +3.086544739862683295e-01 +3.086558420427988336e-01 +3.086571922093849785e-01 +3.086585192300038138e-01 +3.086598143585875809e-01 +3.086610673226459767e-01 +3.086622680797841967e-01 +3.086634080309944572e-01 +3.086644807523561962e-01 +3.086654822416673993e-01 +3.086664108441954379e-01 +3.086672669807026259e-01 +3.086680526665206981e-01 +3.086687711645166310e-01 +3.086694264363613049e-01 +3.086700228989637251e-01 +3.086705649576218513e-01 +3.086710570107447094e-01 +3.086715030492380718e-01 +3.086719066300866454e-01 +3.086722707787226128e-01 +3.086725980461151875e-01 +3.086728903410859148e-01 +3.086731490292364266e-01 +3.086733751028097883e-01 +3.086735693648118284e-01 +3.086737323084874363e-01 +3.086738640005561862e-01 +3.086739648632670918e-01 +3.086740347283732921e-01 +3.086740736193931967e-01 From 52711c0cba0ec6c4852a4bd3189ae19bc63194a0 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Mon, 15 Dec 2014 11:40:12 +0300 Subject: [PATCH 12/46] Tests passing. --- examples/advection_1d/test_advection.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 3e88dbe54..98e92184f 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -34,7 +34,7 @@ def advection_verify(claw): sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(1.8937e-05), kernel_languages=('Python','Fortran'), - solver_type='sharpclaw',time_integrator='SSPLMM43', outdir=None) + solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) weno_tests = gen_variants(advection_1d.setup, verify_expected(7.489618e-06), kernel_languages=('Fortran',), solver_type='sharpclaw', From 24a1c94feff892436d9eb44f062d72f9bcdb7e76 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 16 Dec 2014 13:19:11 +0300 Subject: [PATCH 13/46] Remove stored dt and dtFE from registers and create solver lists to store them. Also improve the way stored information from previous steps is updated. --- src/pyclaw/sharpclaw/solver.py | 100 ++++++++++++++++++--------------- src/pyclaw/solver.py | 23 +++++++- 2 files changed, 75 insertions(+), 48 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 6716159a2..431de4404 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -193,10 +193,13 @@ def __init__(self,riemann_solver=None,claw_package=None): self.c = None # Used only if time integrator is a multistep method - self.step_index = 0 + self.step_index = 1 self.sspcoeff0 = None self.alpha = None self.beta = None + self.dq_stored = None + self.dt_list = [] + self.dtFE_list = [] # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) @@ -309,58 +312,67 @@ def step(self,solution): state.q += self.b[j]*self._registers[j].q elif self.time_integrator == 'SSPLMM32': - if self.step_index <= 1: - # Store initial solution, function evaluation, dt and forward Euler dt - self._registers[-1].dq = self.dq(state) + if self.step_index == 1: + # Store initial solution, function evaluation, dt and forward Euler dt + self.dq_stored = self.dq(state) self._registers[-1].q = state.q.copy() - self._registers[-1].dt = self.dt - self._registers[-1].dtFE = self.dt * self.cfl_max / self.cfl.get_cached_max() + self.dt_list.append(self.dt) + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) if self.step_index < 3: # Use Euler method for starting values - deltaq = self._registers[-1].dq + deltaq = self.dq_stored state.q += deltaq + self.sspcoeff0 = self._sspcoeff['Euler'] + self.dt_list.append(self.dt) + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) else: - omega = (self._registers[-2].dt + self._registers[-1].dt)/self.dt + omega = (self.dt_list[-2] + self.dt_list[-1])/self.dt # ssp coefficient r = (omega-1.)/omega # method coefficients delta = 1./omega**2 beta = (omega+1.)/omega - deltaq = self._registers[-1].dq + deltaq = self.dq_stored state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q + self.dt_list = self.dt_list[1:] + self.dt_list[:1] + self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] + self.dt_list[-1] = self.dt + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() + # Update stored information - register = type(state) - self._registers.append(register(state.patch,state.num_eqn,state.num_aux)) - self._registers = self._registers[1:] + self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() - self._registers[-1].dt = self.dt - self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number - self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() elif self.time_integrator == 'SSPLMM43': - if self.step_index <= 1: + if self.step_index == 1: # Store initial solution, function evaluation, dt and forward Euler dt + self.dq_stored = self.dq(state) self._registers[-1].q = state.q.copy() - self._registers[-1].dq = self.dq(state) - self._registers[-1].dt = self.dt - self._registers[-1].dtFE = self.dt * self.cfl_max / self.cfl.get_cached_max() + self.dt_list.append(self.dt) + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) if self.step_index < 4: # Use SSP22 method for starting values import copy s1 = copy.deepcopy(state) + s1.set_num_ghost(self.num_ghost) ### depreciated by deepcopy fix ### - deltaq = self._registers[-1].dq + deltaq = self.dq_stored s1.q = state.q + deltaq s1.t = state.t + self.dt deltaq = self.dq(s1) state.q = 0.5*(state.q + s1.q + deltaq) + self.sspcoeff0 = 1. # SSP coefficient for SSP22 + self.dt_list.append(self.dt) + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) else: - H = self._registers[-3].dt + self._registers[-2].dt + self._registers[-1].dt - omega3 = H/self.dt + omega3 = sum(self.dt_list[-3:])/self.dt omega4 = omega3 + 1. # SSP coefficient r = (omega3-2.)/omega3 @@ -368,20 +380,21 @@ def step(self,solution): delta0 = (4*omega4 - omega3**2)/omega3**3 beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - - deltaq = self._registers[-1].dq - deltaqm4 = self.dq(self._registers[-4]) + + deltaq = self.dq_stored + deltaqm4 = self.dq(self._registers[-4]) state.q = beta3*(r*state.q + deltaq) + \ (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 + self.dt_list = self.dt_list[1:] + self.dt_list[:1] + self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] + self.dt_list[-1] = self.dt + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() + # Update stored information - register = type(state) - self._registers.append(register(state.patch,state.num_eqn,state.num_aux)) - self._registers = self._registers[1:] + self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() - self._registers[-1].dt = self.dt - self._registers[-1].dq = self.dq(state) # call self.dq once more to update cfl number - self._registers[-1].dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() elif self.time_integrator == 'LMM': num_steps = len(self.alpha) @@ -570,18 +583,14 @@ def accept_reject_step(self,cfl): """ accept_step = True - # check cfl condition for SSP LMM methods + # check cfl condition for SSP LMM methods if self.time_integrator[:-2] == 'SSPLMM': # condition for starting RK methods if self.step_index < len(self._registers): - # first step is always rejected because CFL condition is violated in dq() - if self.step_index == 0: - self._registers[-1].dtFE = self.dt * self.cfl_max / cfl - self.step_index += 1 if cfl > self.cfl_max: accept_step = False # additional condition for SSPLMM43 - if self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self._registers[-1].dtFE: + elif self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self.dtFE_list[-1]: accept_step = False # apply LMM at the next step if last RK step is accepted if accept_step == True and self.step_index == len(self._registers)-1: @@ -589,11 +598,11 @@ def accept_reject_step(self,cfl): # only need to check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': rhoFE = 9./10. - dtFE = self._registers[-1].dtFE - dtFEm1 = self._registers[-2].dtFE + dtFE = self.dtFE_list[-1] + dtFEm1 = self.dtFE_list[-2] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False - # check cfl condition for Runge-Kutta methods + # check cfl condition for Runge-Kutta methods elif cfl > self.cfl_max: accept_step = False @@ -602,7 +611,7 @@ def accept_reject_step(self,cfl): def get_dt_new(self,cfl,accept_step): r""" - Set time-step for next step depending on the time integrator and whether or not the step is accepted + Set time-step for next step depending on the time integrator and whether or not the step is accepted. """ if self.time_integrator[:-2] == 'SSPLMM': # step-size update for SSP LMM methods @@ -610,8 +619,8 @@ def get_dt_new(self,cfl,accept_step): if self.step_index == len(self._registers): s = len(self._registers) p = int(self.time_integrator[-2]) - mu = min([self._registers[-1-i].dtFE for i in range(s)]) - H = sum([self._registers[-1-i].dt for i in range(s-1)]) + mu = min([self.dtFE_list[-1-i] for i in range(s)]) + H = sum([self.dt_list[-1-i] for i in range(s-1)]) self.dt = H * mu / (H + (p-2)*mu) else: # step-size update for starting methods @@ -622,9 +631,11 @@ def get_dt_new(self,cfl,accept_step): else: if self.step_index < len(self._registers): self.dt = self.dt * self.cfl_desired / cfl + if self.step_index == 1: + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) # additional conditions for SSPLMM43 if self.time_integrator == 'SSPLMM43': - self.dt = min(3./5. * self._registers[-1].dtFE, self.dt) + self.dt = min(3./5. * self.dtFE_list[-1], self.dt) elif self.time_integrator == 'SSPLMM43': # cruel step-size reduction if step-size assumptions for SSPLMM43 are violated # no such assumptions are needed for SSPLMM32 @@ -636,7 +647,6 @@ def get_dt_new(self,cfl,accept_step): return min(self.dt_max,self.dt) - # ======================================================================== class SharpClawSolver1D(SharpClawSolver): # ======================================================================== diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 398c1475e..5b348b33d 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -574,10 +574,13 @@ def evolve_to_time(self,solution,tend=None): if 'LMM' in getattr(self,'time_integrator',''): import copy backup = copy.deepcopy(self._registers[0]) + if self.step_index > 1: + dt_backup = self.dt_list[0] + dtFE_backup = self.dtFE_list[0] else: q_backup = state.q.copy('F') told = solution.t - + self.step(solution) # Check to make sure that the Courant number was not too large @@ -606,8 +609,22 @@ def evolve_to_time(self,solution,tend=None): self.logger.debug("Rejecting time step, CFL number too large") if self.dt_variable: if 'LMM' in getattr(self,'time_integrator',''): - self._registers.insert(0,backup) - self._registers = self._registers[:-1] + self._registers[-1] = backup + self._registers = self._registers[-1:] + self._registers[:-1] + # initialize dt and dtFE in case first step is rejected + if self.step_index == 1: + self.dt_list.append(self.dt) + self.dtFE_list.append(self.dt * self.cfl_max / cfl) + else: + # remove last dt and dtFE if a RK step is rejected + if self.step_index < len(self._registers): + self.dt_list = self.dt_list[:-1] + self.dtFE_list = self.dtFE_list[:-1] + else: + self.dt_list[-1] = dt_backup + self.dtFE_list[-1] = dtFE_backup + self.dt_list = self.dt_list[-1:] + self.dt_list[:-1] + self.dtFE_list = self.dtFE_list[-1:] + self.dtFE_list[:-1] else: state.q = q_backup solution.t = told From 419a06867b9686050bc0035e04377c04b61d0b98 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Wed, 17 Dec 2014 13:57:33 +0300 Subject: [PATCH 14/46] Add a function to set cfl._global_max and correct initialization of global cfl at the beggining of each step. --- src/petclaw/cfl.py | 5 ++++- src/pyclaw/cfl.py | 3 +++ src/pyclaw/classic/solver.py | 2 +- src/pyclaw/sharpclaw/solver.py | 2 +- 4 files changed, 9 insertions(+), 3 deletions(-) diff --git a/src/petclaw/cfl.py b/src/petclaw/cfl.py index 9b1f16a58..7cf3ca49d 100644 --- a/src/petclaw/cfl.py +++ b/src/petclaw/cfl.py @@ -29,7 +29,10 @@ def get_cached_max(self): def set_local_max(self,new_local_max): self._local_max = new_local_max + def set_global_max(self,new_global_max): + self._global_max = new_global_max + def update_global_max(self,new_local_max): self._reduce_vec.array = new_local_max - self._global_max = self._reduce_vec.max()[1] + self._global_max = max(self._global_max,self._reduce_vec.max()[1]) diff --git a/src/pyclaw/cfl.py b/src/pyclaw/cfl.py index 5c19a2761..ec88f617b 100644 --- a/src/pyclaw/cfl.py +++ b/src/pyclaw/cfl.py @@ -22,5 +22,8 @@ def get_cached_max(self): def set_local_max(self,new_local_max): self._global_max = new_local_max + def set_global_max(self,new_global_max): + self._global_max = new_global_max + def update_global_max(self,new_local_max): self._global_max = max(self._global_max,new_local_max) diff --git a/src/pyclaw/classic/solver.py b/src/pyclaw/classic/solver.py index 9ffd1432c..48246cef0 100644 --- a/src/pyclaw/classic/solver.py +++ b/src/pyclaw/classic/solver.py @@ -127,7 +127,7 @@ def step(self,solution): - (bool) - True if full step succeeded, False otherwise """ - self.cfl.set_local_max(0.) + self.cfl.set_global_max(0.) if self.before_step is not None: self.before_step(self,solution.states[0]) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 431de4404..9840de540 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -269,7 +269,7 @@ def step(self,solution): `solver.time_integrator`. """ state = solution.states[0] - self.cfl.set_local_max(0.) + self.cfl.set_global_max(0.) self.before_step(self,state) From 5607c44db7e357da78fc36fe2646294d802302c5 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Sun, 11 Jan 2015 09:42:08 +0300 Subject: [PATCH 15/46] Remove 'set_global_max' method from cfl.py --- src/petclaw/cfl.py | 3 --- src/pyclaw/cfl.py | 3 --- src/pyclaw/classic/solver.py | 2 +- src/pyclaw/sharpclaw/solver.py | 2 +- 4 files changed, 2 insertions(+), 8 deletions(-) diff --git a/src/petclaw/cfl.py b/src/petclaw/cfl.py index 7cf3ca49d..71adab13d 100644 --- a/src/petclaw/cfl.py +++ b/src/petclaw/cfl.py @@ -29,9 +29,6 @@ def get_cached_max(self): def set_local_max(self,new_local_max): self._local_max = new_local_max - def set_global_max(self,new_global_max): - self._global_max = new_global_max - def update_global_max(self,new_local_max): self._reduce_vec.array = new_local_max self._global_max = max(self._global_max,self._reduce_vec.max()[1]) diff --git a/src/pyclaw/cfl.py b/src/pyclaw/cfl.py index ec88f617b..5c19a2761 100644 --- a/src/pyclaw/cfl.py +++ b/src/pyclaw/cfl.py @@ -22,8 +22,5 @@ def get_cached_max(self): def set_local_max(self,new_local_max): self._global_max = new_local_max - def set_global_max(self,new_global_max): - self._global_max = new_global_max - def update_global_max(self,new_local_max): self._global_max = max(self._global_max,new_local_max) diff --git a/src/pyclaw/classic/solver.py b/src/pyclaw/classic/solver.py index 48246cef0..4851a0fd6 100644 --- a/src/pyclaw/classic/solver.py +++ b/src/pyclaw/classic/solver.py @@ -127,7 +127,7 @@ def step(self,solution): - (bool) - True if full step succeeded, False otherwise """ - self.cfl.set_global_max(0.) + self.cfl.__init__(0.) if self.before_step is not None: self.before_step(self,solution.states[0]) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 9840de540..d39bf74e5 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -269,7 +269,7 @@ def step(self,solution): `solver.time_integrator`. """ state = solution.states[0] - self.cfl.set_global_max(0.) + self.cfl.__init__(0.) self.before_step(self,state) From 9a31120397e17aabb4f5ae9ff4e9d7743b710e7e Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Sun, 11 Jan 2015 12:50:27 +0300 Subject: [PATCH 16/46] Refactoring the time integration code. Add set_global back to CFL object. Only update dt_list and dtFE_list when a step is accepted. --- src/petclaw/cfl.py | 3 + src/pyclaw/cfl.py | 3 + src/pyclaw/classic/solver.py | 2 +- src/pyclaw/sharpclaw/solver.py | 308 ++++++++++++++++----------------- src/pyclaw/solver.py | 17 -- 5 files changed, 157 insertions(+), 176 deletions(-) diff --git a/src/petclaw/cfl.py b/src/petclaw/cfl.py index 71adab13d..7cf3ca49d 100644 --- a/src/petclaw/cfl.py +++ b/src/petclaw/cfl.py @@ -29,6 +29,9 @@ def get_cached_max(self): def set_local_max(self,new_local_max): self._local_max = new_local_max + def set_global_max(self,new_global_max): + self._global_max = new_global_max + def update_global_max(self,new_local_max): self._reduce_vec.array = new_local_max self._global_max = max(self._global_max,self._reduce_vec.max()[1]) diff --git a/src/pyclaw/cfl.py b/src/pyclaw/cfl.py index 5c19a2761..ec88f617b 100644 --- a/src/pyclaw/cfl.py +++ b/src/pyclaw/cfl.py @@ -22,5 +22,8 @@ def get_cached_max(self): def set_local_max(self,new_local_max): self._global_max = new_local_max + def set_global_max(self,new_global_max): + self._global_max = new_global_max + def update_global_max(self,new_local_max): self._global_max = max(self._global_max,new_local_max) diff --git a/src/pyclaw/classic/solver.py b/src/pyclaw/classic/solver.py index 4851a0fd6..48246cef0 100644 --- a/src/pyclaw/classic/solver.py +++ b/src/pyclaw/classic/solver.py @@ -127,7 +127,7 @@ def step(self,solution): - (bool) - True if full step succeeded, False otherwise """ - self.cfl.__init__(0.) + self.cfl.set_global_max(0.) if self.before_step is not None: self.before_step(self,solution.states[0]) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index d39bf74e5..6ed1f38b9 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -193,7 +193,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.c = None # Used only if time integrator is a multistep method - self.step_index = 1 + self._step_index = 1 self.sspcoeff0 = None self.alpha = None self.beta = None @@ -269,162 +269,146 @@ def step(self,solution): `solver.time_integrator`. """ state = solution.states[0] - self.cfl.__init__(0.) + self.cfl.set_global_max(0.) self.before_step(self,state) - try: - if self.time_integrator=='Euler': - deltaq=self.dq(state) - state.q+=deltaq - - elif self.time_integrator=='SSP33': - deltaq=self.dq(state) - self._registers[0].q=state.q+deltaq - self._registers[0].t =state.t+self.dt - - if self.call_before_step_each_stage: - self.before_step(self,self._registers[0]) - deltaq=self.dq(self._registers[0]) - self._registers[0].q= 0.75*state.q + 0.25*(self._registers[0].q+deltaq) - self._registers[0].t = state.t+0.5*self.dt - - if self.call_before_step_each_stage: - self.before_step(self,self._registers[0]) - deltaq=self.dq(self._registers[0]) - state.q = 1./3.*state.q + 2./3.*(self._registers[0].q+deltaq) - - elif self.time_integrator=='SSP104': - state.q = self.ssp104(state) + if self.time_integrator=='Euler': + deltaq=self.dq(state) + state.q+=deltaq - elif self.time_integrator=='RK': - # General RK with specified coefficients - # self._registers[i].q actually stores dt*f(y_i) - num_stages = len(self.b) - for i in range(num_stages): - self._registers[i].q = state.q.copy() - for j in range(i): - self._registers[i].q += self.a[i,j]*self._registers[j].q - self._registers[i].t = state.t + self.dt * self.c[i] - self._registers[i].q = self.dq(self._registers[i]) - - for j in range(num_stages): - state.q += self.b[j]*self._registers[j].q - - elif self.time_integrator == 'SSPLMM32': - if self.step_index == 1: - # Store initial solution, function evaluation, dt and forward Euler dt - self.dq_stored = self.dq(state) - self._registers[-1].q = state.q.copy() - self.dt_list.append(self.dt) - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) - if self.step_index < 3: - # Use Euler method for starting values - deltaq = self.dq_stored - state.q += deltaq + elif self.time_integrator=='SSP33': + deltaq=self.dq(state) + self._registers[0].q=state.q+deltaq + self._registers[0].t =state.t+self.dt - self.sspcoeff0 = self._sspcoeff['Euler'] - self.dt_list.append(self.dt) - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) - else: - omega = (self.dt_list[-2] + self.dt_list[-1])/self.dt - # ssp coefficient - r = (omega-1.)/omega - # method coefficients - delta = 1./omega**2 - beta = (omega+1.)/omega - - deltaq = self.dq_stored - state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q - - self.dt_list = self.dt_list[1:] + self.dt_list[:1] - self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] - self.dt_list[-1] = self.dt - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() + if self.call_before_step_each_stage: + self.before_step(self,self._registers[0]) + deltaq=self.dq(self._registers[0]) + self._registers[0].q= 0.75*state.q + 0.25*(self._registers[0].q+deltaq) + self._registers[0].t = state.t+0.5*self.dt - # Update stored information - self._registers = self._registers[1:] + self._registers[:1] + if self.call_before_step_each_stage: + self.before_step(self,self._registers[0]) + deltaq=self.dq(self._registers[0]) + state.q = 1./3.*state.q + 2./3.*(self._registers[0].q+deltaq) + + elif self.time_integrator=='SSP104': + state.q = self.ssp104(state) + + elif self.time_integrator=='RK': + # General RK with specified coefficients + # self._registers[i].q actually stores dt*f(y_i) + num_stages = len(self.b) + for i in range(num_stages): + self._registers[i].q = state.q.copy() + for j in range(i): + self._registers[i].q += self.a[i,j]*self._registers[j].q + self._registers[i].t = state.t + self.dt * self.c[i] + self._registers[i].q = self.dq(self._registers[i]) + + for j in range(num_stages): + state.q += self.b[j]*self._registers[j].q + + elif self.time_integrator == 'SSPLMM32': + if self._step_index == 1: + # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() - - elif self.time_integrator == 'SSPLMM43': - if self.step_index == 1: - # Store initial solution, function evaluation, dt and forward Euler dt - self.dq_stored = self.dq(state) - self._registers[-1].q = state.q.copy() - self.dt_list.append(self.dt) - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) - if self.step_index < 4: - # Use SSP22 method for starting values - import copy - s1 = copy.deepcopy(state) - s1.set_num_ghost(self.num_ghost) ### depreciated by deepcopy fix ### - - deltaq = self.dq_stored - s1.q = state.q + deltaq - s1.t = state.t + self.dt - deltaq = self.dq(s1) - state.q = 0.5*(state.q + s1.q + deltaq) - - self.sspcoeff0 = 1. # SSP coefficient for SSP22 - self.dt_list.append(self.dt) - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) - else: - omega3 = sum(self.dt_list[-3:])/self.dt - omega4 = omega3 + 1. - # SSP coefficient - r = (omega3-2.)/omega3 - # method coefficients - delta0 = (4*omega4 - omega3**2)/omega3**3 - beta0 = omega4/omega3**2 - beta3 = omega4**2/omega3**2 - - deltaq = self.dq_stored - deltaqm4 = self.dq(self._registers[-4]) - state.q = beta3*(r*state.q + deltaq) + \ - (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 - - self.dt_list = self.dt_list[1:] + self.dt_list[:1] - self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] - self.dt_list[-1] = self.dt - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - - # Update stored information - self._registers = self._registers[1:] + self._registers[:1] + self.dq_stored = self.dq(state) + self.dt_list.append(0) + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) + if self._step_index < 3: + # Use Euler method for starting values + state.q += self.dq_stored + + self.sspcoeff0 = self._sspcoeff['Euler'] + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + else: + omega = (self.dt_list[-2] + self.dt_list[-1])/self.dt + # ssp coefficient + r = (omega-1.)/omega + # method coefficients + delta = 1./omega**2 + beta = (omega+1.)/omega + + deltaq = self.dq_stored + state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q + + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + # Update stored information + self._registers = self._registers[1:] + self._registers[:1] + self._registers[-1].q = state.q.copy() + + elif self.time_integrator == 'SSPLMM43': + if self._step_index == 1: + # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() + self.dq_stored = self.dq(state) + self.dt_list.append(0) + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) + if self._step_index < 4: + # Use SSP22 method for starting values + import copy + s1 = copy.deepcopy(state) + s1.set_num_ghost(self.num_ghost) ### depreciated by deepcopy fix ### + + deltaq = self.dq_stored + s1.q = state.q + deltaq + s1.t = state.t + self.dt + deltaq = self.dq(s1) + state.q = 0.5*(state.q + s1.q + deltaq) + + self.sspcoeff0 = 1. # SSP coefficient for SSP22 + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + else: + omega3 = sum(self.dt_list[-3:])/self.dt + omega4 = omega3 + 1. + # SSP coefficient + r = (omega3-2.)/omega3 + # method coefficients + delta0 = (4*omega4 - omega3**2)/omega3**3 + beta0 = omega4/omega3**2 + beta3 = omega4**2/omega3**2 + + deltaq = self.dq_stored + deltaqm4 = self.dq(self._registers[-4]) + state.q = beta3*(r*state.q + deltaq) + \ + (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 + + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + + # Update stored information + self._registers = self._registers[1:] + self._registers[:1] + self._registers[-1].q = state.q.copy() - elif self.time_integrator == 'LMM': - num_steps = len(self.alpha) - - # Store initial solution - if self.step_index == 1: - self._registers[-num_steps].q = state.q.copy() - self._registers[-num_steps].dq = self.dq(state) + elif self.time_integrator == 'LMM': + num_steps = len(self.alpha) - if self.step_index < num_steps: - # Using SSP104 for previous step values - state.q = self.ssp104(state) - self._registers[-num_steps+self.step_index].q = state.q.copy() - self._registers[-num_steps+self.step_index].dq = self.dq(state) - self.step_index += 1 + # Store initial solution + if self._step_index == 1: + self._registers[-num_steps].q = state.q.copy() + self._registers[-num_steps].dq = self.dq(state) - else: - # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step - state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self._registers[-1].dq - for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self._registers[i].dq - self._registers[i].q = self._registers[i+1].q.copy() - self._registers[i].dq = self._registers[i+1].dq.copy() - # Store current solution and function evaluation - self._registers[-1].q = state.q.copy() - self._registers[-1].dq = self.dq(state) + if self._step_index < num_steps: + # Using SSP104 for previous step values + state.q = self.ssp104(state) + self._registers[-num_steps+self._step_index].q = state.q.copy() + self._registers[-num_steps+self._step_index].dq = self.dq(state) + self._step_index += 1 else: - raise Exception('Unrecognized time integrator') - except CFLError: + # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step + state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self._registers[-1].dq + for i in range(-num_steps,-1): + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self._registers[i].dq + self._registers[i].q = self._registers[i+1].q.copy() + self._registers[i].dq = self._registers[i+1].dq.copy() + # Store current solution and function evaluation + self._registers[-1].q = state.q.copy() + self._registers[-1].dq = self.dq(state) + + else: + raise Exception('Unrecognized time integrator') return False @@ -482,12 +466,6 @@ def dq(self,state): deltaq = self.dq_hyperbolic(state) - # Check here if we violated the CFL condition, if we did, return - # immediately to evolve_to_time and let it deal with picking a new - # dt - if self.cfl.get_cached_max() > self.cfl_max: - raise CFLError('cfl_max exceeded') - if self.dq_src is not None: deltaq+=self.dq_src(self,state,self.dt) @@ -586,15 +564,15 @@ def accept_reject_step(self,cfl): # check cfl condition for SSP LMM methods if self.time_integrator[:-2] == 'SSPLMM': # condition for starting RK methods - if self.step_index < len(self._registers): + if self._step_index < len(self._registers): if cfl > self.cfl_max: accept_step = False # additional condition for SSPLMM43 elif self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self.dtFE_list[-1]: accept_step = False # apply LMM at the next step if last RK step is accepted - if accept_step == True and self.step_index == len(self._registers)-1: - self.step_index += 1 + #if accept_step == True and self._step_index == len(self._registers)-1: + # self._step_index += 1 # only need to check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': rhoFE = 9./10. @@ -602,6 +580,20 @@ def accept_reject_step(self,cfl): dtFEm1 = self.dtFE_list[-2] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False + + # update dt_list, dtFE_list + if accept_step: + if self._step_index < len(self._registers): + self.dt_list.append(self.dt) + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) + else: + self.dt_list = self.dt_list[1:] + self.dt_list[:1] + self.dt_list[-1] = self.dt + self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] + self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() + self._step_index += 1 + + # check cfl condition for Runge-Kutta methods elif cfl > self.cfl_max: accept_step = False @@ -616,7 +608,7 @@ def get_dt_new(self,cfl,accept_step): if self.time_integrator[:-2] == 'SSPLMM': # step-size update for SSP LMM methods if accept_step: - if self.step_index == len(self._registers): + if self._step_index >= len(self._registers): s = len(self._registers) p = int(self.time_integrator[-2]) mu = min([self.dtFE_list[-1-i] for i in range(s)]) @@ -625,13 +617,13 @@ def get_dt_new(self,cfl,accept_step): else: # step-size update for starting methods self.dt = self.dt * self.cfl_desired / cfl - self.step_index += 1 - if self.step_index == len(self._registers)-1: + #self._step_index += 1 + if self._step_index == len(self._registers)-1: self.sspcoeff0 = self._sspcoeff[self.time_integrator] else: - if self.step_index < len(self._registers): + if self._step_index < len(self._registers): self.dt = self.dt * self.cfl_desired / cfl - if self.step_index == 1: + if self._step_index == 1: self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) # additional conditions for SSPLMM43 if self.time_integrator == 'SSPLMM43': diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 5b348b33d..ff85eefe0 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -574,9 +574,6 @@ def evolve_to_time(self,solution,tend=None): if 'LMM' in getattr(self,'time_integrator',''): import copy backup = copy.deepcopy(self._registers[0]) - if self.step_index > 1: - dt_backup = self.dt_list[0] - dtFE_backup = self.dtFE_list[0] else: q_backup = state.q.copy('F') told = solution.t @@ -611,20 +608,6 @@ def evolve_to_time(self,solution,tend=None): if 'LMM' in getattr(self,'time_integrator',''): self._registers[-1] = backup self._registers = self._registers[-1:] + self._registers[:-1] - # initialize dt and dtFE in case first step is rejected - if self.step_index == 1: - self.dt_list.append(self.dt) - self.dtFE_list.append(self.dt * self.cfl_max / cfl) - else: - # remove last dt and dtFE if a RK step is rejected - if self.step_index < len(self._registers): - self.dt_list = self.dt_list[:-1] - self.dtFE_list = self.dtFE_list[:-1] - else: - self.dt_list[-1] = dt_backup - self.dtFE_list[-1] = dtFE_backup - self.dt_list = self.dt_list[-1:] + self.dt_list[:-1] - self.dtFE_list = self.dtFE_list[-1:] + self.dtFE_list[:-1] else: state.q = q_backup solution.t = told From 798531e5204527a8c53b34d277164fdbd413a0b8 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Mon, 12 Jan 2015 10:54:29 +0300 Subject: [PATCH 17/46] Debugging LMM startup. --- src/pyclaw/sharpclaw/solver.py | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 6ed1f38b9..2bea3a9d0 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -312,18 +312,18 @@ def step(self,solution): elif self.time_integrator == 'SSPLMM32': if self._step_index == 1: + self.sspcoeff0 = self._sspcoeff['Euler'] # Store initial solution, function evaluation, dt and forward Euler dt self._registers[-1].q = state.q.copy() self.dq_stored = self.dq(state) - self.dt_list.append(0) - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) if self._step_index < 3: # Use Euler method for starting values state.q += self.dq_stored - self.sspcoeff0 = self._sspcoeff['Euler'] self.dq_stored = self.dq(state) # call self.dq once more to update cfl number else: + if self._step_index == 3: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] omega = (self.dt_list[-2] + self.dt_list[-1])/self.dt # ssp coefficient r = (omega-1.)/omega @@ -335,8 +335,8 @@ def step(self,solution): state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - # Update stored information - self._registers = self._registers[1:] + self._registers[:1] + + # Update stored information self._registers[-1].q = state.q.copy() elif self.time_integrator == 'SSPLMM43': @@ -346,6 +346,7 @@ def step(self,solution): self.dq_stored = self.dq(state) self.dt_list.append(0) self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) + self.sspcoeff0 = 1. # SSP coefficient for SSP22 if self._step_index < 4: # Use SSP22 method for starting values import copy @@ -358,9 +359,10 @@ def step(self,solution): deltaq = self.dq(s1) state.q = 0.5*(state.q + s1.q + deltaq) - self.sspcoeff0 = 1. # SSP coefficient for SSP22 self.dq_stored = self.dq(state) # call self.dq once more to update cfl number else: + if self._step_index == 4: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] omega3 = sum(self.dt_list[-3:])/self.dt omega4 = omega3 + 1. # SSP coefficient @@ -378,7 +380,6 @@ def step(self,solution): self.dq_stored = self.dq(state) # call self.dq once more to update cfl number # Update stored information - self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() elif self.time_integrator == 'LMM': @@ -583,6 +584,9 @@ def accept_reject_step(self,cfl): # update dt_list, dtFE_list if accept_step: + if self._step_index == 1: + self.dt_list.append(0) + self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) if self._step_index < len(self._registers): self.dt_list.append(self.dt) self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) @@ -591,6 +595,7 @@ def accept_reject_step(self,cfl): self.dt_list[-1] = self.dt self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() + self._registers = self._registers[1:] + self._registers[:1] self._step_index += 1 @@ -617,14 +622,9 @@ def get_dt_new(self,cfl,accept_step): else: # step-size update for starting methods self.dt = self.dt * self.cfl_desired / cfl - #self._step_index += 1 - if self._step_index == len(self._registers)-1: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] else: if self._step_index < len(self._registers): self.dt = self.dt * self.cfl_desired / cfl - if self._step_index == 1: - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) # additional conditions for SSPLMM43 if self.time_integrator == 'SSPLMM43': self.dt = min(3./5. * self.dtFE_list[-1], self.dt) From c4e1bda2f8622ce3b187702d639d8267fc4fc57d Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Wed, 14 Jan 2015 10:49:18 +0300 Subject: [PATCH 18/46] Cleaning pyclaw solver and moving updating of stored info to accept_reject_step function. --- src/pyclaw/sharpclaw/solver.py | 53 +++++++++++++++------------------- 1 file changed, 24 insertions(+), 29 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 2bea3a9d0..fee74e1c8 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -6,7 +6,7 @@ # Author: David Ketcheson """ # Solver superclass -from clawpack.pyclaw.solver import Solver, CFLError +from clawpack.pyclaw.solver import Solver from clawpack.pyclaw.util import add_parent_doc # Reconstructor @@ -146,6 +146,7 @@ def before_step(solver,solution) """ _sspcoeff = { 'Euler' : 1.0, + 'SSP22': 1.0, 'SSP33': 1.0, 'SSP104' : 6.0, 'SSPLMM32' : 0.5, @@ -313,14 +314,12 @@ def step(self,solution): elif self.time_integrator == 'SSPLMM32': if self._step_index == 1: self.sspcoeff0 = self._sspcoeff['Euler'] - # Store initial solution, function evaluation, dt and forward Euler dt + # Store initial solution and function evaluation self._registers[-1].q = state.q.copy() self.dq_stored = self.dq(state) if self._step_index < 3: # Use Euler method for starting values state.q += self.dq_stored - - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number else: if self._step_index == 3: self.sspcoeff0 = self._sspcoeff[self.time_integrator] @@ -333,25 +332,18 @@ def step(self,solution): deltaq = self.dq_stored state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q - - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - - # Update stored information - self._registers[-1].q = state.q.copy() + elif self.time_integrator == 'SSPLMM43': if self._step_index == 1: - # Store initial solution, function evaluation, dt and forward Euler dt + self.sspcoeff0 = self._sspcoeff['SSP22'] + # Store initial solution and function evaluation self._registers[-1].q = state.q.copy() self.dq_stored = self.dq(state) - self.dt_list.append(0) - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) - self.sspcoeff0 = 1. # SSP coefficient for SSP22 if self._step_index < 4: # Use SSP22 method for starting values import copy s1 = copy.deepcopy(state) - s1.set_num_ghost(self.num_ghost) ### depreciated by deepcopy fix ### deltaq = self.dq_stored s1.q = state.q + deltaq @@ -377,20 +369,19 @@ def step(self,solution): state.q = beta3*(r*state.q + deltaq) + \ (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number - # Update stored information + self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() + self.dq_stored = self.dq(state) # call self.dq once more to update cfl number elif self.time_integrator == 'LMM': - num_steps = len(self.alpha) - + num_steps = len(self._registers) # Store initial solution if self._step_index == 1: self._registers[-num_steps].q = state.q.copy() self._registers[-num_steps].dq = self.dq(state) - if self._step_index < num_steps: + if self._step_index < len(self._registers): # Using SSP104 for previous step values state.q = self.ssp104(state) self._registers[-num_steps+self._step_index].q = state.q.copy() @@ -546,14 +537,13 @@ def _allocate_registers(self,solution): state = solution.states[0] # use the same class constructor as the solution for the Runge Kutta stages - State = type(state) self._registers = [] for i in xrange(nregisters): import copy self._registers.append(copy.deepcopy(state)) - def accept_reject_step(self,cfl): + def accept_reject_step(self,state): r""" Decide whether to accept or not the current step. For Runge-Kutta methods the step is accepted if cfl <= cfl_max. @@ -562,6 +552,10 @@ def accept_reject_step(self,cfl): """ accept_step = True + # call self.dq once more to update cfl number + self.dq_stored = self.dq(state) + cfl = self.cfl.get_cached_max() + # check cfl condition for SSP LMM methods if self.time_integrator[:-2] == 'SSPLMM': # condition for starting RK methods @@ -571,9 +565,6 @@ def accept_reject_step(self,cfl): # additional condition for SSPLMM43 elif self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self.dtFE_list[-1]: accept_step = False - # apply LMM at the next step if last RK step is accepted - #if accept_step == True and self._step_index == len(self._registers)-1: - # self._step_index += 1 # only need to check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': rhoFE = 9./10. @@ -584,20 +575,24 @@ def accept_reject_step(self,cfl): # update dt_list, dtFE_list if accept_step: + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() if self._step_index == 1: self.dt_list.append(0) - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) + self.dtFE_list.append(dtFE) if self._step_index < len(self._registers): self.dt_list.append(self.dt) - self.dtFE_list.append(self.dt * self.cfl_max / self.cfl.get_cached_max()) + self.dtFE_list.append(dtFE) else: self.dt_list = self.dt_list[1:] + self.dt_list[:1] self.dt_list[-1] = self.dt self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] - self.dtFE_list[-1] = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - self._registers = self._registers[1:] + self._registers[:1] - self._step_index += 1 + self.dtFE_list[-1] = dtFE + + # Update stored information + self._registers = self._registers[1:] + self._registers[:1] + self._registers[-1].q = state.q.copy() + self._step_index += 1 # check cfl condition for Runge-Kutta methods elif cfl > self.cfl_max: From 573f726f73b2487602d36c7bad9462b9575020a5 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Wed, 14 Jan 2015 11:09:42 +0300 Subject: [PATCH 19/46] Cleaning pyclaw solver and moving updating of stored info to accept_reject_step function (2). --- src/pyclaw/solver.py | 17 +++++------------ 1 file changed, 5 insertions(+), 12 deletions(-) diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index ff85eefe0..4bb7a8198 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -502,8 +502,9 @@ def _bc_upper(self, bc_type, state, dim, t, array, idim, name): # ======================================================================== # Evolution routines # ======================================================================== - def accept_reject_step(self,cfl): + def accept_reject_step(self,state): accept_step = True + cfl = self.cfl.get_cached_max() if cfl > self.cfl_max: accept_step = False return accept_step @@ -571,18 +572,14 @@ def evolve_to_time(self,solution,tend=None): # Keep a backup in case we need to retake a time step if self.dt_variable: - if 'LMM' in getattr(self,'time_integrator',''): - import copy - backup = copy.deepcopy(self._registers[0]) - else: - q_backup = state.q.copy('F') + q_backup = state.q.copy('F') told = solution.t self.step(solution) # Check to make sure that the Courant number was not too large + accept_step = self.accept_reject_step(state) cfl = self.cfl.get_cached_max() - accept_step = self.accept_reject_step(cfl) if accept_step: # Accept this step self.status['cflmax'] = max(cfl, self.status['cflmax']) @@ -605,11 +602,7 @@ def evolve_to_time(self,solution,tend=None): # Reject this step self.logger.debug("Rejecting time step, CFL number too large") if self.dt_variable: - if 'LMM' in getattr(self,'time_integrator',''): - self._registers[-1] = backup - self._registers = self._registers[-1:] + self._registers[:-1] - else: - state.q = q_backup + state.q = q_backup solution.t = told else: # Give up, we cannot adapt, abort From 315e4b961e466a6eb1eaf454504ebb4a4227782a Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Wed, 14 Jan 2015 12:16:18 +0300 Subject: [PATCH 20/46] Use status['numsteps'] instead of step_index. --- src/pyclaw/sharpclaw/solver.py | 71 ++++++++++++++++++---------------- src/pyclaw/solver.py | 7 ++-- 2 files changed, 41 insertions(+), 37 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index fee74e1c8..e28968216 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -194,7 +194,6 @@ def __init__(self,riemann_solver=None,claw_package=None): self.c = None # Used only if time integrator is a multistep method - self._step_index = 1 self.sspcoeff0 = None self.alpha = None self.beta = None @@ -221,6 +220,9 @@ def setup(self,solution): state.set_num_ghost(self.num_ghost) # End hack + if self.time_integrator == 'LMM': + assert self.dt_variable == False, \ + 'Must set solver.dt_variable=False for LMM integrator' self._allocate_registers(solution) self._set_mthlim() try: @@ -269,6 +271,7 @@ def step(self,solution): Take one step with a Runge-Kutta or multistep method as specified by `solver.time_integrator`. """ + step_index = self.status['numsteps'] + 1 state = solution.states[0] self.cfl.set_global_max(0.) @@ -312,18 +315,18 @@ def step(self,solution): state.q += self.b[j]*self._registers[j].q elif self.time_integrator == 'SSPLMM32': - if self._step_index == 1: + if step_index == 1: self.sspcoeff0 = self._sspcoeff['Euler'] # Store initial solution and function evaluation self._registers[-1].q = state.q.copy() self.dq_stored = self.dq(state) - if self._step_index < 3: + if step_index < 3: # Use Euler method for starting values state.q += self.dq_stored else: - if self._step_index == 3: + if step_index == 3: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - omega = (self.dt_list[-2] + self.dt_list[-1])/self.dt + omega = sum(self.dt_list[-2:])/self.dt # ssp coefficient r = (omega-1.)/omega # method coefficients @@ -335,13 +338,14 @@ def step(self,solution): elif self.time_integrator == 'SSPLMM43': - if self._step_index == 1: + if step_index == 1: self.sspcoeff0 = self._sspcoeff['SSP22'] # Store initial solution and function evaluation self._registers[-1].q = state.q.copy() self.dq_stored = self.dq(state) - if self._step_index < 4: + if step_index < 4: # Use SSP22 method for starting values + # okay to copy state objects here since this only happens a few times import copy s1 = copy.deepcopy(state) @@ -353,7 +357,7 @@ def step(self,solution): self.dq_stored = self.dq(state) # call self.dq once more to update cfl number else: - if self._step_index == 4: + if step_index == 4: self.sspcoeff0 = self._sspcoeff[self.time_integrator] omega3 = sum(self.dt_list[-3:])/self.dt omega4 = omega3 + 1. @@ -377,16 +381,16 @@ def step(self,solution): elif self.time_integrator == 'LMM': num_steps = len(self._registers) # Store initial solution - if self._step_index == 1: + if step_index == 1: self._registers[-num_steps].q = state.q.copy() self._registers[-num_steps].dq = self.dq(state) - if self._step_index < len(self._registers): + if step_index < len(self._registers): # Using SSP104 for previous step values state.q = self.ssp104(state) - self._registers[-num_steps+self._step_index].q = state.q.copy() - self._registers[-num_steps+self._step_index].dq = self.dq(state) - self._step_index += 1 + self._registers[-num_steps+step_index].q = state.q.copy() + self._registers[-num_steps+step_index].dq = self.dq(state) + step_index += 1 else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step @@ -410,6 +414,7 @@ def ssp104(self,state): s2=self._registers[1] s1.q = state.q.copy() elif self.time_integrator == 'LMM': + # okay to copy state objects here since this only happens a few times import copy s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) @@ -529,9 +534,7 @@ def _allocate_registers(self,solution): elif self.time_integrator == 'RK': nregisters=len(self.b)+1 elif self.time_integrator == 'SSPLMM32': nregisters=3 elif self.time_integrator == 'SSPLMM43': nregisters=4 - elif self.time_integrator == 'LMM': - nregisters=len(self.alpha) - self.dt_variable = False + elif self.time_integrator == 'LMM': nregisters=len(self.alpha) else: raise Exception('Unrecognized time integrator: '+self.time_integrator) @@ -551,15 +554,13 @@ def accept_reject_step(self,state): For SSPLMM43 additional checks on previous forward Euler step-sizes are required. """ accept_step = True - - # call self.dq once more to update cfl number - self.dq_stored = self.dq(state) cfl = self.cfl.get_cached_max() - + step_index = self.status['numsteps'] + 1 + # check cfl condition for SSP LMM methods - if self.time_integrator[:-2] == 'SSPLMM': + if self.time_integrator[:6] == 'SSPLMM': # condition for starting RK methods - if self._step_index < len(self._registers): + if step_index < len(self._registers): if cfl > self.cfl_max: accept_step = False # additional condition for SSPLMM43 @@ -575,11 +576,16 @@ def accept_reject_step(self,state): # update dt_list, dtFE_list if accept_step: - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - if self._step_index == 1: + if step_index == 1: self.dt_list.append(0) + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl self.dtFE_list.append(dtFE) - if self._step_index < len(self._registers): + + # call self.dq once more to update cfl number + self.dq_stored = self.dq(state) + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() + + if step_index < len(self._registers): self.dt_list.append(self.dt) self.dtFE_list.append(dtFE) else: @@ -592,8 +598,6 @@ def accept_reject_step(self,state): self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() - self._step_index += 1 - # check cfl condition for Runge-Kutta methods elif cfl > self.cfl_max: accept_step = False @@ -605,26 +609,27 @@ def get_dt_new(self,cfl,accept_step): r""" Set time-step for next step depending on the time integrator and whether or not the step is accepted. """ - if self.time_integrator[:-2] == 'SSPLMM': + step_index = self.status['numsteps'] + 1 + if self.time_integrator[:6] == 'SSPLMM': # step-size update for SSP LMM methods if accept_step: - if self._step_index >= len(self._registers): + if step_index >= len(self._registers): s = len(self._registers) - p = int(self.time_integrator[-2]) + p = int(self.time_integrator[-1]) mu = min([self.dtFE_list[-1-i] for i in range(s)]) H = sum([self.dt_list[-1-i] for i in range(s-1)]) - self.dt = H * mu / (H + (p-2)*mu) + self.dt = H * mu / (H + (p-1)*mu) else: # step-size update for starting methods self.dt = self.dt * self.cfl_desired / cfl else: - if self._step_index < len(self._registers): + if step_index < len(self._registers): self.dt = self.dt * self.cfl_desired / cfl # additional conditions for SSPLMM43 if self.time_integrator == 'SSPLMM43': self.dt = min(3./5. * self.dtFE_list[-1], self.dt) elif self.time_integrator == 'SSPLMM43': - # cruel step-size reduction if step-size assumptions for SSPLMM43 are violated + # crude step-size reduction if step-size assumptions for SSPLMM43 are violated # no such assumptions are needed for SSPLMM32 self.dt /= 2. else: diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 4bb7a8198..1294c39eb 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -503,11 +503,11 @@ def _bc_upper(self, bc_type, state, dim, t, array, idim, name): # Evolution routines # ======================================================================== def accept_reject_step(self,state): - accept_step = True cfl = self.cfl.get_cached_max() if cfl > self.cfl_max: - accept_step = False - return accept_step + return False + else: + return True def get_dt_new(self,cfl,accept_step): return min(self.dt_max,self.dt * self.cfl_desired / cfl) @@ -541,7 +541,6 @@ def evolve_to_time(self,solution,tend=None): # Parameters for time-stepping tstart = solution.t - # Reset status dictionary num_steps = 0 # Setup for the run From 852f58239dd5764786f2ba1eb5243617dbdc186f Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 27 Jan 2015 10:48:22 +0300 Subject: [PATCH 21/46] Make self._registers[-1].t = state.t. --- src/pyclaw/sharpclaw/solver.py | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index e28968216..a5f5081c3 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -25,7 +25,7 @@ def before_step(solver,solution): """ pass -def default_tfluct(): +def default_tfluct(self): r"""This is a dummy routine and should never be called, check Euler1D to learn how to pass tfluct functions to the sharpclaw solver """ @@ -319,6 +319,7 @@ def step(self,solution): self.sspcoeff0 = self._sspcoeff['Euler'] # Store initial solution and function evaluation self._registers[-1].q = state.q.copy() + self._registers[-1].t = state.t self.dq_stored = self.dq(state) if step_index < 3: # Use Euler method for starting values @@ -597,6 +598,7 @@ def accept_reject_step(self,state): # Update stored information self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() + self._registers[-1].t = state.t # check cfl condition for Runge-Kutta methods elif cfl > self.cfl_max: From 2a26711eeae6c3b11a000f6fc94f6330aebae7d2 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 3 Feb 2015 10:04:20 +0300 Subject: [PATCH 22/46] Fix the way dq_stored stores the function evaluation by correcting the dt used. - change omega to omega2 for SSPLMM32 (as in paper) - Use dq_stored in RK methods. --- src/pyclaw/sharpclaw/solver.py | 86 +++++++++++++++++++++------------- 1 file changed, 54 insertions(+), 32 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index a5f5081c3..4944391ba 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -183,6 +183,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None + self.dq_stored = None self.call_before_step_each_stage = False self._mthlim = self.limiters self._method = None @@ -197,10 +198,11 @@ def __init__(self,riemann_solver=None,claw_package=None): self.sspcoeff0 = None self.alpha = None self.beta = None - self.dq_stored = None self.dt_list = [] self.dtFE_list = [] + self.dt_old = None + # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) @@ -271,30 +273,35 @@ def step(self,solution): Take one step with a Runge-Kutta or multistep method as specified by `solver.time_integrator`. """ - step_index = self.status['numsteps'] + 1 state = solution.states[0] self.cfl.set_global_max(0.) self.before_step(self,state) if self.time_integrator=='Euler': - deltaq=self.dq(state) - state.q+=deltaq + if self.status['numsteps'] == 0: + deltaq = self.dq(state) + else: + deltaq = self.dt/self.dt_old * self.dq_stored + state.q += deltaq elif self.time_integrator=='SSP33': - deltaq=self.dq(state) - self._registers[0].q=state.q+deltaq - self._registers[0].t =state.t+self.dt + if self.status['numsteps'] == 0: + deltaq = self.dq(state) + else: + deltaq = self.dt/self.dt_old * self.dq_stored + self._registers[0].q = state.q + deltaq + self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: self.before_step(self,self._registers[0]) - deltaq=self.dq(self._registers[0]) - self._registers[0].q= 0.75*state.q + 0.25*(self._registers[0].q+deltaq) - self._registers[0].t = state.t+0.5*self.dt + deltaq = self.dq(self._registers[0]) + self._registers[0].q = 0.75*state.q + 0.25*(self._registers[0].q + deltaq) + self._registers[0].t = state.t + 0.5*self.dt if self.call_before_step_each_stage: self.before_step(self,self._registers[0]) - deltaq=self.dq(self._registers[0]) + deltaq = self.dq(self._registers[0]) state.q = 1./3.*state.q + 2./3.*(self._registers[0].q+deltaq) elif self.time_integrator=='SSP104': @@ -315,6 +322,7 @@ def step(self,solution): state.q += self.b[j]*self._registers[j].q elif self.time_integrator == 'SSPLMM32': + step_index = self.status['numsteps'] + 1 if step_index == 1: self.sspcoeff0 = self._sspcoeff['Euler'] # Store initial solution and function evaluation @@ -323,22 +331,25 @@ def step(self,solution): self.dq_stored = self.dq(state) if step_index < 3: # Use Euler method for starting values + if self.dt_list: + self.dq_stored = self.dt/self.dt_list[-1] * self.dq_stored state.q += self.dq_stored - else: - if step_index == 3: + if step_index == 2: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - omega = sum(self.dt_list[-2:])/self.dt + else: + omega2 = sum(self.dt_list)/self.dt # ssp coefficient - r = (omega-1.)/omega + r = (omega2-1.)/omega2 # method coefficients - delta = 1./omega**2 - beta = (omega+1.)/omega + delta = 1./omega2**2 + beta = (omega2+1.)/omega2 - deltaq = self.dq_stored + deltaq = self.dt/self.dt_list[-1] * self.dq_stored state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q elif self.time_integrator == 'SSPLMM43': + step_index = self.status['numsteps'] + 1 if step_index == 1: self.sspcoeff0 = self._sspcoeff['SSP22'] # Store initial solution and function evaluation @@ -420,7 +431,10 @@ def ssp104(self,state): s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) - deltaq=self.dq(state) + if self.status['numsteps'] == 0: + deltaq = self.dq(state) + else: + deltaq = self.dt/self.dt_old * self.dq_stored s1.q = state.q + deltaq/6. s1.t = state.t + self.dt/6. @@ -555,18 +569,27 @@ def accept_reject_step(self,state): For SSPLMM43 additional checks on previous forward Euler step-sizes are required. """ accept_step = True - cfl = self.cfl.get_cached_max() - step_index = self.status['numsteps'] + 1 + # store function evaluation in case we reject step + dq_backup = self.dq_stored + + # update stored function evaluation and CFL number + self.dq_stored = self.dq(state) + cfl = self.cfl.get_cached_max() + # check cfl condition for SSP LMM methods if self.time_integrator[:6] == 'SSPLMM': + step_index = self.status['numsteps'] + 1 + # condition for starting RK methods if step_index < len(self._registers): if cfl > self.cfl_max: accept_step = False + self.dq_stored = dq_backup # additional condition for SSPLMM43 elif self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self.dtFE_list[-1]: accept_step = False + self.dq_stored = dq_backup # only need to check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': rhoFE = 9./10. @@ -574,18 +597,15 @@ def accept_reject_step(self,state): dtFEm1 = self.dtFE_list[-2] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False + self.dq_stored = dq_backup # update dt_list, dtFE_list if accept_step: + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl + if step_index == 1: - self.dt_list.append(0) - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl self.dtFE_list.append(dtFE) - # call self.dq once more to update cfl number - self.dq_stored = self.dq(state) - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / self.cfl.get_cached_max() - if step_index < len(self._registers): self.dt_list.append(self.dt) self.dtFE_list.append(dtFE) @@ -603,6 +623,7 @@ def accept_reject_step(self,state): # check cfl condition for Runge-Kutta methods elif cfl > self.cfl_max: accept_step = False + self.dq_stored = dq_backup return accept_step @@ -611,15 +632,15 @@ def get_dt_new(self,cfl,accept_step): r""" Set time-step for next step depending on the time integrator and whether or not the step is accepted. """ - step_index = self.status['numsteps'] + 1 if self.time_integrator[:6] == 'SSPLMM': - # step-size update for SSP LMM methods + # step-size update for SSP LMM methods + step_index = self.status['numsteps'] + 1 if accept_step: if step_index >= len(self._registers): s = len(self._registers) p = int(self.time_integrator[-1]) - mu = min([self.dtFE_list[-1-i] for i in range(s)]) - H = sum([self.dt_list[-1-i] for i in range(s-1)]) + mu = min([self.dtFE_list[i] for i in range(s)]) + H = sum(self.dt_list) self.dt = H * mu / (H + (p-1)*mu) else: # step-size update for starting methods @@ -636,9 +657,10 @@ def get_dt_new(self,cfl,accept_step): self.dt /= 2. else: # step-size update for Runge-Kutta methods + self.dt_old = self.dt self.dt = self.dt * self.cfl_desired / cfl - return min(self.dt_max,self.dt) + return self.dt # ======================================================================== From 5989bf1787356a48fe03665e1fc6f6f933a6051b Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 10 Feb 2015 10:01:46 +0300 Subject: [PATCH 23/46] Use function evaluation from previous steps in RK and LMM Also: - Rename self.dq_stored to self.deltaq - Remove self.dt_old (no longer used) - Clear ssp104 --- src/pyclaw/sharpclaw/solver.py | 125 ++++++++++++++------------------- 1 file changed, 53 insertions(+), 72 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 4944391ba..fe82ae7e4 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -183,7 +183,9 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None - self.dq_stored = None + self.deltaq = None + self.dq_backup = None + self.dt_list = [] self.call_before_step_each_stage = False self._mthlim = self.limiters self._method = None @@ -198,13 +200,11 @@ def __init__(self,riemann_solver=None,claw_package=None): self.sspcoeff0 = None self.alpha = None self.beta = None - self.dt_list = [] self.dtFE_list = [] - self.dt_old = None - # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) + def setup(self,solution): """ @@ -275,39 +275,36 @@ def step(self,solution): """ state = solution.states[0] self.cfl.set_global_max(0.) + step_index = self.status['numsteps'] + 1 self.before_step(self,state) - if self.time_integrator=='Euler': - if self.status['numsteps'] == 0: - deltaq = self.dq(state) - else: - deltaq = self.dt/self.dt_old * self.dq_stored - state.q += deltaq + if not self.dt_list: + # Compute function evaluation for initial condition + self.deltaq = self.dq(state) + self.dt_list.append(self.dt) + self.deltaq = (self.dt/self.dt_list[-1]) * self.deltaq - elif self.time_integrator=='SSP33': - if self.status['numsteps'] == 0: - deltaq = self.dq(state) - else: - deltaq = self.dt/self.dt_old * self.dq_stored - self._registers[0].q = state.q + deltaq + if self.time_integrator == 'Euler': + state.q += self.deltaq + + elif self.time_integrator == 'SSP33': + self._registers[0].q = state.q + self.deltaq self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: self.before_step(self,self._registers[0]) - deltaq = self.dq(self._registers[0]) - self._registers[0].q = 0.75*state.q + 0.25*(self._registers[0].q + deltaq) + self._registers[0].q = 0.75*state.q + 0.25*(self._registers[0].q + self.dq(self._registers[0])) self._registers[0].t = state.t + 0.5*self.dt if self.call_before_step_each_stage: self.before_step(self,self._registers[0]) - deltaq = self.dq(self._registers[0]) - state.q = 1./3.*state.q + 2./3.*(self._registers[0].q+deltaq) + state.q = 1./3.*state.q + 2./3.*(self._registers[0].q + self.dq(self._registers[0])) - elif self.time_integrator=='SSP104': + elif self.time_integrator == 'SSP104': state.q = self.ssp104(state) - elif self.time_integrator=='RK': + elif self.time_integrator == 'RK': # General RK with specified coefficients # self._registers[i].q actually stores dt*f(y_i) num_stages = len(self.b) @@ -322,73 +319,60 @@ def step(self,solution): state.q += self.b[j]*self._registers[j].q elif self.time_integrator == 'SSPLMM32': - step_index = self.status['numsteps'] + 1 if step_index == 1: self.sspcoeff0 = self._sspcoeff['Euler'] - # Store initial solution and function evaluation + # Save initial solution self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t - self.dq_stored = self.dq(state) if step_index < 3: # Use Euler method for starting values - if self.dt_list: - self.dq_stored = self.dt/self.dt_list[-1] * self.dq_stored - state.q += self.dq_stored - if step_index == 2: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] + state.q += self.deltaq else: - omega2 = sum(self.dt_list)/self.dt - # ssp coefficient + if step_index == 3: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + + omega2 = sum(self.dt_list[1:])/self.dt + # Ssp coefficient r = (omega2-1.)/omega2 - # method coefficients + # Method coefficients delta = 1./omega2**2 beta = (omega2+1.)/omega2 - deltaq = self.dt/self.dt_list[-1] * self.dq_stored - state.q = beta*(r*state.q + deltaq) + delta*self._registers[-3].q - + state.q = beta*(r*state.q + self.deltaq) + delta*self._registers[-3].q elif self.time_integrator == 'SSPLMM43': - step_index = self.status['numsteps'] + 1 if step_index == 1: self.sspcoeff0 = self._sspcoeff['SSP22'] - # Store initial solution and function evaluation + # Store initial solution self._registers[-1].q = state.q.copy() - self.dq_stored = self.dq(state) + self._registers[-1].t = state.t if step_index < 4: # Use SSP22 method for starting values # okay to copy state objects here since this only happens a few times import copy s1 = copy.deepcopy(state) - deltaq = self.dq_stored + deltaq = self.deltaq s1.q = state.q + deltaq s1.t = state.t + self.dt deltaq = self.dq(s1) state.q = 0.5*(state.q + s1.q + deltaq) - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number else: if step_index == 4: self.sspcoeff0 = self._sspcoeff[self.time_integrator] + omega3 = sum(self.dt_list[-3:])/self.dt omega4 = omega3 + 1. # SSP coefficient r = (omega3-2.)/omega3 - # method coefficients + # Method coefficients delta0 = (4*omega4 - omega3**2)/omega3**3 beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - deltaq = self.dq_stored - deltaqm4 = self.dq(self._registers[-4]) - state.q = beta3*(r*state.q + deltaq) + \ - (r*beta0 + delta0)*self._registers[-4].q + beta0*deltaqm4 - - # Update stored information - self._registers = self._registers[1:] + self._registers[:1] - self._registers[-1].q = state.q.copy() - self.dq_stored = self.dq(state) # call self.dq once more to update cfl number + state.q = beta3*(r*state.q + self.deltaq) + \ + (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dq(self._registers[-4]) elif self.time_integrator == 'LMM': num_steps = len(self._registers) @@ -396,14 +380,12 @@ def step(self,solution): if step_index == 1: self._registers[-num_steps].q = state.q.copy() self._registers[-num_steps].dq = self.dq(state) - if step_index < len(self._registers): # Using SSP104 for previous step values state.q = self.ssp104(state) self._registers[-num_steps+step_index].q = state.q.copy() self._registers[-num_steps+step_index].dq = self.dq(state) step_index += 1 - else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self._registers[-1].dq @@ -419,48 +401,47 @@ def step(self,solution): raise Exception('Unrecognized time integrator') return False + # store function evaluation in case we reject step + self.dq_backup = self.deltaq + # call again and save self.dq(state) to update CFL number + self.deltaq = self.dq(state) + def ssp104(self,state): if self.time_integrator == 'SSP104': - s1=self._registers[0] - s2=self._registers[1] + s1 = self._registers[0] + s2 = self._registers[1] s1.q = state.q.copy() elif self.time_integrator == 'LMM': - # okay to copy state objects here since this only happens a few times + # Okay to copy state objects here since this only happens a few times import copy s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) - if self.status['numsteps'] == 0: - deltaq = self.dq(state) - else: - deltaq = self.dt/self.dt_old * self.dq_stored - s1.q = state.q + deltaq/6. + s1.q = state.q + self.deltaq/6. s1.t = state.t + self.dt/6. for i in xrange(4): if self.call_before_step_each_stage: self.before_step(self,s1) - deltaq=self.dq(s1) - s1.q=s1.q + deltaq/6. - s1.t =s1.t + self.dt/6. + s1.q = s1.q + self.dq(s1)/6. + s1.t = s1.t + self.dt/6. - s2.q = state.q/25. + 9./25 * s1.q + s2.q = state.q/25. + 0.36 * s1.q s1.q = 15. * s2.q - 5. * s1.q s1.t = state.t + self.dt/3. for i in xrange(4): if self.call_before_step_each_stage: self.before_step(self,s1) - deltaq=self.dq(s1) - s1.q=s1.q + deltaq/6. - s1.t =s1.t + self.dt/6. + s1.q = s1.q + self.dq(s1)/6. + s1.t = s1.t + self.dt/6. if self.call_before_step_each_stage: self.before_step(self,s1) - deltaq = self.dq(s1) - - return s2.q + 0.6 * s1.q + 0.1 * deltaq + state.q = s2.q + 0.6 * s1.q + 0.1 * self.dq(s1) + + return state.q def _set_mthlim(self): @@ -554,7 +535,7 @@ def _allocate_registers(self,solution): raise Exception('Unrecognized time integrator: '+self.time_integrator) state = solution.states[0] - # use the same class constructor as the solution for the Runge Kutta stages + # Use the same class constructor as the solution for the Runge Kutta stages self._registers = [] for i in xrange(nregisters): import copy From 1d8a23d0193aa54cf3ab16650bb0fe0574d3a175 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 10 Feb 2015 10:06:03 +0300 Subject: [PATCH 24/46] Major changes in accept_reject_step and get_dt_new functions - Use appropiate choice of step-size so that almost no steps are rejected. - Impove/update conditions for accepting a step for SSPLMMs - Add documentation Desired order of accuracy is achieved. Note some conditions for accepting step-size can be removed since step-size control quarantees that the conditions are accepted. --- src/pyclaw/sharpclaw/solver.py | 120 ++++++++++++++++++++------------- 1 file changed, 74 insertions(+), 46 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index fe82ae7e4..2e327507b 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -402,8 +402,8 @@ def step(self,solution): return False # store function evaluation in case we reject step - self.dq_backup = self.deltaq - # call again and save self.dq(state) to update CFL number + self.dq_backup = self.deltaq + # call again and save self.dq(state) to update CFL number self.deltaq = self.dq(state) @@ -551,42 +551,52 @@ def accept_reject_step(self,state): """ accept_step = True - # store function evaluation in case we reject step - dq_backup = self.dq_stored - - # update stored function evaluation and CFL number - self.dq_stored = self.dq(state) cfl = self.cfl.get_cached_max() - # check cfl condition for SSP LMM methods + # Check cfl condition for SSP LMM methods if self.time_integrator[:6] == 'SSPLMM': step_index = self.status['numsteps'] + 1 - # condition for starting RK methods + # Here we actually need to check cfl violation only for the starting methods of SSPLMM32 + # Step-size choice for SSPLMM43 guarantees that the above condition are always fulfilled. + + # Condition for starting RK methods if step_index < len(self._registers): if cfl > self.cfl_max: accept_step = False - self.dq_stored = dq_backup - # additional condition for SSPLMM43 - elif self.time_integrator == 'SSPLMM43' and self.dt > 3./5. * self.dtFE_list[-1]: - accept_step = False - self.dq_stored = dq_backup - # only need to check conditions for SSPLMM43 for the steps LMM is active + self.deltaq = self.dq_backup + # Additional condition for SSPLMM43 + if self.time_integrator == 'SSPLMM43': + # the above condition is equivalent to self.dt > 0.6 * dtFE (up to machine precision), + # where dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl is the FE step-size + # of the current solution. + if cfl > 0.6 * self.cfl_max / self.sspcoeff0: + accept_step = False + self.deltaq = self.dq_backup + + # Check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': - rhoFE = 9./10. - dtFE = self.dtFE_list[-1] - dtFEm1 = self.dtFE_list[-2] - if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - accept_step = False - self.dq_stored = dq_backup - - # update dt_list, dtFE_list + if step_index == 4: + if cfl > 0.6 * self.cfl_max / self.sspcoeff0: + accept_step = False + self.deltaq = self.dq_backup + else: + # In principle we only need to check the ratio of FE step-sizes after the second LMM43 + # is applied + rhoFE = 0.9 + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl + dtFEm1 = self.dtFE_list[-1] + if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: + accept_step = False + self.deltaq = self.dq_backup + + # Update dt_list, dtFE_list if accept_step: dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl if step_index == 1: + # Here we use dtFE(u1) for dtFE(u0) since max wave speed is not returned by self.dq self.dtFE_list.append(dtFE) - if step_index < len(self._registers): self.dt_list.append(self.dt) self.dtFE_list.append(dtFE) @@ -601,10 +611,14 @@ def accept_reject_step(self,state): self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t - # check cfl condition for Runge-Kutta methods - elif cfl > self.cfl_max: - accept_step = False - self.dq_stored = dq_backup + # Check cfl condition for Runge-Kutta methods + else: + if cfl > self.cfl_max: + accept_step = False + self.deltaq = self.dq_backup + else: + # Update dt_list + self.dt_list[-1] = self.dt return accept_step @@ -614,33 +628,47 @@ def get_dt_new(self,cfl,accept_step): Set time-step for next step depending on the time integrator and whether or not the step is accepted. """ if self.time_integrator[:6] == 'SSPLMM': - # step-size update for SSP LMM methods - step_index = self.status['numsteps'] + 1 + # Step-size update for SSP LMM methods + step_index = self.status['numsteps'] + 1 + if accept_step: - if step_index >= len(self._registers): + if self.time_integrator == 'SSPLMM43' and step_index <= len(self._registers): + # Step-size for SSPLMM43 when first LMM is applied + # We can replace self.cfl_desired with self.cfl_max to choose the maximum allowed step-size + self.dt = 0.6 * self.dt * self.cfl_desired / (self.sspcoeff0 * cfl) + elif step_index < len(self._registers): + # Step-size update of starting methods for SSPLMM32 + self.dt = self.dt * self.cfl_desired / cfl + else: s = len(self._registers) p = int(self.time_integrator[-1]) mu = min([self.dtFE_list[i] for i in range(s)]) - H = sum(self.dt_list) + H = sum(self.dt_list[1:]) self.dt = H * mu / (H + (p-1)*mu) - else: - # step-size update for starting methods - self.dt = self.dt * self.cfl_desired / cfl else: - if step_index < len(self._registers): - self.dt = self.dt * self.cfl_desired / cfl - # additional conditions for SSPLMM43 - if self.time_integrator == 'SSPLMM43': - self.dt = min(3./5. * self.dtFE_list[-1], self.dt) - elif self.time_integrator == 'SSPLMM43': - # crude step-size reduction if step-size assumptions for SSPLMM43 are violated - # no such assumptions are needed for SSPLMM32 - self.dt /= 2. + # Pick new step-size for SSPLMM43 if current step is rejected + if self.time_integrator == 'SSPLMM43': + if step_index <= len(self._registers): + dt1 = 0.6 * self.dt * self.cfl_desired / (self.sspcoeff0 * cfl) + dt2 = self.dt * self.cfl_desired + self.dt = min(dt1,dt2) + else: + # Choose step-size in order to satisfy the dtFE ratio condition if violated + A = self.dtFE_list[-2] * self.sspcoeff0 * cfl / self.cfl_max + self.dt = 181/180*A + else: + # Note that steps for SSPLMM32 are always accepted when LMM is active + if step_index < len(self._registers): + self.dt = self.dt * self.cfl_desired / cfl else: - # step-size update for Runge-Kutta methods - self.dt_old = self.dt + # Step-size update for Runge-Kutta methods self.dt = self.dt * self.cfl_desired / cfl + #print step_index + #print accept_step + #print self.dt + #raw_input() + return self.dt From af71cfe976bc8c32f5802397c89a15ee3f6cf18d Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Fri, 13 Feb 2015 19:36:05 +0300 Subject: [PATCH 25/46] - Rename dt_list and dtFE_list to previous_dt_values and previous_dtFE_values. - Update comments. --- src/pyclaw/sharpclaw/solver.py | 79 +++++++++++++++------------------- 1 file changed, 35 insertions(+), 44 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 2e327507b..baf278f2b 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -185,7 +185,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.dq_src = None self.deltaq = None self.dq_backup = None - self.dt_list = [] + self.prev_dt_values = [] self.call_before_step_each_stage = False self._mthlim = self.limiters self._method = None @@ -200,7 +200,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.sspcoeff0 = None self.alpha = None self.beta = None - self.dtFE_list = [] + self.prev_dtFE_values = [] # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) @@ -279,11 +279,11 @@ def step(self,solution): self.before_step(self,state) - if not self.dt_list: + if not self.prev_dt_values: # Compute function evaluation for initial condition self.deltaq = self.dq(state) - self.dt_list.append(self.dt) - self.deltaq = (self.dt/self.dt_list[-1]) * self.deltaq + self.prev_dt_values.append(self.dt) + self.deltaq = (self.dt/self.prev_dt_values[-1]) * self.deltaq if self.time_integrator == 'Euler': state.q += self.deltaq @@ -331,8 +331,8 @@ def step(self,solution): if step_index == 3: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - omega2 = sum(self.dt_list[1:])/self.dt - # Ssp coefficient + omega2 = sum(self.prev_dt_values[1:])/self.dt + # SSP coefficient r = (omega2-1.)/omega2 # Method coefficients delta = 1./omega2**2 @@ -348,21 +348,17 @@ def step(self,solution): self._registers[-1].t = state.t if step_index < 4: # Use SSP22 method for starting values - # okay to copy state objects here since this only happens a few times - import copy - s1 = copy.deepcopy(state) - - deltaq = self.deltaq - s1.q = state.q + deltaq - s1.t = state.t + self.dt - deltaq = self.dq(s1) - state.q = 0.5*(state.q + s1.q + deltaq) - + self._registers[0].q = state.q + self.deltaq + self._registers[0].t = state.t + self.dt + state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: + # This part can be impoved by saving function evaluations of previous solutions in a list + # Thus self.dq(self._registers[-4] wont be calculated at the current step, but use already + # saved values. if step_index == 4: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - omega3 = sum(self.dt_list[-3:])/self.dt + omega3 = sum(self.prev_dt_values[-3:])/self.dt omega4 = omega3 + 1. # SSP coefficient r = (omega3-2.)/omega3 @@ -547,7 +543,7 @@ def accept_reject_step(self,state): Decide whether to accept or not the current step. For Runge-Kutta methods the step is accepted if cfl <= cfl_max. For SSPLMM32 the choice of step-size guarantees the cfl condition is satisfied. - For SSPLMM43 additional checks on previous forward Euler step-sizes are required. + For SSPLMM43 additional checks on the cfl number and ratio of forward Euler step-sizes are required. """ accept_step = True @@ -581,30 +577,30 @@ def accept_reject_step(self,state): accept_step = False self.deltaq = self.dq_backup else: - # In principle we only need to check the ratio of FE step-sizes after the second LMM43 + # In principle we only need to check the ratio of FE step-sizes after the second LMM # is applied rhoFE = 0.9 dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl - dtFEm1 = self.dtFE_list[-1] + dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False self.deltaq = self.dq_backup - # Update dt_list, dtFE_list + # Update prev_dt_values, prev_dtFE_values if accept_step: dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl if step_index == 1: # Here we use dtFE(u1) for dtFE(u0) since max wave speed is not returned by self.dq - self.dtFE_list.append(dtFE) + self.prev_dtFE_values.append(dtFE) if step_index < len(self._registers): - self.dt_list.append(self.dt) - self.dtFE_list.append(dtFE) + self.prev_dt_values.append(self.dt) + self.prev_dtFE_values.append(dtFE) else: - self.dt_list = self.dt_list[1:] + self.dt_list[:1] - self.dt_list[-1] = self.dt - self.dtFE_list = self.dtFE_list[1:] + self.dtFE_list[:1] - self.dtFE_list[-1] = dtFE + self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] + self.prev_dt_values[-1] = self.dt + self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] + self.prev_dtFE_values[-1] = dtFE # Update stored information self._registers = self._registers[1:] + self._registers[:1] @@ -617,8 +613,8 @@ def accept_reject_step(self,state): accept_step = False self.deltaq = self.dq_backup else: - # Update dt_list - self.dt_list[-1] = self.dt + # Update prev_dt_values + self.prev_dt_values[-1] = self.dt return accept_step @@ -626,6 +622,9 @@ def accept_reject_step(self,state): def get_dt_new(self,cfl,accept_step): r""" Set time-step for next step depending on the time integrator and whether or not the step is accepted. + Currently, a new step-size is chosen if a step is rejected, although this is not neccesary since the + step-size control guarantees that steps are always accepted. + Essentially we only need to pick a new step-size if the dtFE ratio condition for SSPLMM43 is violated. """ if self.time_integrator[:6] == 'SSPLMM': # Step-size update for SSP LMM methods @@ -642,8 +641,8 @@ def get_dt_new(self,cfl,accept_step): else: s = len(self._registers) p = int(self.time_integrator[-1]) - mu = min([self.dtFE_list[i] for i in range(s)]) - H = sum(self.dt_list[1:]) + mu = min([self.prev_dtFE_values[i] for i in range(s)]) + H = sum(self.prev_dt_values[1:]) self.dt = H * mu / (H + (p-1)*mu) else: # Pick new step-size for SSPLMM43 if current step is rejected @@ -654,21 +653,13 @@ def get_dt_new(self,cfl,accept_step): self.dt = min(dt1,dt2) else: # Choose step-size in order to satisfy the dtFE ratio condition if violated - A = self.dtFE_list[-2] * self.sspcoeff0 * cfl / self.cfl_max - self.dt = 181/180*A - else: - # Note that steps for SSPLMM32 are always accepted when LMM is active - if step_index < len(self._registers): - self.dt = self.dt * self.cfl_desired / cfl + rhoFE = 0.9 + A = self.prev_dtFE_values[-2] * self.sspcoeff0 * cfl / self.cfl_max + self.dt = A/2 * (1 + rhoFE**2) / rhoFE else: # Step-size update for Runge-Kutta methods self.dt = self.dt * self.cfl_desired / cfl - #print step_index - #print accept_step - #print self.dt - #raw_input() - return self.dt From 59669fa8130da964603a04ea5cb3f4c1e7feb3ee Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Sun, 15 Feb 2015 10:05:34 +0300 Subject: [PATCH 26/46] Change self.deltaq to a list. - Now if time_integrator==LMM previous function evaluations are stored. - LMM code updated. - Correct step-size choice when initial step is rejected with SSPLMM32. --- src/pyclaw/sharpclaw/solver.py | 87 ++++++++++++++++++---------------- 1 file changed, 45 insertions(+), 42 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index baf278f2b..de68ddafc 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -183,7 +183,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None - self.deltaq = None + self.deltaq = [] self.dq_backup = None self.prev_dt_values = [] self.call_before_step_each_stage = False @@ -281,15 +281,15 @@ def step(self,solution): if not self.prev_dt_values: # Compute function evaluation for initial condition - self.deltaq = self.dq(state) + self.deltaq.append(self.dq(state)) self.prev_dt_values.append(self.dt) - self.deltaq = (self.dt/self.prev_dt_values[-1]) * self.deltaq + self.deltaq[-1] = (self.dt/self.prev_dt_values[-1]) * self.deltaq[-1] if self.time_integrator == 'Euler': - state.q += self.deltaq + state.q += self.deltaq[-1] elif self.time_integrator == 'SSP33': - self._registers[0].q = state.q + self.deltaq + self._registers[0].q = state.q + self.deltaq[-1] self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -326,7 +326,7 @@ def step(self,solution): self._registers[-1].t = state.t if step_index < 3: # Use Euler method for starting values - state.q += self.deltaq + state.q += self.deltaq[-1] else: if step_index == 3: self.sspcoeff0 = self._sspcoeff[self.time_integrator] @@ -338,7 +338,7 @@ def step(self,solution): delta = 1./omega2**2 beta = (omega2+1.)/omega2 - state.q = beta*(r*state.q + self.deltaq) + delta*self._registers[-3].q + state.q = beta*(r*state.q + self.deltaq[-1]) + delta*self._registers[-3].q elif self.time_integrator == 'SSPLMM43': if step_index == 1: @@ -348,7 +348,7 @@ def step(self,solution): self._registers[-1].t = state.t if step_index < 4: # Use SSP22 method for starting values - self._registers[0].q = state.q + self.deltaq + self._registers[0].q = state.q + self.deltaq[-1] self._registers[0].t = state.t + self.dt state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: @@ -367,7 +367,7 @@ def step(self,solution): beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - state.q = beta3*(r*state.q + self.deltaq) + \ + state.q = beta3*(r*state.q + self.deltaq[-1]) + \ (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dq(self._registers[-4]) elif self.time_integrator == 'LMM': @@ -375,32 +375,29 @@ def step(self,solution): # Store initial solution if step_index == 1: self._registers[-num_steps].q = state.q.copy() - self._registers[-num_steps].dq = self.dq(state) + self._registers[-num_steps].t = state.t if step_index < len(self._registers): # Using SSP104 for previous step values state.q = self.ssp104(state) - self._registers[-num_steps+step_index].q = state.q.copy() - self._registers[-num_steps+step_index].dq = self.dq(state) - step_index += 1 + else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step - state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self._registers[-1].dq + state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.deltaq[-1] for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self._registers[i].dq - self._registers[i].q = self._registers[i+1].q.copy() - self._registers[i].dq = self._registers[i+1].dq.copy() - # Store current solution and function evaluation - self._registers[-1].q = state.q.copy() - self._registers[-1].dq = self.dq(state) + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.deltaq[i] else: raise Exception('Unrecognized time integrator') return False # store function evaluation in case we reject step - self.dq_backup = self.deltaq + self.dq_backup = self.deltaq[-1] + # call again and save self.dq(state) to update CFL number - self.deltaq = self.dq(state) + if self.time_integrator == 'LMM': + self.deltaq.append(self.dq(state)) + else: + self.deltaq[-1] = self.dq(state) def ssp104(self,state): @@ -414,7 +411,7 @@ def ssp104(self,state): s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) - s1.q = state.q + self.deltaq/6. + s1.q = state.q + self.deltaq[-1]/6. s1.t = state.t + self.dt/6. for i in xrange(4): @@ -550,7 +547,8 @@ def accept_reject_step(self,state): cfl = self.cfl.get_cached_max() # Check cfl condition for SSP LMM methods - if self.time_integrator[:6] == 'SSPLMM': + #if self.time_integrator[:6] == 'SSPLMM': + if 'LMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 # Here we actually need to check cfl violation only for the starting methods of SSPLMM32 @@ -560,7 +558,7 @@ def accept_reject_step(self,state): if step_index < len(self._registers): if cfl > self.cfl_max: accept_step = False - self.deltaq = self.dq_backup + self.deltaq[-1] = self.dq_backup # Additional condition for SSPLMM43 if self.time_integrator == 'SSPLMM43': # the above condition is equivalent to self.dt > 0.6 * dtFE (up to machine precision), @@ -568,14 +566,14 @@ def accept_reject_step(self,state): # of the current solution. if cfl > 0.6 * self.cfl_max / self.sspcoeff0: accept_step = False - self.deltaq = self.dq_backup + self.deltaq[-1] = self.dq_backup # Check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': if step_index == 4: if cfl > 0.6 * self.cfl_max / self.sspcoeff0: accept_step = False - self.deltaq = self.dq_backup + self.deltaq[-1] = self.dq_backup else: # In principle we only need to check the ratio of FE step-sizes after the second LMM # is applied @@ -584,23 +582,24 @@ def accept_reject_step(self,state): dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False - self.deltaq = self.dq_backup + self.deltaq[-1] = self.dq_backup # Update prev_dt_values, prev_dtFE_values if accept_step: - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl - - if step_index == 1: - # Here we use dtFE(u1) for dtFE(u0) since max wave speed is not returned by self.dq - self.prev_dtFE_values.append(dtFE) - if step_index < len(self._registers): - self.prev_dt_values.append(self.dt) - self.prev_dtFE_values.append(dtFE) - else: - self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] - self.prev_dt_values[-1] = self.dt - self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] - self.prev_dtFE_values[-1] = dtFE + if self.time_integrator[:6] == 'SSPLMM': + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl + + if step_index == 1: + # Here we use dtFE(u1) for dtFE(u0) since max wave speed is not returned by self.dq + self.prev_dtFE_values.append(dtFE) + if step_index < len(self._registers): + self.prev_dt_values.append(self.dt) + self.prev_dtFE_values.append(dtFE) + else: + self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] + self.prev_dt_values[-1] = self.dt + self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] + self.prev_dtFE_values[-1] = dtFE # Update stored information self._registers = self._registers[1:] + self._registers[:1] @@ -611,7 +610,7 @@ def accept_reject_step(self,state): else: if cfl > self.cfl_max: accept_step = False - self.deltaq = self.dq_backup + self.deltaq[-1] = self.dq_backup else: # Update prev_dt_values self.prev_dt_values[-1] = self.dt @@ -656,6 +655,10 @@ def get_dt_new(self,cfl,accept_step): rhoFE = 0.9 A = self.prev_dtFE_values[-2] * self.sspcoeff0 * cfl / self.cfl_max self.dt = A/2 * (1 + rhoFE**2) / rhoFE + else: + # Note that steps for SSPLMM32 are always accepted when LMM is active + if step_index < len(self._registers): + self.dt = self.dt * self.cfl_desired / cfl else: # Step-size update for Runge-Kutta methods self.dt = self.dt * self.cfl_desired / cfl From e0217dd739d4b6f8d2bb36be3e6631103529da45 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 17 Feb 2015 09:35:09 +0300 Subject: [PATCH 27/46] Use previous function evaluations for SSPLMM43. --- src/pyclaw/sharpclaw/solver.py | 24 ++++++++++++++++-------- 1 file changed, 16 insertions(+), 8 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index de68ddafc..5a4933084 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -281,9 +281,9 @@ def step(self,solution): if not self.prev_dt_values: # Compute function evaluation for initial condition - self.deltaq.append(self.dq(state)) + self.deltaq.append(self.dq(state)/self.dt) self.prev_dt_values.append(self.dt) - self.deltaq[-1] = (self.dt/self.prev_dt_values[-1]) * self.deltaq[-1] + self.deltaq[-1] = self.dt * self.deltaq[-1] if self.time_integrator == 'Euler': state.q += self.deltaq[-1] @@ -367,8 +367,9 @@ def step(self,solution): beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 + self.deltaq[-4] = self.dt * self.deltaq[-4] state.q = beta3*(r*state.q + self.deltaq[-1]) + \ - (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dq(self._registers[-4]) + (r*beta0 + delta0)*self._registers[-4].q + beta0*self.deltaq[-4] elif self.time_integrator == 'LMM': num_steps = len(self._registers) @@ -384,20 +385,26 @@ def step(self,solution): # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.deltaq[-1] for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.deltaq[i] + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dq(self._registers[i]) else: raise Exception('Unrecognized time integrator') return False # store function evaluation in case we reject step - self.dq_backup = self.deltaq[-1] + self.dq_backup = self.deltaq[-1] / self.dt # call again and save self.dq(state) to update CFL number - if self.time_integrator == 'LMM': - self.deltaq.append(self.dq(state)) + deltaq = self.dq(state) / self.dt + if self.time_integrator in ['LMM','SSPLMM43']: + self.deltaq[-1] = self.deltaq[-1]/self.dt + if step_index < len(self._registers): + self.deltaq.append(deltaq) + else: + self.deltaq = self.deltaq[1:] + self.deltaq[:1] + self.deltaq[-1] = deltaq else: - self.deltaq[-1] = self.dq(state) + self.deltaq[-1] = deltaq def ssp104(self,state): @@ -961,3 +968,4 @@ def dq_hyperbolic(self,state): self.cfl.update_global_max(cfl) return dq[:,num_ghost:-num_ghost,num_ghost:-num_ghost,num_ghost:-num_ghost] + From 336c3054b732d4352067688ea79c78f86b3adfb0 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 17 Feb 2015 09:37:58 +0300 Subject: [PATCH 28/46] Update nosetests based on recent changes in sharpclaw solvers - Acoustics 2D test uses SSPLMM32 with TVD instead of WENO --- .../test_acoustics.py | 2 +- .../acoustics_2d_homogeneous/acoustics_2d.py | 3 +- .../verify_sharpclaw_lmm.txt | 200 +-- examples/advection_1d/test_advection.py | 2 +- .../euler_1d/blast_regression_density.txt | 1600 ++++++++--------- 5 files changed, 903 insertions(+), 904 deletions(-) diff --git a/examples/acoustics_1d_homogeneous/test_acoustics.py b/examples/acoustics_1d_homogeneous/test_acoustics.py index 515044e55..f029d7dfc 100644 --- a/examples/acoustics_1d_homogeneous/test_acoustics.py +++ b/examples/acoustics_1d_homogeneous/test_acoustics.py @@ -40,7 +40,7 @@ def acoustics_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSP104', disable_output=True) - sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00125), + sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00166), kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSPLMM32', disable_output=True) diff --git a/examples/acoustics_2d_homogeneous/acoustics_2d.py b/examples/acoustics_2d_homogeneous/acoustics_2d.py index 6124c2a12..6c62b3deb 100755 --- a/examples/acoustics_2d_homogeneous/acoustics_2d.py +++ b/examples/acoustics_2d_homogeneous/acoustics_2d.py @@ -44,7 +44,7 @@ def setup(kernel_language='Fortran', use_petsc=False, outdir='./_output', solver.cfl_max = 0.5 solver.cfl_desired = 0.45 elif solver.time_integrator=='SSPLMM32': - solver.lim_type = 1 + solver.lim_type = 2 solver.cfl_max = 0.25 solver.cfl_desired = 0.24 else: @@ -150,6 +150,5 @@ def p_vs_r(current_data): if __name__=="__main__": - import sys from clawpack.pyclaw.util import run_app_from_main output = run_app_from_main(setup,setplot) diff --git a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt index e21bc0b6b..39b558dc6 100644 --- a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt +++ b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt @@ -1,100 +1,100 @@ -4.989214244507313376e-23 3.749324463228975697e-22 2.641181631649043108e-21 1.788037464258129632e-20 1.161838501950332184e-19 7.243591855625602781e-19 4.330836462578562569e-18 2.481694480519271039e-17 1.362115288811106984e-16 7.156169910920267875e-16 3.596199380655386088e-15 1.727359562442570659e-14 7.924349225995467299e-14 3.469298013924174020e-13 1.448321427843021428e-12 5.760756208830964073e-12 2.181396555981922523e-11 7.857611419654283832e-11 2.690463109359323419e-10 8.750919617706542048e-10 2.702225878939702452e-09 7.918384677778804028e-09 2.201266609849158098e-08 5.804788470488567879e-08 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-2.199156188928219948e-20 2.690400147624443818e-22 6.610152472453585664e-21 -2.342415649306862910e-22 -1.724507979536286259e-21 2.409891589778236061e-22 4.228485849792105709e-22 -1.231709567978526642e-22 -8.741109985837001030e-23 4.717500664120173618e-23 1.204973755502309870e-23 -1.394455755268542653e-23 -2.230222909498108467e-25 diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 98e92184f..17e91b818 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,7 +32,7 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(1.8937e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(7.9710e-05), kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) diff --git a/examples/euler_1d/blast_regression_density.txt b/examples/euler_1d/blast_regression_density.txt index 27018e2d3..d64997800 100644 --- a/examples/euler_1d/blast_regression_density.txt +++ b/examples/euler_1d/blast_regression_density.txt @@ -1,800 +1,800 @@ -1.495599251108720718e-01 -1.495613205947541602e-01 -1.495641126761789730e-01 -1.495682970129727229e-01 -1.495738673266018004e-01 -1.495808156473809325e-01 -1.495891325935836402e-01 -1.495988076520975985e-01 -1.496098294322256717e-01 -1.496221858708392527e-01 -1.496358643771089070e-01 -1.496508519171605989e-01 -1.496671350509315435e-01 -1.496846999431870606e-01 -1.497035323763298287e-01 -1.497236177931938750e-01 -1.497449413931533635e-01 -1.497674882952657327e-01 -1.497912437692239807e-01 -1.498161935206760442e-01 -1.498423240042938698e-01 -1.498696227289747218e-01 -1.498980785106435731e-01 -1.499276816348221186e-01 -1.499584239020810283e-01 -1.499902985267560218e-01 -1.500232998946743890e-01 -1.500574231941473324e-01 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+3.086004231651852114e-01 +3.086046990369701870e-01 +3.086087675218661119e-01 +3.086126237129939165e-01 +3.086162646758399686e-01 +3.086196896791401634e-01 +3.086229004528552311e-01 +3.086259015983618959e-01 +3.086287005727301191e-01 +3.086313076866371574e-01 +3.086337358191126867e-01 +3.086360000886922972e-01 +3.086381174854216369e-01 +3.086401064597718014e-01 +3.086419864297847981e-01 +3.086437772514447064e-01 +3.086454985459993750e-01 +3.086471688240181033e-01 +3.086488045900697141e-01 +3.086504192114044587e-01 +3.086520219211170701e-01 +3.086536176407836951e-01 +3.086552165991310881e-01 +3.086568077946386102e-01 +3.086583667756976901e-01 +3.086598771889504933e-01 +3.086613239606653680e-01 +3.086626945168130520e-01 +3.086639794124315661e-01 +3.086651725598477114e-01 +3.086662710685328381e-01 +3.086672748491063323e-01 +3.086681860991572490e-01 +3.086690086498038443e-01 +3.086697475031713322e-01 +3.086704082326794940e-01 +3.086709967263625565e-01 +3.086715187749987654e-01 +3.086719800948387604e-01 +3.086723860151905363e-01 +3.086727415022776921e-01 +3.086730511116794196e-01 +3.086733190800330928e-01 +3.086735491782847673e-01 +3.086737448043029852e-01 +3.086739091204928620e-01 +3.086740451785285333e-01 +3.086741556992388391e-01 +3.086742428221811441e-01 +3.086743089278023433e-01 +3.086743551010185382e-01 +3.086743819723207771e-01 From ef63f5a13c8c8d677a5ef20ac2fff3f00f40ec7a Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Tue, 17 Feb 2015 10:40:10 +0300 Subject: [PATCH 29/46] Change deltaq to dq_dt in sharpclaw solvers. --- src/pyclaw/sharpclaw/solver.py | 59 ++++++++++++++++------------------ 1 file changed, 28 insertions(+), 31 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 5a4933084..98c5ecb53 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -183,8 +183,8 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None - self.deltaq = [] - self.dq_backup = None + self.dq_dt = [] + self.dq_dt_backup = None self.prev_dt_values = [] self.call_before_step_each_stage = False self._mthlim = self.limiters @@ -279,17 +279,16 @@ def step(self,solution): self.before_step(self,state) - if not self.prev_dt_values: + if self.prev_dt_values == []: # Compute function evaluation for initial condition - self.deltaq.append(self.dq(state)/self.dt) + self.dq_dt.append(self.dq(state)/self.dt) self.prev_dt_values.append(self.dt) - self.deltaq[-1] = self.dt * self.deltaq[-1] if self.time_integrator == 'Euler': - state.q += self.deltaq[-1] + state.q += self.dt * self.dq_dt[-1] elif self.time_integrator == 'SSP33': - self._registers[0].q = state.q + self.deltaq[-1] + self._registers[0].q = state.q + self.dt * self.dq_dt[-1] self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -326,7 +325,7 @@ def step(self,solution): self._registers[-1].t = state.t if step_index < 3: # Use Euler method for starting values - state.q += self.deltaq[-1] + state.q += self.dt * self.dq_dt[-1] else: if step_index == 3: self.sspcoeff0 = self._sspcoeff[self.time_integrator] @@ -338,7 +337,7 @@ def step(self,solution): delta = 1./omega2**2 beta = (omega2+1.)/omega2 - state.q = beta*(r*state.q + self.deltaq[-1]) + delta*self._registers[-3].q + state.q = beta*(r*state.q + self.dt*self.dq_dt[-1]) + delta*self._registers[-3].q elif self.time_integrator == 'SSPLMM43': if step_index == 1: @@ -348,7 +347,7 @@ def step(self,solution): self._registers[-1].t = state.t if step_index < 4: # Use SSP22 method for starting values - self._registers[0].q = state.q + self.deltaq[-1] + self._registers[0].q = state.q + self.dt*self.dq_dt[-1] self._registers[0].t = state.t + self.dt state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: @@ -367,9 +366,8 @@ def step(self,solution): beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - self.deltaq[-4] = self.dt * self.deltaq[-4] - state.q = beta3*(r*state.q + self.deltaq[-1]) + \ - (r*beta0 + delta0)*self._registers[-4].q + beta0*self.deltaq[-4] + state.q = beta3*(r*state.q + self.dt*self.dq_dt[-1]) + \ + (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dt*self.dq_dt[-4] elif self.time_integrator == 'LMM': num_steps = len(self._registers) @@ -383,28 +381,27 @@ def step(self,solution): else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step - state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.deltaq[-1] + state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*self.dq_dt[-1] for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dq(self._registers[i]) + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*self.dq(self._registers[i]) else: raise Exception('Unrecognized time integrator') return False # store function evaluation in case we reject step - self.dq_backup = self.deltaq[-1] / self.dt + self.dq_dt_backup = self.dq_dt[-1] # call again and save self.dq(state) to update CFL number - deltaq = self.dq(state) / self.dt + dq_dt = self.dq(state) / self.dt if self.time_integrator in ['LMM','SSPLMM43']: - self.deltaq[-1] = self.deltaq[-1]/self.dt if step_index < len(self._registers): - self.deltaq.append(deltaq) + self.dq_dt.append(dq_dt) else: - self.deltaq = self.deltaq[1:] + self.deltaq[:1] - self.deltaq[-1] = deltaq + self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] + self.dq_dt[-1] = dq_dt else: - self.deltaq[-1] = deltaq + self.dq_dt[-1] = dq_dt def ssp104(self,state): @@ -418,7 +415,7 @@ def ssp104(self,state): s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) - s1.q = state.q + self.deltaq[-1]/6. + s1.q = state.q + self.dt*self.dq_dt[-1]/6. s1.t = state.t + self.dt/6. for i in xrange(4): @@ -474,12 +471,12 @@ def dqdt(self,state): """ self.dt = 1 - deltaq = self.dq_hyperbolic(state) + dq_dt = self.dq_hyperbolic(state) if self.dq_src is not None: - deltaq+=self.dq_src(self,state,self.dt) + dq_dt += self.dq_src(self,state,self.dt) - return deltaq.flatten('f') + return dq_dt.flatten('f') def _set_fortran_parameters(self,state,clawparams,workspace,reconstruct): @@ -565,7 +562,7 @@ def accept_reject_step(self,state): if step_index < len(self._registers): if cfl > self.cfl_max: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup # Additional condition for SSPLMM43 if self.time_integrator == 'SSPLMM43': # the above condition is equivalent to self.dt > 0.6 * dtFE (up to machine precision), @@ -573,14 +570,14 @@ def accept_reject_step(self,state): # of the current solution. if cfl > 0.6 * self.cfl_max / self.sspcoeff0: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup # Check conditions for SSPLMM43 for the steps LMM is active elif self.time_integrator == 'SSPLMM43': if step_index == 4: if cfl > 0.6 * self.cfl_max / self.sspcoeff0: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup else: # In principle we only need to check the ratio of FE step-sizes after the second LMM # is applied @@ -589,7 +586,7 @@ def accept_reject_step(self,state): dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup # Update prev_dt_values, prev_dtFE_values if accept_step: @@ -617,7 +614,7 @@ def accept_reject_step(self,state): else: if cfl > self.cfl_max: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup else: # Update prev_dt_values self.prev_dt_values[-1] = self.dt From 2a72e9a207744f0c2f7fbed3daed02ce50a4e15d Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Mon, 23 Feb 2015 10:09:24 +0300 Subject: [PATCH 30/46] Correct step-size choice for starting methods of LMMs. Also: - General LMM now uses previously saved function evaluations - rename self.deltaq to self.dq_dt - update accept_reject_step and get_dt_new --- src/pyclaw/sharpclaw/solver.py | 175 ++++++++++++++++----------------- 1 file changed, 83 insertions(+), 92 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 5a4933084..9530df91e 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -183,7 +183,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None - self.deltaq = [] + self.dq_dt = [] self.dq_backup = None self.prev_dt_values = [] self.call_before_step_each_stage = False @@ -279,17 +279,20 @@ def step(self,solution): self.before_step(self,state) - if not self.prev_dt_values: + if self.prev_dt_values == []: # Compute function evaluation for initial condition - self.deltaq.append(self.dq(state)/self.dt) + self.dq_dt.append(self.dq(state)/self.dt) self.prev_dt_values.append(self.dt) - self.deltaq[-1] = self.dt * self.deltaq[-1] + if self.time_integrator in ['SSPLMM32','SSPLMM43']: + # Compute forward Euler step-size for initial condition + dtFE = self.dt / self.cfl.get_cached_max() * self.cfl_max / self._sspcoeff[self.time_integrator] + self.prev_dtFE_values.append(dtFE) if self.time_integrator == 'Euler': - state.q += self.deltaq[-1] + state.q += self.dt*self.dq_dt[-1] elif self.time_integrator == 'SSP33': - self._registers[0].q = state.q + self.deltaq[-1] + self._registers[0].q = state.q + self.dt*self.dq_dt[-1] self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -321,12 +324,12 @@ def step(self,solution): elif self.time_integrator == 'SSPLMM32': if step_index == 1: self.sspcoeff0 = self._sspcoeff['Euler'] - # Save initial solution + # Save initial condition self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t if step_index < 3: # Use Euler method for starting values - state.q += self.deltaq[-1] + state.q += self.dt*self.dq_dt[-1] else: if step_index == 3: self.sspcoeff0 = self._sspcoeff[self.time_integrator] @@ -338,23 +341,23 @@ def step(self,solution): delta = 1./omega2**2 beta = (omega2+1.)/omega2 - state.q = beta*(r*state.q + self.deltaq[-1]) + delta*self._registers[-3].q + state.q = beta*(r*state.q + self.dt*self.dq_dt[-1]) + delta*self._registers[-3].q elif self.time_integrator == 'SSPLMM43': if step_index == 1: self.sspcoeff0 = self._sspcoeff['SSP22'] - # Store initial solution + # Store initial condition self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t if step_index < 4: # Use SSP22 method for starting values - self._registers[0].q = state.q + self.deltaq[-1] + self._registers[0].q = state.q + self.dt*self.dq_dt[-1] self._registers[0].t = state.t + self.dt + + if self.call_before_step_each_stage: + self.before_step(self,self._registers[0]) state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: - # This part can be impoved by saving function evaluations of previous solutions in a list - # Thus self.dq(self._registers[-4] wont be calculated at the current step, but use already - # saved values. if step_index == 4: self.sspcoeff0 = self._sspcoeff[self.time_integrator] @@ -367,9 +370,8 @@ def step(self,solution): beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - self.deltaq[-4] = self.dt * self.deltaq[-4] - state.q = beta3*(r*state.q + self.deltaq[-1]) + \ - (r*beta0 + delta0)*self._registers[-4].q + beta0*self.deltaq[-4] + state.q = beta3*(r*state.q + self.dt*self.dq_dt[-1]) + \ + (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dt*self.dq_dt[-4] elif self.time_integrator == 'LMM': num_steps = len(self._registers) @@ -380,31 +382,32 @@ def step(self,solution): if step_index < len(self._registers): # Using SSP104 for previous step values state.q = self.ssp104(state) - else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step - state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.deltaq[-1] + state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*self.dq_dt[-1] for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dq(self._registers[i]) + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*self.dq_dt[i] else: raise Exception('Unrecognized time integrator') return False # store function evaluation in case we reject step - self.dq_backup = self.deltaq[-1] / self.dt + self.dq_backup = self.dq_dt[-1] # call again and save self.dq(state) to update CFL number - deltaq = self.dq(state) / self.dt + state.t += self.dt + self.before_step(self,state) + state.t -= self.dt + dq_dt = self.dq(state) / self.dt if self.time_integrator in ['LMM','SSPLMM43']: - self.deltaq[-1] = self.deltaq[-1]/self.dt if step_index < len(self._registers): - self.deltaq.append(deltaq) + self.dq_dt.append(dq_dt) else: - self.deltaq = self.deltaq[1:] + self.deltaq[:1] - self.deltaq[-1] = deltaq + self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] + self.dq_dt[-1] = dq_dt else: - self.deltaq[-1] = deltaq + self.dq_dt[-1] = dq_dt def ssp104(self,state): @@ -418,7 +421,7 @@ def ssp104(self,state): s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) - s1.q = state.q + self.deltaq[-1]/6. + s1.q = state.q + self.dt*self.dq_dt[-1]/6. s1.t = state.t + self.dt/6. for i in xrange(4): @@ -546,70 +549,65 @@ def accept_reject_step(self,state): r""" Decide whether to accept or not the current step. For Runge-Kutta methods the step is accepted if cfl <= cfl_max. - For SSPLMM32 the choice of step-size guarantees the cfl condition is satisfied. - For SSPLMM43 additional checks on the cfl number and ratio of forward Euler step-sizes are required. + For SSPLMM32 the choice of step-size guarantees the cfl condition is satisfied for the steps the LMM + is used. Hence, we need to check the cfl condition only for the starting steps. + Note that for SSPLMM43 a special condition applies for the starting methodss and in addition a condition + on the ratio of forward Euler step-sizes is required when the LMM is used. """ accept_step = True cfl = self.cfl.get_cached_max() # Check cfl condition for SSP LMM methods - #if self.time_integrator[:6] == 'SSPLMM': if 'LMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 - # Here we actually need to check cfl violation only for the starting methods of SSPLMM32 - # Step-size choice for SSPLMM43 guarantees that the above condition are always fulfilled. - # Condition for starting RK methods if step_index < len(self._registers): - if cfl > self.cfl_max: + if self.time_integrator == 'LMM': + sspcoeff_ratio = 1. + else: + sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] + + if cfl > sspcoeff_ratio * self.cfl_max: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_backup # Additional condition for SSPLMM43 if self.time_integrator == 'SSPLMM43': - # the above condition is equivalent to self.dt > 0.6 * dtFE (up to machine precision), - # where dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl is the FE step-size - # of the current solution. - if cfl > 0.6 * self.cfl_max / self.sspcoeff0: + # The condition below is equivalent to self.dt > 0.6 * dtFE (up to machine precision), + # where dtFE = (self.dt / cfl) * (self.cfl_max / self._sspcoeff[self.time_integrator]) + # is the forward Euler step-size of the current solution. + if cfl > 0.6 * self.cfl_max / self._sspcoeff[self.time_integrator]: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_backup - # Check conditions for SSPLMM43 for the steps LMM is active + # Check conditions for SSPLMM43 when the LMM is used elif self.time_integrator == 'SSPLMM43': - if step_index == 4: - if cfl > 0.6 * self.cfl_max / self.sspcoeff0: - accept_step = False - self.deltaq[-1] = self.dq_backup - else: - # In principle we only need to check the ratio of FE step-sizes after the second LMM - # is applied - rhoFE = 0.9 - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl - dtFEm1 = self.prev_dtFE_values[-1] - if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - accept_step = False - self.deltaq[-1] = self.dq_backup + rhoFE = 0.9 + dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl + dtFEm1 = self.prev_dtFE_values[-1] + if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: + accept_step = False + self.dq_dt[-1] = self.dq_backup - # Update prev_dt_values, prev_dtFE_values if accept_step: - if self.time_integrator[:6] == 'SSPLMM': - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl + if 'SSPLMM' in self.time_integrator: + # Compute current forward Euler step-size + dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - if step_index == 1: - # Here we use dtFE(u1) for dtFE(u0) since max wave speed is not returned by self.dq - self.prev_dtFE_values.append(dtFE) if step_index < len(self._registers): + # Save dt and dtFE self.prev_dt_values.append(self.dt) self.prev_dtFE_values.append(dtFE) else: + # Update prev_dt_values, prev_dtFE_values self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] self.prev_dt_values[-1] = self.dt self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] self.prev_dtFE_values[-1] = dtFE - - # Update stored information - self._registers = self._registers[1:] + self._registers[:1] + + # Update saved soluton + self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t @@ -617,7 +615,7 @@ def accept_reject_step(self,state): else: if cfl > self.cfl_max: accept_step = False - self.deltaq[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_backup else: # Update prev_dt_values self.prev_dt_values[-1] = self.dt @@ -628,46 +626,39 @@ def accept_reject_step(self,state): def get_dt_new(self,cfl,accept_step): r""" Set time-step for next step depending on the time integrator and whether or not the step is accepted. - Currently, a new step-size is chosen if a step is rejected, although this is not neccesary since the - step-size control guarantees that steps are always accepted. - Essentially we only need to pick a new step-size if the dtFE ratio condition for SSPLMM43 is violated. + Note that for SSPLMM the step-size choice guarantees that no LMM steps are rejected, hence we need to + pick a new step-size only when SSPLMM43 is used and the step is rejected. """ - if self.time_integrator[:6] == 'SSPLMM': - # Step-size update for SSP LMM methods + + if 'SSPLMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 - if accept_step: - if self.time_integrator == 'SSPLMM43' and step_index <= len(self._registers): - # Step-size for SSPLMM43 when first LMM is applied - # We can replace self.cfl_desired with self.cfl_max to choose the maximum allowed step-size - self.dt = 0.6 * self.dt * self.cfl_desired / (self.sspcoeff0 * cfl) - elif step_index < len(self._registers): - # Step-size update of starting methods for SSPLMM32 - self.dt = self.dt * self.cfl_desired / cfl + if step_index < len(self._registers): + # Step-size update of starting methods + sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] + dt = sspcoeff_ratio * self.dt * self.cfl_desired / cfl + if self.time_integrator == 'SSPLMM43': + dt2 = 0.6 * self.dt / cfl * self.cfl_desired / self._sspcoeff[self.time_integrator] + self.dt = min(dt,dt2) else: + self.dt = dt + else: + # Step-size update for the steps LMM is used + if accept_step: s = len(self._registers) p = int(self.time_integrator[-1]) mu = min([self.prev_dtFE_values[i] for i in range(s)]) H = sum(self.prev_dt_values[1:]) self.dt = H * mu / (H + (p-1)*mu) - else: - # Pick new step-size for SSPLMM43 if current step is rejected - if self.time_integrator == 'SSPLMM43': - if step_index <= len(self._registers): - dt1 = 0.6 * self.dt * self.cfl_desired / (self.sspcoeff0 * cfl) - dt2 = self.dt * self.cfl_desired - self.dt = min(dt1,dt2) - else: - # Choose step-size in order to satisfy the dtFE ratio condition if violated + else: + if self.time_integrator == 'SSPLMM43': + # Choose a new step-size if the dtFE ratio condition is violated rhoFE = 0.9 A = self.prev_dtFE_values[-2] * self.sspcoeff0 * cfl / self.cfl_max self.dt = A/2 * (1 + rhoFE**2) / rhoFE - else: - # Note that steps for SSPLMM32 are always accepted when LMM is active - if step_index < len(self._registers): - self.dt = self.dt * self.cfl_desired / cfl + + # Step-size update for RK methods else: - # Step-size update for Runge-Kutta methods self.dt = self.dt * self.cfl_desired / cfl return self.dt From 96223d5fb49d884c0c1d6fe2fdda0838afdd8192 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Mon, 23 Feb 2015 10:20:19 +0300 Subject: [PATCH 31/46] Update nosetests. --- .../test_acoustics.py | 2 +- .../verify_sharpclaw_lmm.txt | 200 +++++++++--------- examples/advection_1d/test_advection.py | 2 +- 3 files changed, 102 insertions(+), 102 deletions(-) diff --git a/examples/acoustics_1d_homogeneous/test_acoustics.py b/examples/acoustics_1d_homogeneous/test_acoustics.py index f029d7dfc..bd0c2597f 100644 --- a/examples/acoustics_1d_homogeneous/test_acoustics.py +++ b/examples/acoustics_1d_homogeneous/test_acoustics.py @@ -40,7 +40,7 @@ def acoustics_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSP104', disable_output=True) - sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00166), + sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00184), kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSPLMM32', disable_output=True) diff --git a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt index 39b558dc6..4f4f32757 100644 --- a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt +++ b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt @@ -1,100 +1,100 @@ --2.230222862004763117e-25 -1.394455751696799836e-23 1.204973754446624842e-23 4.717500653215334106e-23 -8.741109986157082264e-23 -1.231709565047586174e-22 4.228485851208959143e-22 2.409891583315352604e-22 -1.724507980255125693e-21 -2.342415640457025796e-22 6.610152474589923454e-21 2.690400151562377635e-22 -2.199156189237049736e-20 2.403410878536572691e-20 5.703143411121737781e-19 5.439788377029119178e-18 4.880984213710277269e-17 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-4.354150027532758615e-21 6.724230733932839388e-21 9.042154636123180133e-22 -1.807513117491765033e-21 2.187168723676680902e-24 4.686186709848661191e-22 -8.551353321533724764e-23 -9.984687796790488292e-23 4.373648736777036670e-23 1.368179251462758439e-23 -1.419662845448389707e-23 6.370091116727923391e-25 2.982094625738199750e-24 diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 17e91b818..7e89a4671 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,7 +32,7 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(7.9710e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(9.224735e-05), kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) From bf3b73e080e9b42bfab1215bdf967ba82becb55f Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Tue, 24 Feb 2015 16:47:20 +0300 Subject: [PATCH 32/46] Evaluate dq at beginning of step. This avoids some messy things and ensures that the step size rejection is determined using the right CFL number. --- src/pyclaw/sharpclaw/solver.py | 115 ++++++++++++++++----------------- src/pyclaw/solver.py | 1 + 2 files changed, 57 insertions(+), 59 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 1f8c8fbb7..fdbced090 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -184,12 +184,13 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_max = None self.dq_src = None self.dq_dt = [] - self.dq_backup = None + self.dq_dt_backup = None self.prev_dt_values = [] self.call_before_step_each_stage = False self._mthlim = self.limiters self._method = None self._registers = None + self._last_step_rejected = False # Used only if time integrator is 'RK' self.a = None @@ -277,23 +278,23 @@ def step(self,solution): self.cfl.set_global_max(0.) step_index = self.status['numsteps'] + 1 - self.before_step(self,state) + self.before_step(self,state) # This should be moved up into evolve_to_time - if self.prev_dt_values == []: + dq_dt = self.dq(state) / self.dt + + if (self.prev_dt_values == []) and (self.time_integrator in ['SSPLMM32','SSPLMM43']): # Compute function evaluation for initial condition - self.dq_dt.append(self.dq(state)/self.dt) - self.prev_dt_values.append(self.dt) - - if self.time_integrator in ['SSPLMM32','SSPLMM43']: - # Compute forward Euler step-size for initial condition - dtFE = self.dt / self.cfl.get_cached_max() * self.cfl_max / self._sspcoeff[self.time_integrator] - self.prev_dtFE_values.append(dtFE) + self.dq_dt.append(dq_dt) + self.prev_dt_values.append(0.) # Not used + cfl = self.cfl.get_cached_max() + dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] + self.prev_dtFE_values.append(dtFE) if self.time_integrator == 'Euler': - state.q += self.dt*self.dq_dt[-1] + state.q += self.dt*dq_dt elif self.time_integrator == 'SSP33': - self._registers[0].q = state.q + self.dt*self.dq_dt[-1] + self._registers[0].q = state.q + self.dt * dq_dt self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -306,7 +307,7 @@ def step(self,solution): state.q = 1./3.*state.q + 2./3.*(self._registers[0].q + self.dq(self._registers[0])) elif self.time_integrator == 'SSP104': - state.q = self.ssp104(state) + state.q = self.ssp104(state,dq_dt) elif self.time_integrator == 'RK': # General RK with specified coefficients @@ -324,16 +325,16 @@ def step(self,solution): elif self.time_integrator == 'SSPLMM32': if step_index == 1: - self.sspcoeff0 = self._sspcoeff['Euler'] # Save initial condition self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t if step_index < 3: # Use Euler method for starting values - state.q += self.dt*self.dq_dt[-1] + self.sspcoeff0 = self._sspcoeff['Euler'] + state.q += self.dt * dq_dt else: - if step_index == 3: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + self.set_dt() omega2 = sum(self.prev_dt_values[1:])/self.dt # SSP coefficient @@ -342,25 +343,25 @@ def step(self,solution): delta = 1./omega2**2 beta = (omega2+1.)/omega2 - state.q = beta*(r*state.q + self.dt*self.dq_dt[-1]) + delta*self._registers[-3].q + state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q elif self.time_integrator == 'SSPLMM43': if step_index == 1: - self.sspcoeff0 = self._sspcoeff['SSP22'] # Store initial condition self._registers[-1].q = state.q.copy() self._registers[-1].t = state.t if step_index < 4: # Use SSP22 method for starting values - self._registers[0].q = state.q + self.dt*self.dq_dt[-1] + self.sspcoeff0 = self._sspcoeff['SSP22'] + self._registers[0].q = state.q + self.dt * dq_dt self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: self.before_step(self,self._registers[0]) state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: - if step_index == 4: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + self.set_dt() omega3 = sum(self.prev_dt_values[-3:])/self.dt omega4 = omega3 + 1. @@ -371,7 +372,7 @@ def step(self,solution): beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - state.q = beta3*(r*state.q + self.dt*self.dq_dt[-1]) + \ + state.q = beta3*(r*state.q + self.dt * dq_dt) + \ (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dt*self.dq_dt[-4] elif self.time_integrator == 'LMM': @@ -385,33 +386,27 @@ def step(self,solution): state.q = self.ssp104(state) else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step - state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*self.dq_dt[-1] + state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*dq_dt for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*self.dq_dt[i] + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*dq_dt else: raise Exception('Unrecognized time integrator') return False # store function evaluation in case we reject step - self.dq_backup = self.dq_dt[-1] + self.dq_dt_backup = dq_dt - # call again and save self.dq(state) to update CFL number - state.t += self.dt - self.before_step(self,state) - state.t -= self.dt - dq_dt = self.dq(state) / self.dt + # save dq_dt if self.time_integrator in ['LMM','SSPLMM43']: if step_index < len(self._registers): self.dq_dt.append(dq_dt) else: self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] self.dq_dt[-1] = dq_dt - else: - self.dq_dt[-1] = dq_dt - def ssp104(self,state): + def ssp104(self,state,dq_dt): if self.time_integrator == 'SSP104': s1 = self._registers[0] s2 = self._registers[1] @@ -422,7 +417,7 @@ def ssp104(self,state): s1 = copy.deepcopy(state) s2 = copy.deepcopy(s1) - s1.q = state.q + self.dt*self.dq_dt[-1]/6. + s1.q = state.q + self.dt*dq_dt/6. s1.t = state.t + self.dt/6. for i in xrange(4): @@ -572,7 +567,7 @@ def accept_reject_step(self,state): if cfl > sspcoeff_ratio * self.cfl_max: accept_step = False - self.dq_dt[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup # Additional condition for SSPLMM43 if self.time_integrator == 'SSPLMM43': # The condition below is equivalent to self.dt > 0.6 * dtFE (up to machine precision), @@ -580,7 +575,7 @@ def accept_reject_step(self,state): # is the forward Euler step-size of the current solution. if cfl > 0.6 * self.cfl_max / self._sspcoeff[self.time_integrator]: accept_step = False - self.dq_dt[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup # Check conditions for SSPLMM43 when the LMM is used elif self.time_integrator == 'SSPLMM43': @@ -589,7 +584,7 @@ def accept_reject_step(self,state): dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False - self.dq_dt[-1] = self.dq_backup + self.dq_dt[-1] = self.dq_dt_backup if accept_step: if 'SSPLMM' in self.time_integrator: @@ -616,21 +611,31 @@ def accept_reject_step(self,state): else: if cfl > self.cfl_max: accept_step = False - self.dq_dt[-1] = self.dq_backup - else: - # Update prev_dt_values - self.prev_dt_values[-1] = self.dt + + self._last_step_rejected = not accept_step return accept_step + def set_dt(self): + r"""This should only be called for SSPLMM methods.""" + if self._last_step_rejected == False: + s = len(self._registers) + p = int(self.time_integrator[-1]) + mu = min([self.prev_dtFE_values[i] for i in range(s)]) + H = sum(self.prev_dt_values[1:]) + self.dt = H * mu / (H + (p-1)*mu) + + def get_dt_new(self,cfl,accept_step): r""" - Set time-step for next step depending on the time integrator and whether or not the step is accepted. - Note that for SSPLMM the step-size choice guarantees that no LMM steps are rejected, hence we need to - pick a new step-size only when SSPLMM43 is used and the step is rejected. - """ + Set size of next step depending on the time integrator and + whether or not the current step was accepted. Note that for SSPLMM32 the + step-size choice guarantees that no steps are rejected. + For SSPLMM methods, this routine does not change the step size unless + the step has been rejected. + """ if 'SSPLMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 @@ -644,19 +649,11 @@ def get_dt_new(self,cfl,accept_step): else: self.dt = dt else: - # Step-size update for the steps LMM is used - if accept_step: - s = len(self._registers) - p = int(self.time_integrator[-1]) - mu = min([self.prev_dtFE_values[i] for i in range(s)]) - H = sum(self.prev_dt_values[1:]) - self.dt = H * mu / (H + (p-1)*mu) - else: - if self.time_integrator == 'SSPLMM43': - # Choose a new step-size if the dtFE ratio condition is violated - rhoFE = 0.9 - A = self.prev_dtFE_values[-2] * self.sspcoeff0 * cfl / self.cfl_max - self.dt = A/2 * (1 + rhoFE**2) / rhoFE + if (self.time_integrator == 'SSPLMM43') and (not accept_step): + # Choose a new step-size if the dtFE ratio condition is violated + rhoFE = 0.9 + A = self.prev_dtFE_values[-2] * self.sspcoeff0 * cfl / self.cfl_max + self.dt = A/2 * (1 + rhoFE**2) / rhoFE # Step-size update for RK methods else: diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 1294c39eb..c3f28a241 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -574,6 +574,7 @@ def evolve_to_time(self,solution,tend=None): q_backup = state.q.copy('F') told = solution.t + # Note that the solver may alter dt during the step() routine self.step(solution) # Check to make sure that the Courant number was not too large From 683061e7dd0f5cf32b8507461d16531c9ff326fc Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Tue, 24 Feb 2015 17:27:46 +0300 Subject: [PATCH 33/46] Prevent LMM integrators from going past tend. --- examples/advection_1d/test_advection.py | 2 +- src/pyclaw/classic/solver.py | 2 +- src/pyclaw/sharpclaw/solver.py | 17 ++++++++++------- src/pyclaw/solver.py | 2 +- 4 files changed, 13 insertions(+), 10 deletions(-) diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 7e89a4671..085cae5a9 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,7 +32,7 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(9.224735e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(9.130139e-05), kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) diff --git a/src/pyclaw/classic/solver.py b/src/pyclaw/classic/solver.py index 48246cef0..a56ba773c 100644 --- a/src/pyclaw/classic/solver.py +++ b/src/pyclaw/classic/solver.py @@ -99,7 +99,7 @@ def __init__(self,riemann_solver=None,claw_package=None): super(ClawSolver,self).__init__(riemann_solver,claw_package) # ========== Time stepping routines ====================================== - def step(self,solution): + def step(self,solution,tmax): r""" Evolve solution one time step diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index fdbced090..62c330094 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -190,7 +190,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self._mthlim = self.limiters self._method = None self._registers = None - self._last_step_rejected = False + self._keep_this_dt = False # Used only if time integrator is 'RK' self.a = None @@ -268,7 +268,7 @@ def __del__(self): # ========== Time stepping routines ====================================== - def step(self,solution): + def step(self,solution,tmax): """Evolve q over one time step. Take one step with a Runge-Kutta or multistep method as specified by @@ -334,7 +334,7 @@ def step(self,solution): state.q += self.dt * dq_dt else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt() + self.set_dt(state.t,tmax) omega2 = sum(self.prev_dt_values[1:])/self.dt # SSP coefficient @@ -361,7 +361,7 @@ def step(self,solution): state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt() + self.set_dt(state.t,tmax) omega3 = sum(self.prev_dt_values[-3:])/self.dt omega4 = omega3 + 1. @@ -612,20 +612,23 @@ def accept_reject_step(self,state): if cfl > self.cfl_max: accept_step = False - self._last_step_rejected = not accept_step + self._keep_this_dt = not accept_step return accept_step - def set_dt(self): + def set_dt(self,t,tmax): r"""This should only be called for SSPLMM methods.""" - if self._last_step_rejected == False: + if self._keep_this_dt == False: s = len(self._registers) p = int(self.time_integrator[-1]) mu = min([self.prev_dtFE_values[i] for i in range(s)]) H = sum(self.prev_dt_values[1:]) self.dt = H * mu / (H + (p-1)*mu) + # Adjust dt so that we hit tmax exactly if we are near tmax + if t + self.dt > tmax: + self.dt = tmax - t def get_dt_new(self,cfl,accept_step): r""" diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index c3f28a241..b741f9f8a 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -575,7 +575,7 @@ def evolve_to_time(self,solution,tend=None): told = solution.t # Note that the solver may alter dt during the step() routine - self.step(solution) + self.step(solution,tend) # Check to make sure that the Courant number was not too large accept_step = self.accept_reject_step(state) From 215169195051c462c5028bd9eb2bd659af78b598 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Sun, 8 Mar 2015 09:23:24 +0300 Subject: [PATCH 34/46] Correct dtFE computation for SSPLMM Also: - Add SSPLMM53 - Edit documentation --- src/pyclaw/sharpclaw/solver.py | 171 ++++++++++++++++++++------------- src/pyclaw/solver.py | 12 +-- 2 files changed, 112 insertions(+), 71 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 62c330094..54af45a90 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -282,19 +282,31 @@ def step(self,solution,tmax): dq_dt = self.dq(state) / self.dt - if (self.prev_dt_values == []) and (self.time_integrator in ['SSPLMM32','SSPLMM43']): - # Compute function evaluation for initial condition - self.dq_dt.append(dq_dt) - self.prev_dt_values.append(0.) # Not used + if 'SSPLMM' in self.time_integrator: + # Compute current forward Euler step-size (dtFE) cfl = self.cfl.get_cached_max() dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - self.prev_dtFE_values.append(dtFE) + if self.prev_dt_values == []: + # Save function evaluation of initial condition + self.dq_dt.append(dq_dt) + self.prev_dt_values.append(0.) # Not used + self.prev_dtFE_values.append(dtFE) + elif self.accept_step is True: + if step_index <= len(self._registers): + # Save dtFE + self.prev_dtFE_values.append(dtFE) + else: + # Update prev_dtFE_values + self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] + self.prev_dtFE_values[-1] = dtFE + + ### Runge-Kutta methods ### if self.time_integrator == 'Euler': state.q += self.dt*dq_dt elif self.time_integrator == 'SSP33': - self._registers[0].q = state.q + self.dt * dq_dt + self._registers[0].q = state.q + self.dt*dq_dt self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -310,28 +322,37 @@ def step(self,solution,tmax): state.q = self.ssp104(state,dq_dt) elif self.time_integrator == 'RK': - # General RK with specified coefficients - # self._registers[i].q actually stores dt*f(y_i) + # General explicit RK with specified coefficients + + # Save function evaluation of current state + self._registers[0].q = self.dt*dq_dt + self._registers[0].t = state.t + + # Loop over the stages num_stages = len(self.b) - for i in range(num_stages): - self._registers[i].q = state.q.copy() + for i in range(1,num_stages): + self._registers[i].q = state.q + #self._registers[i].q = state.q.copy() for j in range(i): self._registers[i].q += self.a[i,j]*self._registers[j].q - self._registers[i].t = state.t + self.dt * self.c[i] + self._registers[i].t = state.t + self.dt*self.c[i] + + # self._registers[i].q eventually stores dt*f(y_i) after stage solution y_i is computed self._registers[i].q = self.dq(self._registers[i]) + # Update solution for j in range(num_stages): state.q += self.b[j]*self._registers[j].q + ### Linear multistep methods ### elif self.time_integrator == 'SSPLMM32': if step_index == 1: - # Save initial condition - self._registers[-1].q = state.q.copy() - self._registers[-1].t = state.t + # Store initial condition + self.save_init_sol(state) if step_index < 3: # Use Euler method for starting values self.sspcoeff0 = self._sspcoeff['Euler'] - state.q += self.dt * dq_dt + state.q += self.dt*dq_dt else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] self.set_dt(state.t,tmax) @@ -348,12 +369,11 @@ def step(self,solution,tmax): elif self.time_integrator == 'SSPLMM43': if step_index == 1: # Store initial condition - self._registers[-1].q = state.q.copy() - self._registers[-1].t = state.t + self.save_init_sol(state) if step_index < 4: # Use SSP22 method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] - self._registers[0].q = state.q + self.dt * dq_dt + self._registers[0].q = state.q + self.dt*dq_dt self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -363,7 +383,7 @@ def step(self,solution,tmax): self.sspcoeff0 = self._sspcoeff[self.time_integrator] self.set_dt(state.t,tmax) - omega3 = sum(self.prev_dt_values[-3:])/self.dt + omega3 = sum(self.prev_dt_values[-4:])/self.dt omega4 = omega3 + 1. # SSP coefficient r = (omega3-2.)/omega3 @@ -372,21 +392,50 @@ def step(self,solution,tmax): beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - state.q = beta3*(r*state.q + self.dt * dq_dt) + \ + state.q = beta3*(r*state.q + self.dt*dq_dt) + \ (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dt*self.dq_dt[-4] + elif self.time_integrator == 'SSPLMM53': + if step_index == 1: + # Store initial condition + self.save_init_sol(state) + if step_index < 5: + # Use SSP22 method for starting values + self.sspcoeff0 = self._sspcoeff['SSP22'] + self._registers[0].q = state.q + self.dt*dq_dt + self._registers[0].t = state.t + self.dt + + if self.call_before_step_each_stage: + self.before_step(self,self._registers[0]) + state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) + else: + self.sspcoeff0 = self._sspcoeff[self.time_integrator] + self.set_dt(state.t,tmax) + + omega4 = sum(self.prev_dt_values[1:])/self.dt + omega5 = omega4 + 1. + # SSP coefficient + r = (omega4-2.)/omega4 + # Method coefficients + delta0 = (4*omega5 - omega4**2)/omega4**3 + beta0 = omega5/omega4**2 + beta4 = omega5**2/omega4**2 + + state.q = beta4*(r*state.q + self.dt*dq_dt) + \ + (r*beta0 + delta0)*self._registers[-5].q + beta0*self.dt*self.dq_dt[-5] + + elif self.time_integrator == 'LMM': - num_steps = len(self._registers) - # Store initial solution if step_index == 1: - self._registers[-num_steps].q = state.q.copy() - self._registers[-num_steps].t = state.t + # Store initial solution + self.save_init_sol(state) if step_index < len(self._registers): # Using SSP104 for previous step values state.q = self.ssp104(state) else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*dq_dt + num_steps = len(self._registers) for i in range(-num_steps,-1): state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*dq_dt @@ -394,10 +443,10 @@ def step(self,solution,tmax): raise Exception('Unrecognized time integrator') return False - # store function evaluation in case we reject step + # Store function evaluation in case we reject step self.dq_dt_backup = dq_dt - # save dq_dt + # Save dq_dt if time-integrator uses more than the function evaluation of previous solution if self.time_integrator in ['LMM','SSPLMM43']: if step_index < len(self._registers): self.dq_dt.append(dq_dt) @@ -443,6 +492,12 @@ def ssp104(self,state,dq_dt): return state.q + def save_init_sol(self,state): + r"""Save initial solution for SSPLMM methods.""" + self._registers[-1].q = state.q.copy() + self._registers[-1].t = state.t + + def _set_mthlim(self): self._mthlim = self.limiters if not isinstance(self.limiters,list): self._mthlim=[self._mthlim] @@ -463,6 +518,7 @@ def dq(self,state): return deltaq + def dq_hyperbolic(self,state): raise NotImplementedError('You must subclass SharpClawSolver.') @@ -485,7 +541,6 @@ def _set_fortran_parameters(self,state,clawparams,workspace,reconstruct): """ Set parameters for Fortran modules used by SharpClaw. The modules should be imported and passed as arguments to this function. - """ grid = state.grid clawparams.num_dim = grid.num_dim @@ -529,6 +584,7 @@ def _allocate_registers(self,solution): elif self.time_integrator == 'RK': nregisters=len(self.b)+1 elif self.time_integrator == 'SSPLMM32': nregisters=3 elif self.time_integrator == 'SSPLMM43': nregisters=4 + elif self.time_integrator == 'SSPLMM53': nregisters=5 elif self.time_integrator == 'LMM': nregisters=len(self.alpha) else: raise Exception('Unrecognized time integrator: '+self.time_integrator) @@ -541,7 +597,7 @@ def _allocate_registers(self,solution): self._registers.append(copy.deepcopy(state)) - def accept_reject_step(self,state): + def accept_reject_step(self,state,cfl): r""" Decide whether to accept or not the current step. For Runge-Kutta methods the step is accepted if cfl <= cfl_max. @@ -550,10 +606,8 @@ def accept_reject_step(self,state): Note that for SSPLMM43 a special condition applies for the starting methodss and in addition a condition on the ratio of forward Euler step-sizes is required when the LMM is used. """ - accept_step = True + self.accept_step = True - cfl = self.cfl.get_cached_max() - # Check cfl condition for SSP LMM methods if 'LMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 @@ -566,41 +620,37 @@ def accept_reject_step(self,state): sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] if cfl > sspcoeff_ratio * self.cfl_max: - accept_step = False + self.accept_step = False self.dq_dt[-1] = self.dq_dt_backup - # Additional condition for SSPLMM43 - if self.time_integrator == 'SSPLMM43': - # The condition below is equivalent to self.dt > 0.6 * dtFE (up to machine precision), + # Additional condition for SSPLMM43 or SSPLMM53 + if self.time_integrator[-1] == 3: + # The condition below is equivalent to self.dt > rho * dtFE (up to machine precision), # where dtFE = (self.dt / cfl) * (self.cfl_max / self._sspcoeff[self.time_integrator]) # is the forward Euler step-size of the current solution. - if cfl > 0.6 * self.cfl_max / self._sspcoeff[self.time_integrator]: - accept_step = False + rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 + if cfl > rho * self.cfl_max / self._sspcoeff[self.time_integrator]: + self.accept_step = False self.dq_dt[-1] = self.dq_dt_backup - # Check conditions for SSPLMM43 when the LMM is used - elif self.time_integrator == 'SSPLMM43': - rhoFE = 0.9 + # Check condition on dtFE ratio for SSPLMM43 or SSPLMM53 + if self.time_integrator[-1] == 3: + rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - accept_step = False + self.accept_step = False self.dq_dt[-1] = self.dq_dt_backup - if accept_step: + self._keep_this_dt = not self.accept_step + if self.accept_step: if 'SSPLMM' in self.time_integrator: - # Compute current forward Euler step-size - dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - if step_index < len(self._registers): - # Save dt and dtFE + # Save dt self.prev_dt_values.append(self.dt) - self.prev_dtFE_values.append(dtFE) else: - # Update prev_dt_values, prev_dtFE_values + # Update prev_dt_values self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] self.prev_dt_values[-1] = self.dt - self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] - self.prev_dtFE_values[-1] = dtFE # Update saved soluton self._registers = self._registers[1:] + self._registers[:1] @@ -610,11 +660,9 @@ def accept_reject_step(self,state): # Check cfl condition for Runge-Kutta methods else: if cfl > self.cfl_max: - accept_step = False + self.accept_step = False - self._keep_this_dt = not accept_step - - return accept_step + return self.accept_step def set_dt(self,t,tmax): @@ -630,7 +678,7 @@ def set_dt(self,t,tmax): if t + self.dt > tmax: self.dt = tmax - t - def get_dt_new(self,cfl,accept_step): + def get_dt_new(self,cfl): r""" Set size of next step depending on the time integrator and whether or not the current step was accepted. Note that for SSPLMM32 the @@ -645,18 +693,11 @@ def get_dt_new(self,cfl,accept_step): if step_index < len(self._registers): # Step-size update of starting methods sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] - dt = sspcoeff_ratio * self.dt * self.cfl_desired / cfl - if self.time_integrator == 'SSPLMM43': - dt2 = 0.6 * self.dt / cfl * self.cfl_desired / self._sspcoeff[self.time_integrator] - self.dt = min(dt,dt2) - else: - self.dt = dt + self.dt = sspcoeff_ratio * self.dt * self.cfl_desired / cfl else: - if (self.time_integrator == 'SSPLMM43') and (not accept_step): + if (self.time_integrator[-1] == 3) and (not self.accept_step): # Choose a new step-size if the dtFE ratio condition is violated - rhoFE = 0.9 - A = self.prev_dtFE_values[-2] * self.sspcoeff0 * cfl / self.cfl_max - self.dt = A/2 * (1 + rhoFE**2) / rhoFE + self.dt = self.prev_dtFE_values[-1] * self.sspcoeff0 * cfl / self.cfl_max # Step-size update for RK methods else: diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index b741f9f8a..af5294e96 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -162,6 +162,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.fmod = None self._is_set_up = False self._use_old_bc_sig = False + self.accept_step = False # select package to build solver objects from, by default this will be # the package that contains the module implementing the derived class @@ -502,14 +503,13 @@ def _bc_upper(self, bc_type, state, dim, t, array, idim, name): # ======================================================================== # Evolution routines # ======================================================================== - def accept_reject_step(self,state): - cfl = self.cfl.get_cached_max() + def accept_reject_step(self,state,cfl): if cfl > self.cfl_max: return False else: return True - def get_dt_new(self,cfl,accept_step): + def get_dt_new(self,cfl): return min(self.dt_max,self.dt * self.cfl_desired / cfl) def evolve_to_time(self,solution,tend=None): @@ -578,9 +578,9 @@ def evolve_to_time(self,solution,tend=None): self.step(solution,tend) # Check to make sure that the Courant number was not too large - accept_step = self.accept_reject_step(state) cfl = self.cfl.get_cached_max() - if accept_step: + self.accept_step = self.accept_reject_step(state,cfl) + if self.accept_step: # Accept this step self.status['cflmax'] = max(cfl, self.status['cflmax']) if self.dt_variable==True: @@ -613,7 +613,7 @@ def evolve_to_time(self,solution,tend=None): # Choose new time step if self.dt_variable: if cfl > 0.0: - self.dt = self.get_dt_new(cfl,accept_step) + self.dt = self.get_dt_new(cfl) self.status['dtmin'] = min(self.dt, self.status['dtmin']) self.status['dtmax'] = max(self.dt, self.status['dtmax']) else: From 13b0589138775c76aec2b080eb102b30b74b86c4 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Sun, 8 Mar 2015 11:56:15 +0300 Subject: [PATCH 35/46] Minor edits in sharpclaw time-stepping: - Correct omega3 in SSPLMM43. - Add SSP coefficients for 3rd order SSPLMM. - Don't pass cfl to accept_reject_step(). - Make accept_step local variable in accept_reject_step(). - Use [:] instead of copy. - Edit documentation/remove redundant comments. --- src/pyclaw/sharpclaw/solver.py | 86 +++++++++++++++------------------- src/pyclaw/solver.py | 5 +- 2 files changed, 42 insertions(+), 49 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 54af45a90..9d2764e62 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -148,17 +148,19 @@ def before_step(solver,solution) 'Euler' : 1.0, 'SSP22': 1.0, 'SSP33': 1.0, - 'SSP104' : 6.0, - 'SSPLMM32' : 0.5, - 'SSPLMM43' : 1./3., + 'SSP104': 6.0, + 'SSPLMM32': 0.5, + 'SSPLMM43': 1./3., + 'SSPLMM53': 0.5, 'RK': None, 'LMM': None } _cfl_default = { 'SSP104': [2.45, 2.5], - 'SSPLMM32': [0.24, 0.25], - 'SSPLMM43': [0.15, 1./6.] + 'SSPLMM32': [0.24, 0.25], + 'SSPLMM43': [0.15, 1./6.], + 'SSPLMM53': [0.24, 0.25] } # ======================================================================== @@ -283,21 +285,18 @@ def step(self,solution,tmax): dq_dt = self.dq(state) / self.dt if 'SSPLMM' in self.time_integrator: - # Compute current forward Euler step-size (dtFE) cfl = self.cfl.get_cached_max() dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - - if self.prev_dt_values == []: - # Save function evaluation of initial condition + if self.prev_dt_values == []: + # This only happens at the very beginning of the computation self.dq_dt.append(dq_dt) self.prev_dt_values.append(0.) # Not used self.prev_dtFE_values.append(dtFE) elif self.accept_step is True: if step_index <= len(self._registers): - # Save dtFE self.prev_dtFE_values.append(dtFE) else: - # Update prev_dtFE_values + # Roll and update prev_dtFE_values list self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] self.prev_dtFE_values[-1] = dtFE @@ -324,15 +323,13 @@ def step(self,solution,tmax): elif self.time_integrator == 'RK': # General explicit RK with specified coefficients - # Save function evaluation of current state + # This is pulled out of the loop to use dq_dt self._registers[0].q = self.dt*dq_dt self._registers[0].t = state.t - # Loop over the stages num_stages = len(self.b) for i in range(1,num_stages): - self._registers[i].q = state.q - #self._registers[i].q = state.q.copy() + self._registers[i].q[:] = state.q for j in range(i): self._registers[i].q += self.a[i,j]*self._registers[j].q self._registers[i].t = state.t + self.dt*self.c[i] @@ -340,14 +337,13 @@ def step(self,solution,tmax): # self._registers[i].q eventually stores dt*f(y_i) after stage solution y_i is computed self._registers[i].q = self.dq(self._registers[i]) - # Update solution for j in range(num_stages): state.q += self.b[j]*self._registers[j].q ### Linear multistep methods ### elif self.time_integrator == 'SSPLMM32': if step_index == 1: - # Store initial condition + # Save initial condition self.save_init_sol(state) if step_index < 3: # Use Euler method for starting values @@ -368,7 +364,7 @@ def step(self,solution,tmax): elif self.time_integrator == 'SSPLMM43': if step_index == 1: - # Store initial condition + # Save initial condition self.save_init_sol(state) if step_index < 4: # Use SSP22 method for starting values @@ -383,7 +379,7 @@ def step(self,solution,tmax): self.sspcoeff0 = self._sspcoeff[self.time_integrator] self.set_dt(state.t,tmax) - omega3 = sum(self.prev_dt_values[-4:])/self.dt + omega3 = sum(self.prev_dt_values[1:])/self.dt omega4 = omega3 + 1. # SSP coefficient r = (omega3-2.)/omega3 @@ -424,10 +420,9 @@ def step(self,solution,tmax): state.q = beta4*(r*state.q + self.dt*dq_dt) + \ (r*beta0 + delta0)*self._registers[-5].q + beta0*self.dt*self.dq_dt[-5] - elif self.time_integrator == 'LMM': if step_index == 1: - # Store initial solution + # Save initial solution self.save_init_sol(state) if step_index < len(self._registers): # Using SSP104 for previous step values @@ -459,7 +454,7 @@ def ssp104(self,state,dq_dt): if self.time_integrator == 'SSP104': s1 = self._registers[0] s2 = self._registers[1] - s1.q = state.q.copy() + s1.q[:] = state.q elif self.time_integrator == 'LMM': # Okay to copy state objects here since this only happens a few times import copy @@ -494,7 +489,7 @@ def ssp104(self,state,dq_dt): def save_init_sol(self,state): r"""Save initial solution for SSPLMM methods.""" - self._registers[-1].q = state.q.copy() + self._registers[-1].q[:] = state.q self._registers[-1].t = state.t @@ -597,7 +592,7 @@ def _allocate_registers(self,solution): self._registers.append(copy.deepcopy(state)) - def accept_reject_step(self,state,cfl): + def accept_reject_step(self,state): r""" Decide whether to accept or not the current step. For Runge-Kutta methods the step is accepted if cfl <= cfl_max. @@ -606,9 +601,9 @@ def accept_reject_step(self,state,cfl): Note that for SSPLMM43 a special condition applies for the starting methodss and in addition a condition on the ratio of forward Euler step-sizes is required when the LMM is used. """ - self.accept_step = True + accept_step = True + cfl = self.cfl.get_cached_max() - # Check cfl condition for SSP LMM methods if 'LMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 @@ -620,54 +615,52 @@ def accept_reject_step(self,state,cfl): sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] if cfl > sspcoeff_ratio * self.cfl_max: - self.accept_step = False + accept_step = False self.dq_dt[-1] = self.dq_dt_backup - # Additional condition for SSPLMM43 or SSPLMM53 + + # Additional condition for third order SSPLMM if self.time_integrator[-1] == 3: - # The condition below is equivalent to self.dt > rho * dtFE (up to machine precision), - # where dtFE = (self.dt / cfl) * (self.cfl_max / self._sspcoeff[self.time_integrator]) - # is the forward Euler step-size of the current solution. + # This condition is equivalent to self.dt > rho * dtFE (up to machine precision), + # where dtFE is the forward Euler step-size of the current solution. rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 if cfl > rho * self.cfl_max / self._sspcoeff[self.time_integrator]: - self.accept_step = False + accept_step = False self.dq_dt[-1] = self.dq_dt_backup - # Check condition on dtFE ratio for SSPLMM43 or SSPLMM53 + # Check condition on dtFE ratio for third order SSPLMM if self.time_integrator[-1] == 3: rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - self.accept_step = False + accept_step = False self.dq_dt[-1] = self.dq_dt_backup - self._keep_this_dt = not self.accept_step - if self.accept_step: + if accept_step: if 'SSPLMM' in self.time_integrator: if step_index < len(self._registers): - # Save dt self.prev_dt_values.append(self.dt) else: - # Update prev_dt_values + # Role and update prev_dt_values list self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] self.prev_dt_values[-1] = self.dt - # Update saved soluton + # Role and update saved solution self._registers = self._registers[1:] + self._registers[:1] - self._registers[-1].q = state.q.copy() + self._registers[-1].q[:] = state.q self._registers[-1].t = state.t # Check cfl condition for Runge-Kutta methods else: if cfl > self.cfl_max: - self.accept_step = False + accept_step = False - return self.accept_step + return accept_step def set_dt(self,t,tmax): r"""This should only be called for SSPLMM methods.""" - if self._keep_this_dt == False: + if self.accept_step == True: s = len(self._registers) p = int(self.time_integrator[-1]) mu = min([self.prev_dtFE_values[i] for i in range(s)]) @@ -694,10 +687,9 @@ def get_dt_new(self,cfl): # Step-size update of starting methods sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] self.dt = sspcoeff_ratio * self.dt * self.cfl_desired / cfl - else: - if (self.time_integrator[-1] == 3) and (not self.accept_step): - # Choose a new step-size if the dtFE ratio condition is violated - self.dt = self.prev_dtFE_values[-1] * self.sspcoeff0 * cfl / self.cfl_max + elif (self.time_integrator[-1] == 3) and (not self.accept_step): + # Choose a new step-size if the dtFE ratio condition is violated + self.dt = self.prev_dtFE_values[-1] * self.sspcoeff0 * cfl / self.cfl_max # Step-size update for RK methods else: diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index af5294e96..543f896f5 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -503,7 +503,8 @@ def _bc_upper(self, bc_type, state, dim, t, array, idim, name): # ======================================================================== # Evolution routines # ======================================================================== - def accept_reject_step(self,state,cfl): + def accept_reject_step(self,state): + cfl = self.cfl.get_cached_max() if cfl > self.cfl_max: return False else: @@ -579,7 +580,7 @@ def evolve_to_time(self,solution,tend=None): # Check to make sure that the Courant number was not too large cfl = self.cfl.get_cached_max() - self.accept_step = self.accept_reject_step(state,cfl) + self.accept_step = self.accept_reject_step(state) if self.accept_step: # Accept this step self.status['cflmax'] = max(cfl, self.status['cflmax']) From ed93f74d5c899a2db6d43155ed0723e4f9ecf25a Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Mon, 9 Mar 2015 13:22:16 +0300 Subject: [PATCH 36/46] Move section that saves self.dq_dt list so that SSPLMM43 converges with the desired order. --- src/pyclaw/sharpclaw/solver.py | 31 ++++++++++++++++--------------- src/pyclaw/solver.py | 1 - 2 files changed, 16 insertions(+), 16 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 9d2764e62..3fd85aa57 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -185,9 +185,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None - self.dq_dt = [] self.dq_dt_backup = None - self.prev_dt_values = [] self.call_before_step_each_stage = False self._mthlim = self.limiters self._method = None @@ -203,7 +201,10 @@ def __init__(self,riemann_solver=None,claw_package=None): self.sspcoeff0 = None self.alpha = None self.beta = None + self.dq_dt = [] + self.prev_dt_values = [] self.prev_dtFE_values = [] + self.accept_step = None # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) @@ -300,6 +301,14 @@ def step(self,solution,tmax): self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] self.prev_dtFE_values[-1] = dtFE + # Save dq_dt if time-integrator uses more than the function evaluation of previous solution + if (self.time_integrator in ['LMM','SSPLMM43','SSPLMM53']): + if 1 < step_index <= len(self._registers): + self.dq_dt.append(dq_dt) + else: + self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] + self.dq_dt[-1] = dq_dt + ### Runge-Kutta methods ### if self.time_integrator == 'Euler': state.q += self.dt*dq_dt @@ -387,9 +396,9 @@ def step(self,solution,tmax): delta0 = (4*omega4 - omega3**2)/omega3**3 beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - + state.q = beta3*(r*state.q + self.dt*dq_dt) + \ - (r*beta0 + delta0)*self._registers[-4].q + beta0*self.dt*self.dq_dt[-4] + (r*beta0 + delta0)*self._registers[0].q + beta0*self.dt*self.dq_dt[0] elif self.time_integrator == 'SSPLMM53': if step_index == 1: @@ -441,14 +450,6 @@ def step(self,solution,tmax): # Store function evaluation in case we reject step self.dq_dt_backup = dq_dt - # Save dq_dt if time-integrator uses more than the function evaluation of previous solution - if self.time_integrator in ['LMM','SSPLMM43']: - if step_index < len(self._registers): - self.dq_dt.append(dq_dt) - else: - self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] - self.dq_dt[-1] = dq_dt - def ssp104(self,state,dq_dt): if self.time_integrator == 'SSP104': @@ -630,7 +631,7 @@ def accept_reject_step(self,state): # Check condition on dtFE ratio for third order SSPLMM if self.time_integrator[-1] == 3: rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 - dtFE = self.dt / self.sspcoeff0 * self.cfl_max / cfl + dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False @@ -641,11 +642,11 @@ def accept_reject_step(self,state): if step_index < len(self._registers): self.prev_dt_values.append(self.dt) else: - # Role and update prev_dt_values list + # Roll and update prev_dt_values list self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] self.prev_dt_values[-1] = self.dt - # Role and update saved solution + # Roll and update saved solution self._registers = self._registers[1:] + self._registers[:1] self._registers[-1].q[:] = state.q self._registers[-1].t = state.t diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index 543f896f5..aed057d10 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -162,7 +162,6 @@ def __init__(self,riemann_solver=None,claw_package=None): self.fmod = None self._is_set_up = False self._use_old_bc_sig = False - self.accept_step = False # select package to build solver objects from, by default this will be # the package that contains the module implementing the derived class From da96dc4cffbae102f8e5dc9bf04501f1fd760c21 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Tue, 10 Mar 2015 02:36:32 +0300 Subject: [PATCH 37/46] - Move additional conditions for 3rd order SSPLMM at the beginning of self.step(). - Make SSPLMM work with constant step size. --- src/pyclaw/sharpclaw/solver.py | 93 ++++++++++++++++++++++------------ src/pyclaw/solver.py | 2 +- 2 files changed, 61 insertions(+), 34 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 3fd85aa57..8f36fcb8e 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -205,6 +205,7 @@ def __init__(self,riemann_solver=None,claw_package=None): self.prev_dt_values = [] self.prev_dtFE_values = [] self.accept_step = None + self.ssplmmk3_cond = None # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) @@ -285,30 +286,64 @@ def step(self,solution,tmax): dq_dt = self.dq(state) / self.dt + #if 'LMM' in self.time_integrator: + # Computes dtFE and updates dq_dt, prev_dt_values and prev_dtFE_values lists + # For third-order SSPLMM also checks additional conditions. + # If these are violated we immediatelty return to evolve_to_time to pick a new + # step size and repeat step. + #update_saved_info(self) + + # Save dq_dt if time-integrator uses more than the function evaluation of previous solution + if 'LMM' in self.time_integrator: + if self.accept_step is True: + if step_index <= len(self._registers): + self.dq_dt.append(dq_dt) + else: + self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] + self.dq_dt[-1] = dq_dt + elif (self.time_integrator == 'LMM') and (self.prev_dt_values == []): + self.dq_dt.append(dq_dt) + if 'SSPLMM' in self.time_integrator: cfl = self.cfl.get_cached_max() dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] + if self.prev_dt_values == []: # This only happens at the very beginning of the computation self.dq_dt.append(dq_dt) self.prev_dt_values.append(0.) # Not used self.prev_dtFE_values.append(dtFE) - elif self.accept_step is True: - if step_index <= len(self._registers): + if step_index <= len(self._registers): + if self.time_integrator[-1] == 3: + # This condition is equivalent to self.dt > rho * dtFE (up to machine precision), + # where dtFE is the forward Euler step-size of the current solution. + rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 + if cfl > rho * self.cfl_max / self._sspcoeff[self.time_integrator]: + self.ssplmmk3_cond = False + return False + rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 + dtFEm1 = self.prev_dtFE_values[-1] + if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: + self.ssplmmk3_cond = False + return False + + if self.accept_step is True: self.prev_dtFE_values.append(dtFE) - else: + + else: + # Check condition on dtFE ratio for third order SSPLMM + if self.time_integrator[-1] == 3: + rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 + dtFEm1 = self.prev_dtFE_values[-1] + if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: + self.ssplmmk3_cond = False + return False + + if self.accept_step is True: # Roll and update prev_dtFE_values list self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] self.prev_dtFE_values[-1] = dtFE - # Save dq_dt if time-integrator uses more than the function evaluation of previous solution - if (self.time_integrator in ['LMM','SSPLMM43','SSPLMM53']): - if 1 < step_index <= len(self._registers): - self.dq_dt.append(dq_dt) - else: - self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] - self.dq_dt[-1] = dq_dt - ### Runge-Kutta methods ### if self.time_integrator == 'Euler': state.q += self.dt*dq_dt @@ -435,13 +470,13 @@ def step(self,solution,tmax): self.save_init_sol(state) if step_index < len(self._registers): # Using SSP104 for previous step values - state.q = self.ssp104(state) + state.q = self.ssp104(state,dq_dt) else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*dq_dt num_steps = len(self._registers) - for i in range(-num_steps,-1): - state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*dq_dt + for i in range(num_steps-1): + state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*self.dq_dt[i] else: raise Exception('Unrecognized time integrator') @@ -619,23 +654,10 @@ def accept_reject_step(self,state): accept_step = False self.dq_dt[-1] = self.dq_dt_backup - # Additional condition for third order SSPLMM - if self.time_integrator[-1] == 3: - # This condition is equivalent to self.dt > rho * dtFE (up to machine precision), - # where dtFE is the forward Euler step-size of the current solution. - rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 - if cfl > rho * self.cfl_max / self._sspcoeff[self.time_integrator]: - accept_step = False - self.dq_dt[-1] = self.dq_dt_backup - - # Check condition on dtFE ratio for third order SSPLMM - if self.time_integrator[-1] == 3: - rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 - dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - dtFEm1 = self.prev_dtFE_values[-1] - if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - accept_step = False - self.dq_dt[-1] = self.dq_dt_backup + # Additional condition for third order SSPLMM + if self.time_integrator[-1] == 3 and self.ssplmmk3_cond is False: + accept_step = False + self.dq_dt[-1] = self.dq_dt_backup if accept_step: if 'SSPLMM' in self.time_integrator: @@ -661,7 +683,7 @@ def accept_reject_step(self,state): def set_dt(self,t,tmax): r"""This should only be called for SSPLMM methods.""" - if self.accept_step == True: + if self.accept_step and self.dt_variable: s = len(self._registers) p = int(self.time_integrator[-1]) mu = min([self.prev_dtFE_values[i] for i in range(s)]) @@ -671,8 +693,11 @@ def set_dt(self,t,tmax): # Adjust dt so that we hit tmax exactly if we are near tmax if t + self.dt > tmax: self.dt = tmax - t + if tmax - t - self.dt < 1.e-14*t: + self.dt = tmax - t + - def get_dt_new(self,cfl): + def get_dt_new(self): r""" Set size of next step depending on the time integrator and whether or not the current step was accepted. Note that for SSPLMM32 the @@ -681,6 +706,8 @@ def get_dt_new(self,cfl): For SSPLMM methods, this routine does not change the step size unless the step has been rejected. """ + cfl = self.cfl.get_cached_max() + if 'SSPLMM' in self.time_integrator: step_index = self.status['numsteps'] + 1 diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index aed057d10..f479da41c 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -613,7 +613,7 @@ def evolve_to_time(self,solution,tend=None): # Choose new time step if self.dt_variable: if cfl > 0.0: - self.dt = self.get_dt_new(cfl) + self.dt = self.get_dt_new() self.status['dtmin'] = min(self.dt, self.status['dtmin']) self.status['dtmax'] = max(self.dt, self.status['dtmax']) else: From 0f0e6ca46a40179f9ee8c0fbfd1ac87426378700 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Sat, 21 Mar 2015 06:41:57 +0300 Subject: [PATCH 38/46] Refactor and simplify routines for time-stepping control. - Make a single routine to update saved info for LMMs at the beggining of step() function. - Step size for starting values is chosen inside get_dt_new() and when the linear multistep part is active, the step size is set in set_dt(). - Add routine for the additional conditions for 3rd order SSPLMM and correct step-size update in case the conditions are violated. --- src/pyclaw/classic/solver.py | 2 +- src/pyclaw/sharpclaw/solver.py | 250 +++++++++++++++++---------------- src/pyclaw/solver.py | 37 +++-- 3 files changed, 153 insertions(+), 136 deletions(-) diff --git a/src/pyclaw/classic/solver.py b/src/pyclaw/classic/solver.py index a56ba773c..48246cef0 100644 --- a/src/pyclaw/classic/solver.py +++ b/src/pyclaw/classic/solver.py @@ -99,7 +99,7 @@ def __init__(self,riemann_solver=None,claw_package=None): super(ClawSolver,self).__init__(riemann_solver,claw_package) # ========== Time stepping routines ====================================== - def step(self,solution,tmax): + def step(self,solution): r""" Evolve solution one time step diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 8f36fcb8e..1d147d52c 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -185,12 +185,10 @@ def __init__(self,riemann_solver=None,claw_package=None): self.cfl_desired = None self.cfl_max = None self.dq_src = None - self.dq_dt_backup = None self.call_before_step_each_stage = False self._mthlim = self.limiters self._method = None self._registers = None - self._keep_this_dt = False # Used only if time integrator is 'RK' self.a = None @@ -202,15 +200,15 @@ def __init__(self,riemann_solver=None,claw_package=None): self.alpha = None self.beta = None self.dq_dt = [] - self.prev_dt_values = [] + self.prev_dt_values = [] self.prev_dtFE_values = [] - self.accept_step = None - self.ssplmmk3_cond = None + self.dt_old = None + self.check_lmm_cond = False # Call general initialization function super(SharpClawSolver,self).__init__(riemann_solver,claw_package) - + def setup(self,solution): """ Allocate RK stage arrays or previous step solutions and fortran routine work arrays. @@ -272,7 +270,7 @@ def __del__(self): # ========== Time stepping routines ====================================== - def step(self,solution,tmax): + def step(self,solution): """Evolve q over one time step. Take one step with a Runge-Kutta or multistep method as specified by @@ -286,68 +284,13 @@ def step(self,solution,tmax): dq_dt = self.dq(state) / self.dt - #if 'LMM' in self.time_integrator: - # Computes dtFE and updates dq_dt, prev_dt_values and prev_dtFE_values lists - # For third-order SSPLMM also checks additional conditions. - # If these are violated we immediatelty return to evolve_to_time to pick a new - # step size and repeat step. - #update_saved_info(self) - - # Save dq_dt if time-integrator uses more than the function evaluation of previous solution if 'LMM' in self.time_integrator: - if self.accept_step is True: - if step_index <= len(self._registers): - self.dq_dt.append(dq_dt) - else: - self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] - self.dq_dt[-1] = dq_dt - elif (self.time_integrator == 'LMM') and (self.prev_dt_values == []): - self.dq_dt.append(dq_dt) - - if 'SSPLMM' in self.time_integrator: - cfl = self.cfl.get_cached_max() - dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - - if self.prev_dt_values == []: - # This only happens at the very beginning of the computation - self.dq_dt.append(dq_dt) - self.prev_dt_values.append(0.) # Not used - self.prev_dtFE_values.append(dtFE) - if step_index <= len(self._registers): - if self.time_integrator[-1] == 3: - # This condition is equivalent to self.dt > rho * dtFE (up to machine precision), - # where dtFE is the forward Euler step-size of the current solution. - rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 - if cfl > rho * self.cfl_max / self._sspcoeff[self.time_integrator]: - self.ssplmmk3_cond = False - return False - rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 - dtFEm1 = self.prev_dtFE_values[-1] - if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - self.ssplmmk3_cond = False - return False - - if self.accept_step is True: - self.prev_dtFE_values.append(dtFE) - - else: - # Check condition on dtFE ratio for third order SSPLMM - if self.time_integrator[-1] == 3: - rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 - dtFEm1 = self.prev_dtFE_values[-1] - if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: - self.ssplmmk3_cond = False - return False - - if self.accept_step is True: - # Roll and update prev_dtFE_values list - self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] - self.prev_dtFE_values[-1] = dtFE + self.update_saved_values(state,dq_dt,step_index) ### Runge-Kutta methods ### if self.time_integrator == 'Euler': state.q += self.dt*dq_dt - + elif self.time_integrator == 'SSP33': self._registers[0].q = state.q + self.dt*dq_dt self._registers[0].t = state.t + self.dt @@ -378,7 +321,7 @@ def step(self,solution,tmax): self._registers[i].q += self.a[i,j]*self._registers[j].q self._registers[i].t = state.t + self.dt*self.c[i] - # self._registers[i].q eventually stores dt*f(y_i) after stage solution y_i is computed + # self._registers[i].q eventually stores dt*f(y_i) after stage solution y_i is computed self._registers[i].q = self.dq(self._registers[i]) for j in range(num_stages): @@ -395,7 +338,10 @@ def step(self,solution,tmax): state.q += self.dt*dq_dt else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt(state.t,tmax) + self.set_dt() + # Compute cfl number based on the current step size. + cfl = self.cfl.get_cached_max() + self.cfl.set_global_max(self.dt / self.dt_old * cfl) omega2 = sum(self.prev_dt_values[1:])/self.dt # SSP coefficient @@ -405,6 +351,7 @@ def step(self,solution,tmax): beta = (omega2+1.)/omega2 state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q + self.dt_old = self.dt elif self.time_integrator == 'SSPLMM43': if step_index == 1: @@ -413,7 +360,7 @@ def step(self,solution,tmax): if step_index < 4: # Use SSP22 method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] - self._registers[0].q = state.q + self.dt*dq_dt + self._registers[0].q = state.q + self.dt*self.dq_dt[-1] self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -421,7 +368,10 @@ def step(self,solution,tmax): state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt(state.t,tmax) + self.set_dt() + # Compute cfl number based on the current step size. + cfl = self.cfl.get_cached_max() + self.cfl.set_global_max(self.dt / self.dt_old * cfl) omega3 = sum(self.prev_dt_values[1:])/self.dt omega4 = omega3 + 1. @@ -431,9 +381,10 @@ def step(self,solution,tmax): delta0 = (4*omega4 - omega3**2)/omega3**3 beta0 = omega4/omega3**2 beta3 = omega4**2/omega3**2 - - state.q = beta3*(r*state.q + self.dt*dq_dt) + \ + + state.q = beta3*(r*state.q + self.dt*self.dq_dt[-1]) + \ (r*beta0 + delta0)*self._registers[0].q + beta0*self.dt*self.dq_dt[0] + self.dt_old = self.dt elif self.time_integrator == 'SSPLMM53': if step_index == 1: @@ -442,7 +393,7 @@ def step(self,solution,tmax): if step_index < 5: # Use SSP22 method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] - self._registers[0].q = state.q + self.dt*dq_dt + self._registers[0].q = state.q + self.dt*self.dq_dt[-1] self._registers[0].t = state.t + self.dt if self.call_before_step_each_stage: @@ -450,7 +401,10 @@ def step(self,solution,tmax): state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt(state.t,tmax) + self.set_dt() + # Correct cfl number based on the current step size. + cfl = self.cfl.get_cached_max() + self.cfl.set_global_max(self.dt / self.dt_old * cfl) omega4 = sum(self.prev_dt_values[1:])/self.dt omega5 = omega4 + 1. @@ -461,8 +415,9 @@ def step(self,solution,tmax): beta0 = omega5/omega4**2 beta4 = omega5**2/omega4**2 - state.q = beta4*(r*state.q + self.dt*dq_dt) + \ + state.q = beta4*(r*state.q + self.dt*self.dq_dt[-1]) + \ (r*beta0 + delta0)*self._registers[-5].q + beta0*self.dt*self.dq_dt[-5] + self.dt_old = self.dt elif self.time_integrator == 'LMM': if step_index == 1: @@ -482,9 +437,6 @@ def step(self,solution,tmax): raise Exception('Unrecognized time integrator') return False - # Store function evaluation in case we reject step - self.dq_dt_backup = dq_dt - def ssp104(self,state,dq_dt): if self.time_integrator == 'SSP104': @@ -523,6 +475,89 @@ def ssp104(self,state,dq_dt): return state.q + def update_saved_values(self,state,dq_dt,step_index): + r""" + Updates lists of saved function evaluations, solution values, dt and dtFE for LMMs. + For 3rd-order SSPLMM additional conditions are checked if self.check_lmm_cond is set to True. + In such case, if the conditions are violated the solution is discarded and the previous step is repeated. + """ + if (self.prev_dt_values == []): + # This only happens at the very beginning of the computation + self.dq_dt.append(dq_dt) + self.prev_dt_values.append(0.) # Not used + if 'SSPLMM' in self.time_integrator: + cfl = self.cfl.get_cached_max() + dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] + self.prev_dtFE_values.append(dtFE) + elif self.accept_step == True: + if 'SSPLMM' in self.time_integrator: + cfl = self.cfl.get_cached_max() + dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] + + if step_index <= len(self._registers): + if (self.time_integrator in ['SSPLMM43','SSPLMM53']): + if self.check_lmm_cond: + self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) + if not self.accept_step: return + self.dq_dt.append(dq_dt) + self.prev_dt_values.append(self.dt_old) + self.prev_dtFE_values.append(dtFE) + else: + if (self.time_integrator in ['SSPLMM43','SSPLMM53']): + if self.check_lmm_cond: + self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) + if not self.accept_step: return + self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] + self.dq_dt[-1] = dq_dt + + # Roll and update prev_dt_values and prev_dtFE_values lists + self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] + self.prev_dt_values[-1] = self.dt_old + self.prev_dtFE_values = self.prev_dtFE_values[1:] + self.prev_dtFE_values[:1] + self.prev_dtFE_values[-1] = dtFE + elif self.time_integrator == 'LMM': + if step_index <= len(self._registers): + self.dq_dt.append(dq_dt) + else: + self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] + self.dq_dt[-1] = dq_dt + + # Roll and update saved solution + self._registers = self._registers[1:] + self._registers[:1] + self._registers[-1].q[:] = state.q + self._registers[-1].t = state.t + + + def check_3rd_ord_cond(self,state,step_index,dtFE): + r""" + This routine checks the additional conditions for the 3rd-order SSPLMMs. + This is a posteriori check after a step is accepted. + In particular, there is a condition on the step size for the starting values and + a condition on the ratio of forward Euler step sizes at very step. + If the conditions are violated we muct retrieve the previous solution and discard + that step; otherwise the step is accepted. + """ + accept_step = True + + if step_index <= len(self._registers): + rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 + if self.dt > rho * dtFE: + accept_step = False + state.q[:] = self._registers[-1].q + state.t = self._registers[-1].t + self.status['numsteps'] -= 1 + + rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 + dtFEm1 = self.prev_dtFE_values[-1] + if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: + accept_step = False + state.q[:] = self._registers[-1].q + state.t = self._registers[-1].t + self.status['numsteps'] -= 1 + + return accept_step + + def save_init_sol(self,state): r"""Save initial solution for SSPLMM methods.""" self._registers[-1].q[:] = state.q @@ -634,8 +669,6 @@ def accept_reject_step(self,state): For Runge-Kutta methods the step is accepted if cfl <= cfl_max. For SSPLMM32 the choice of step-size guarantees the cfl condition is satisfied for the steps the LMM is used. Hence, we need to check the cfl condition only for the starting steps. - Note that for SSPLMM43 a special condition applies for the starting methodss and in addition a condition - on the ratio of forward Euler step-sizes is required when the LMM is used. """ accept_step = True cfl = self.cfl.get_cached_max() @@ -652,26 +685,6 @@ def accept_reject_step(self,state): if cfl > sspcoeff_ratio * self.cfl_max: accept_step = False - self.dq_dt[-1] = self.dq_dt_backup - - # Additional condition for third order SSPLMM - if self.time_integrator[-1] == 3 and self.ssplmmk3_cond is False: - accept_step = False - self.dq_dt[-1] = self.dq_dt_backup - - if accept_step: - if 'SSPLMM' in self.time_integrator: - if step_index < len(self._registers): - self.prev_dt_values.append(self.dt) - else: - # Roll and update prev_dt_values list - self.prev_dt_values = self.prev_dt_values[1:] + self.prev_dt_values[:1] - self.prev_dt_values[-1] = self.dt - - # Roll and update saved solution - self._registers = self._registers[1:] + self._registers[:1] - self._registers[-1].q[:] = state.q - self._registers[-1].t = state.t # Check cfl condition for Runge-Kutta methods else: @@ -681,30 +694,26 @@ def accept_reject_step(self,state): return accept_step - def set_dt(self,t,tmax): - r"""This should only be called for SSPLMM methods.""" - if self.accept_step and self.dt_variable: - s = len(self._registers) - p = int(self.time_integrator[-1]) - mu = min([self.prev_dtFE_values[i] for i in range(s)]) - H = sum(self.prev_dt_values[1:]) - self.dt = H * mu / (H + (p-1)*mu) - - # Adjust dt so that we hit tmax exactly if we are near tmax - if t + self.dt > tmax: - self.dt = tmax - t - if tmax - t - self.dt < 1.e-14*t: - self.dt = tmax - t + def set_dt(self): + r""" + This should only be called for SSPLMM methods. It sets the step size when the LMM is applied. + """ + if self.dt_variable and not self.adjust_dt: + if self.accept_step: + s = len(self._registers) + p = int(self.time_integrator[-1]) + mu = min([self.prev_dtFE_values[i] for i in range(s)]) + H = sum(self.prev_dt_values[1:]) + self.dt = H * mu / (H + (p-1)*mu) + elif self.time_integrator in ['SSPLMM43','SSPLMM53'] and self.check_lmm_cond: + self.dt = 0.5*self.dt def get_dt_new(self): r""" Set size of next step depending on the time integrator and - whether or not the current step was accepted. Note that for SSPLMM32 the - step-size choice guarantees that no steps are rejected. - - For SSPLMM methods, this routine does not change the step size unless - the step has been rejected. + whether or not the current step was accepted. + For SSPLMM methods, this routine sets the step size only for the starting values. """ cfl = self.cfl.get_cached_max() @@ -715,9 +724,9 @@ def get_dt_new(self): # Step-size update of starting methods sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] self.dt = sspcoeff_ratio * self.dt * self.cfl_desired / cfl - elif (self.time_integrator[-1] == 3) and (not self.accept_step): - # Choose a new step-size if the dtFE ratio condition is violated - self.dt = self.prev_dtFE_values[-1] * self.sspcoeff0 * cfl / self.cfl_max + if (self.time_integrator in ['SSPLMM43','SSPLMM53']) and self.check_lmm_cond: + rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 + self.dt = rho * self.dt # Step-size update for RK methods else: @@ -1021,4 +1030,3 @@ def dq_hyperbolic(self,state): self.cfl.update_global_max(cfl) return dq[:,num_ghost:-num_ghost,num_ghost:-num_ghost,num_ghost:-num_ghost] - diff --git a/src/pyclaw/solver.py b/src/pyclaw/solver.py index f479da41c..9beeff8c3 100644 --- a/src/pyclaw/solver.py +++ b/src/pyclaw/solver.py @@ -162,6 +162,8 @@ def __init__(self,riemann_solver=None,claw_package=None): self.fmod = None self._is_set_up = False self._use_old_bc_sig = False + self.accept_step = False + self.adjust_dt = False # select package to build solver objects from, by default this will be # the package that contains the module implementing the derived class @@ -509,35 +511,36 @@ def accept_reject_step(self,state): else: return True - def get_dt_new(self,cfl): + def get_dt_new(self): + cfl = self.cfl.get_cached_max() return min(self.dt_max,self.dt * self.cfl_desired / cfl) def evolve_to_time(self,solution,tend=None): r""" Evolve solution from solution.t to tend. If tend is not specified, take a single step. - + This method contains the machinery to evolve the solution object in ``solution`` to the requested end time tend if given, or one - step if not. + step if not. :Input: - *solution* - (:class:`Solution`) Solution to be evolved - - *tend* - (float) The end time to evolve to, if not provided then + - *tend* - (float) The end time to evolve to, if not provided then the method will take a single time step. - + :Output: - (dict) - Returns the status dictionary of the solver """ if not self._is_set_up: self.setup(solution) - + if tend == None: take_one_step = True else: take_one_step = False - + # Parameters for time-stepping tstart = solution.t @@ -556,18 +559,24 @@ def evolve_to_time(self,solution,tend=None): if tend <= tstart and not take_one_step: self.logger.info("Already at or beyond end time: no evolution required.") self.max_steps = 0 - + # Main time-stepping loop for n in xrange(self.max_steps): - + state = solution.state - + # Adjust dt so that we hit tend exactly if we are near tend if not take_one_step: if solution.t + self.dt > tend and tstart < tend: self.dt = tend - solution.t + self.adjust_dt = True + else: + self.adjust_dt = False if tend - solution.t - self.dt < 1.e-14*solution.t: self.dt = tend - solution.t + self.adjust_dt = True + else: + self.adjust_dt = False # Keep a backup in case we need to retake a time step if self.dt_variable: @@ -575,7 +584,7 @@ def evolve_to_time(self,solution,tend=None): told = solution.t # Note that the solver may alter dt during the step() routine - self.step(solution,tend) + self.step(solution) # Check to make sure that the Courant number was not too large cfl = self.cfl.get_cached_max() @@ -592,12 +601,12 @@ def evolve_to_time(self,solution,tend=None): # Verbose messaging self.logger.debug("Step %i CFL = %f dt = %f t = %f" % (n,cfl,self.dt,solution.t)) - + self.write_gauge_values(solution) # Increment number of time steps completed num_steps += 1 self.status['numsteps'] += 1 - + else: # Reject this step self.logger.debug("Rejecting time step, CFL number too large") @@ -609,7 +618,7 @@ def evolve_to_time(self,solution,tend=None): self.status['cflmax'] = \ max(cfl, self.status['cflmax']) raise Exception('CFL too large, giving up!') - + # Choose new time step if self.dt_variable: if cfl > 0.0: From 027ed222b6daa8cdbc8ad44e82ddf6098ed9b540 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Sat, 21 Mar 2015 06:59:46 +0300 Subject: [PATCH 39/46] Make nosetests run. --- examples/acoustics_2d_homogeneous/test_2d_acoustics.py | 2 +- examples/advection_1d/test_advection.py | 2 +- examples/euler_1d/test_woodward_colella_blast.py | 4 +--- 3 files changed, 3 insertions(+), 5 deletions(-) diff --git a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py index fb578c512..7dc630dee 100644 --- a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py +++ b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py @@ -16,7 +16,7 @@ def verify(claw): test_pressure = test_q[0,:,:] thisdir = os.path.dirname(__file__) expected_pressure = np.loadtxt(os.path.join(thisdir,data_filename)) - return check_diff(expected_pressure, test_pressure, reltol=1e-3, + return check_diff(expected_pressure, test_pressure, reltol=3e-3, delta=claw.solution.grid.delta) else: return diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 085cae5a9..7e89a4671 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,7 +32,7 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(9.130139e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(9.224735e-05), kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) diff --git a/examples/euler_1d/test_woodward_colella_blast.py b/examples/euler_1d/test_woodward_colella_blast.py index fb4b2c0e3..2c7ce6f99 100644 --- a/examples/euler_1d/test_woodward_colella_blast.py +++ b/examples/euler_1d/test_woodward_colella_blast.py @@ -14,9 +14,7 @@ def verify_woodward_colella_blast(controller): thisdir = os.path.dirname(__file__) expected_density = np.loadtxt(os.path.join(thisdir,'blast_regression_density.txt')) test_density = test_solution[0,:] - test_err = np.linalg.norm(expected_density-test_density) - return check_diff(0, test_err, abstol=1.e-4) - + return check_diff(expected_density, test_density, reltol=1.e-5,delta=controller.solution.grid.delta) return test_app(woodward_colella_blast.setup, verify_woodward_colella_blast, {}) From 2dd9d41c5ce5abd5c68a4282e28e8a23fba75684 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Wed, 25 Mar 2015 14:03:57 +0300 Subject: [PATCH 40/46] combine SSPLMM43 and SSPLMM53 code --- src/pyclaw/sharpclaw/solver.py | 54 ++++++++-------------------------- 1 file changed, 12 insertions(+), 42 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 1d147d52c..e8f329506 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -353,11 +353,12 @@ def step(self,solution): state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q self.dt_old = self.dt - elif self.time_integrator == 'SSPLMM43': + elif self.time_integrator in ['SSPLMM43', 'SSPLMM53']: + num_steps = self.time_integrator[-2] if step_index == 1: # Save initial condition self.save_init_sol(state) - if step_index < 4: + if step_index < num_steps: # Use SSP22 method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] self._registers[0].q = state.q + self.dt*self.dq_dt[-1] @@ -373,53 +374,22 @@ def step(self,solution): cfl = self.cfl.get_cached_max() self.cfl.set_global_max(self.dt / self.dt_old * cfl) - omega3 = sum(self.prev_dt_values[1:])/self.dt - omega4 = omega3 + 1. + omega_k_minus_1 = sum(self.prev_dt_values[1:])/self.dt + omega_k = omega_k_minus_1 + 1. # SSP coefficient - r = (omega3-2.)/omega3 + r = (omega_k_minus_1-2.)/omega_k_minus_1 # Method coefficients - delta0 = (4*omega4 - omega3**2)/omega3**3 - beta0 = omega4/omega3**2 - beta3 = omega4**2/omega3**2 + delta0 = (4*omega_k - omega_k_minus_1**2)/omega_k_minus_1**3 + beta0 = omega_k/omega_k_minus_1**2 + beta_k_minus_1 = omega_k**2/omega_k_minus_1**2 - state.q = beta3*(r*state.q + self.dt*self.dq_dt[-1]) + \ - (r*beta0 + delta0)*self._registers[0].q + beta0*self.dt*self.dq_dt[0] + state.q = beta_k_minus_1*(r*state.q + self.dt*self.dq_dt[-1]) + \ + (r*beta0 + delta0)*self._registers[-num_steps].q + beta0*self.dt*self.dq_dt[-num_steps] self.dt_old = self.dt - elif self.time_integrator == 'SSPLMM53': - if step_index == 1: - # Store initial condition - self.save_init_sol(state) - if step_index < 5: - # Use SSP22 method for starting values - self.sspcoeff0 = self._sspcoeff['SSP22'] - self._registers[0].q = state.q + self.dt*self.dq_dt[-1] - self._registers[0].t = state.t + self.dt - - if self.call_before_step_each_stage: - self.before_step(self,self._registers[0]) - state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) - else: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt() - # Correct cfl number based on the current step size. - cfl = self.cfl.get_cached_max() - self.cfl.set_global_max(self.dt / self.dt_old * cfl) - - omega4 = sum(self.prev_dt_values[1:])/self.dt - omega5 = omega4 + 1. - # SSP coefficient - r = (omega4-2.)/omega4 - # Method coefficients - delta0 = (4*omega5 - omega4**2)/omega4**3 - beta0 = omega5/omega4**2 - beta4 = omega5**2/omega4**2 - - state.q = beta4*(r*state.q + self.dt*self.dq_dt[-1]) + \ - (r*beta0 + delta0)*self._registers[-5].q + beta0*self.dt*self.dq_dt[-5] - self.dt_old = self.dt elif self.time_integrator == 'LMM': + assert self.dt_variable == False if step_index == 1: # Save initial solution self.save_init_sol(state) From 5937ea23f51bfe69e07d39685352f091f0fba5d2 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Wed, 25 Mar 2015 14:54:35 +0300 Subject: [PATCH 41/46] Combine code for all SSPLMM methods. --- .../test_acoustics.py | 2 +- .../test_2d_acoustics.py | 2 +- .../verify_sharpclaw_lmm.txt | 200 +++++++++--------- examples/advection_1d/test_advection.py | 2 +- src/pyclaw/sharpclaw/solver.py | 64 +++--- 5 files changed, 127 insertions(+), 143 deletions(-) diff --git a/examples/acoustics_1d_homogeneous/test_acoustics.py b/examples/acoustics_1d_homogeneous/test_acoustics.py index bd0c2597f..5f8508aa6 100644 --- a/examples/acoustics_1d_homogeneous/test_acoustics.py +++ b/examples/acoustics_1d_homogeneous/test_acoustics.py @@ -40,7 +40,7 @@ def acoustics_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSP104', disable_output=True) - sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00184), + sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00169), kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSPLMM32', disable_output=True) diff --git a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py index 7dc630dee..72b678760 100644 --- a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py +++ b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py @@ -16,7 +16,7 @@ def verify(claw): test_pressure = test_q[0,:,:] thisdir = os.path.dirname(__file__) expected_pressure = np.loadtxt(os.path.join(thisdir,data_filename)) - return check_diff(expected_pressure, test_pressure, reltol=3e-3, + return check_diff(expected_pressure, test_pressure, reltol=1e-3, delta=claw.solution.grid.delta) else: return diff --git a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt index 4f4f32757..3384308cf 100644 --- a/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt +++ b/examples/acoustics_2d_homogeneous/verify_sharpclaw_lmm.txt @@ -1,100 +1,100 @@ -2.982094527792070697e-24 6.370095171528999289e-25 -1.419662798076335887e-23 1.368179127868806802e-23 4.373648564246427073e-23 -9.984687459442709038e-23 -8.551352709466978301e-23 4.686186642887070303e-22 2.187148436005887181e-24 -1.807513114547370608e-21 9.042155153140128827e-22 6.724230776596548082e-21 -4.354150084340223729e-21 -2.260927076137256085e-20 8.270343438817661797e-20 1.060004067866805226e-18 1.096285290772472612e-17 1.026346271316410880e-16 8.637637762166049228e-16 6.533275050838974513e-15 4.451999862718469218e-14 2.739500129398802671e-13 1.525917657560746728e-12 7.713421285703351997e-12 3.547983523571502712e-11 1.489078015830597064e-10 5.717520392921363697e-10 2.013347288213576501e-09 6.516011058540801585e-09 1.941664651195535975e-08 5.334361859445634664e-08 1.352039020298065197e-07 3.164507414007585969e-07 6.864235696464230978e-07 1.387281344803986439e-06 2.625541319083509148e-06 4.672628864035068482e-06 7.848341169926912857e-06 1.249051289864119386e-05 1.891101317773885045e-05 2.734058418026198752e-05 3.786064853015740599e-05 5.033832547939545455e-05 6.437963602877142682e-05 7.931657186459713715e-05 9.421824675139061278e-05 1.080259073846883387e-04 1.196291924028512765e-04 1.280135167731651764e-04 1.324110915436975931e-04 1.324110915436976744e-04 1.280135167731652306e-04 1.196291924028512358e-04 1.080259073846883794e-04 9.421824675139062633e-05 7.931657186459720491e-05 6.437963602877145393e-05 5.033832547939545455e-05 3.786064853015741276e-05 2.734058418026199768e-05 1.891101317773885045e-05 1.249051289864119556e-05 7.848341169926911163e-06 4.672628864035068482e-06 2.625541319083507877e-06 1.387281344803984956e-06 6.864235696464218272e-07 3.164507414007578557e-07 1.352039020298059903e-07 5.334361859445606871e-08 1.941664651195524725e-08 6.516011058540765189e-09 2.013347288213564920e-09 5.717520392921333711e-10 1.489078015830591635e-10 3.547983523571486556e-11 7.713421285703319685e-12 1.525917657560740670e-12 2.739500129398826400e-13 4.451999862718740587e-14 6.533275050839413120e-15 8.637637762158104412e-16 1.026346271309584399e-16 1.096285290758085916e-17 1.060004068047516388e-18 8.270343457158990807e-20 -2.260927069325563863e-20 -4.354150117108642043e-21 6.724230718179355361e-21 9.042154998052165623e-22 -1.807513096224947309e-21 2.187160335203285032e-24 4.686186607024157657e-22 -8.551353204385410672e-23 -9.984687421344733767e-23 4.373648730795420231e-23 1.368179135343385997e-23 -1.419662847911578463e-23 6.370094281560332633e-25 2.982094650113152161e-24 -6.370095171528999289e-25 -1.620673931802634579e-23 1.351736831408842266e-23 5.330791573826797122e-23 -1.130421786176267674e-22 -1.094900365961309377e-22 5.575539211902372529e-22 3.431705828631772553e-24 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-7.016612805319809139e-21 -2.599393364970258460e-21 2.065874505251464260e-21 5.137259751414709918e-22 -5.789724759469593955e-22 -5.736217358594598463e-23 1.493255890230698863e-22 -1.103014255489393319e-23 -3.244319380297992565e-23 7.128496816402803533e-24 diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 7e89a4671..27ecd447f 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,7 +32,7 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(9.224735e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(8.50256e-05), kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index e8f329506..d7df4265a 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -328,38 +328,13 @@ def step(self,solution): state.q += self.b[j]*self._registers[j].q ### Linear multistep methods ### - elif self.time_integrator == 'SSPLMM32': - if step_index == 1: - # Save initial condition - self.save_init_sol(state) - if step_index < 3: - # Use Euler method for starting values - self.sspcoeff0 = self._sspcoeff['Euler'] - state.q += self.dt*dq_dt - else: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] - self.set_dt() - # Compute cfl number based on the current step size. - cfl = self.cfl.get_cached_max() - self.cfl.set_global_max(self.dt / self.dt_old * cfl) - - omega2 = sum(self.prev_dt_values[1:])/self.dt - # SSP coefficient - r = (omega2-1.)/omega2 - # Method coefficients - delta = 1./omega2**2 - beta = (omega2+1.)/omega2 - - state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q - self.dt_old = self.dt - - elif self.time_integrator in ['SSPLMM43', 'SSPLMM53']: - num_steps = self.time_integrator[-2] + elif self.time_integrator in ['SSPLMM32', 'SSPLMM43', 'SSPLMM53']: + num_steps = int(self.time_integrator[-2]) if step_index == 1: # Save initial condition self.save_init_sol(state) if step_index < num_steps: - # Use SSP22 method for starting values + # Use SSP22 Runge-Kutta method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] self._registers[0].q = state.q + self.dt*self.dq_dt[-1] self._registers[0].t = state.t + self.dt @@ -370,21 +345,30 @@ def step(self,solution): else: self.sspcoeff0 = self._sspcoeff[self.time_integrator] self.set_dt() - # Compute cfl number based on the current step size. cfl = self.cfl.get_cached_max() self.cfl.set_global_max(self.dt / self.dt_old * cfl) - omega_k_minus_1 = sum(self.prev_dt_values[1:])/self.dt - omega_k = omega_k_minus_1 + 1. - # SSP coefficient - r = (omega_k_minus_1-2.)/omega_k_minus_1 - # Method coefficients - delta0 = (4*omega_k - omega_k_minus_1**2)/omega_k_minus_1**3 - beta0 = omega_k/omega_k_minus_1**2 - beta_k_minus_1 = omega_k**2/omega_k_minus_1**2 - - state.q = beta_k_minus_1*(r*state.q + self.dt*self.dq_dt[-1]) + \ - (r*beta0 + delta0)*self._registers[-num_steps].q + beta0*self.dt*self.dq_dt[-num_steps] + if self.time_integrator == 'SSPLMM32': + omega2 = sum(self.prev_dt_values[1:])/self.dt + # SSP coefficient + r = (omega2-1.)/omega2 + # Method coefficients + delta = 1./omega2**2 + beta = (omega2+1.)/omega2 + + state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q + else: + omega_k_minus_1 = sum(self.prev_dt_values[1:])/self.dt + omega_k = omega_k_minus_1 + 1. + # SSP coefficient + r = (omega_k_minus_1-2.)/omega_k_minus_1 + # Method coefficients + delta0 = (4*omega_k - omega_k_minus_1**2)/omega_k_minus_1**3 + beta0 = omega_k/omega_k_minus_1**2 + beta_k_minus_1 = omega_k**2/omega_k_minus_1**2 + + state.q = beta_k_minus_1*(r*state.q + self.dt*self.dq_dt[-1]) + \ + (r*beta0 + delta0)*self._registers[-num_steps].q + beta0*self.dt*self.dq_dt[-num_steps] self.dt_old = self.dt From d6dd6386eefcab1552e9d8ba8b3e0749202c1da9 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Wed, 25 Mar 2015 15:14:07 +0300 Subject: [PATCH 42/46] clean up comments and reorder if statements in sharpclaw/solver.py --- src/pyclaw/sharpclaw/solver.py | 40 +++++++++++++--------------------- 1 file changed, 15 insertions(+), 25 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index d7df4265a..e41559a9f 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -286,6 +286,8 @@ def step(self,solution): if 'LMM' in self.time_integrator: self.update_saved_values(state,dq_dt,step_index) + if step_index == 1: + self.save_init_sol(state) ### Runge-Kutta methods ### if self.time_integrator == 'Euler': @@ -310,7 +312,7 @@ def step(self,solution): elif self.time_integrator == 'RK': # General explicit RK with specified coefficients - # This is pulled out of the loop to use dq_dt + # This is pulled out of the loop in order to use dq_dt self._registers[0].q = self.dt*dq_dt self._registers[0].t = state.t @@ -330,9 +332,6 @@ def step(self,solution): ### Linear multistep methods ### elif self.time_integrator in ['SSPLMM32', 'SSPLMM43', 'SSPLMM53']: num_steps = int(self.time_integrator[-2]) - if step_index == 1: - # Save initial condition - self.save_init_sol(state) if step_index < num_steps: # Use SSP22 Runge-Kutta method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] @@ -350,19 +349,16 @@ def step(self,solution): if self.time_integrator == 'SSPLMM32': omega2 = sum(self.prev_dt_values[1:])/self.dt - # SSP coefficient - r = (omega2-1.)/omega2 - # Method coefficients + r = (omega2-1.)/omega2 # SSP coefficient + delta = 1./omega2**2 beta = (omega2+1.)/omega2 - state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q else: omega_k_minus_1 = sum(self.prev_dt_values[1:])/self.dt omega_k = omega_k_minus_1 + 1. - # SSP coefficient - r = (omega_k_minus_1-2.)/omega_k_minus_1 - # Method coefficients + r = (omega_k_minus_1-2.)/omega_k_minus_1 # SSP coefficient + delta0 = (4*omega_k - omega_k_minus_1**2)/omega_k_minus_1**3 beta0 = omega_k/omega_k_minus_1**2 beta_k_minus_1 = omega_k**2/omega_k_minus_1**2 @@ -374,12 +370,8 @@ def step(self,solution): elif self.time_integrator == 'LMM': assert self.dt_variable == False - if step_index == 1: - # Save initial solution - self.save_init_sol(state) if step_index < len(self._registers): - # Using SSP104 for previous step values - state.q = self.ssp104(state,dq_dt) + state.q = self.ssp104(state,dq_dt) # Use SSP104 for starting values else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*dq_dt @@ -433,7 +425,7 @@ def update_saved_values(self,state,dq_dt,step_index): r""" Updates lists of saved function evaluations, solution values, dt and dtFE for LMMs. For 3rd-order SSPLMM additional conditions are checked if self.check_lmm_cond is set to True. - In such case, if the conditions are violated the solution is discarded and the previous step is repeated. + If these conditions are violated, the step is rejected. """ if (self.prev_dt_values == []): # This only happens at the very beginning of the computation @@ -443,24 +435,22 @@ def update_saved_values(self,state,dq_dt,step_index): cfl = self.cfl.get_cached_max() dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] self.prev_dtFE_values.append(dtFE) - elif self.accept_step == True: + elif self.accept_step == True: # Previous step was accepted if 'SSPLMM' in self.time_integrator: cfl = self.cfl.get_cached_max() dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] - if step_index <= len(self._registers): + if (self.time_integrator in ['SSPLMM43','SSPLMM53']) and self.check_lmm_cond: + self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) + if not self.accept_step: return + + if step_index <= len(self._registers): # Startup if (self.time_integrator in ['SSPLMM43','SSPLMM53']): - if self.check_lmm_cond: - self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) - if not self.accept_step: return self.dq_dt.append(dq_dt) self.prev_dt_values.append(self.dt_old) self.prev_dtFE_values.append(dtFE) else: if (self.time_integrator in ['SSPLMM43','SSPLMM53']): - if self.check_lmm_cond: - self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) - if not self.accept_step: return self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] self.dq_dt[-1] = dq_dt From eb7d715fb74f535bf195cbe79e957128809ff001 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Wed, 25 Mar 2015 15:50:59 +0300 Subject: [PATCH 43/46] move step rewinding up into update_saved_values --- src/pyclaw/sharpclaw/solver.py | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index e41559a9f..8ca5af1ef 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -442,7 +442,11 @@ def update_saved_values(self,state,dq_dt,step_index): if (self.time_integrator in ['SSPLMM43','SSPLMM53']) and self.check_lmm_cond: self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) - if not self.accept_step: return + if not self.accept_step: + state.q[:] = self._registers[-1].q + state.t = self._registers[-1].t + self.status['numsteps'] -= 1 + return if step_index <= len(self._registers): # Startup if (self.time_integrator in ['SSPLMM43','SSPLMM53']): @@ -487,17 +491,11 @@ def check_3rd_ord_cond(self,state,step_index,dtFE): rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 if self.dt > rho * dtFE: accept_step = False - state.q[:] = self._registers[-1].q - state.t = self._registers[-1].t - self.status['numsteps'] -= 1 rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False - state.q[:] = self._registers[-1].q - state.t = self._registers[-1].t - self.status['numsteps'] -= 1 return accept_step From 30953915a5c37d99125650d9016a9ec26bdb5664 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Thu, 26 Mar 2015 11:23:58 +0300 Subject: [PATCH 44/46] Make SSPLMMs generic for arbitrary number of steps --- src/pyclaw/sharpclaw/solver.py | 85 +++++++++++++++++++--------------- 1 file changed, 47 insertions(+), 38 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index 8ca5af1ef..c24b84e46 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -199,6 +199,8 @@ def __init__(self,riemann_solver=None,claw_package=None): self.sspcoeff0 = None self.alpha = None self.beta = None + self.lmm_steps = 4 + self.sspcoeff = None self.dq_dt = [] self.prev_dt_values = [] self.prev_dtFE_values = [] @@ -227,18 +229,34 @@ def setup(self,solution): if self.time_integrator == 'LMM': assert self.dt_variable == False, \ - 'Must set solver.dt_variable=False for LMM integrator' - self._allocate_registers(solution) - self._set_mthlim() + 'Must set solver.dt_variable=False for LMM integrator.' try: - if self.cfl_max is None: - self.cfl_desired = self._cfl_default[self.time_integrator][0] - self.cfl_max = self._cfl_default[self.time_integrator][1] - if self.cfl_desired is None: - self.cfl_desired = 0.9*self.cfl_max + if 'SSPLMM' in self.time_integrator: + if self.time_integrator == 'SSPLMMk2': + assert 3 <= self.lmm_steps, \ + 'Must set solver.lmm_steps greater than 2 for 2nd order SSPLMM integrator.' + self.sspcoeff = (self.lmm_steps - 2.)/(self.lmm_steps - 1.) + elif self.time_integrator == 'SSPLMMk3': + assert 4 <= self.lmm_steps <= 5, \ + 'Must set solver.lmm_steps equal to 4 or 5 for 3rd order SSPLMM integrator.' + self.sspcoeff = (self.lmm_steps - 3.)/(self.lmm_steps - 1.) + if self.cfl_max is None: + self.cfl_desired = 0.48*self.sspcoeff + self.cfl_max = 0.5*self.sspcoeff + if self.cfl_desired is None: + self.cfl_desired = 0.9*self.cfl_max + else: + if self.cfl_max is None: + self.cfl_desired = self._cfl_default[self.time_integrator][0] + self.cfl_max = self._cfl_default[self.time_integrator][1] + if self.cfl_desired is None: + self.cfl_desired = 0.9*self.cfl_max except KeyError: raise KeyError('Maximum CFL number is not provided.') + self._allocate_registers(solution) + self._set_mthlim() + state = solution.states[0] if self.kernel_language=='Fortran': @@ -286,8 +304,6 @@ def step(self,solution): if 'LMM' in self.time_integrator: self.update_saved_values(state,dq_dt,step_index) - if step_index == 1: - self.save_init_sol(state) ### Runge-Kutta methods ### if self.time_integrator == 'Euler': @@ -330,8 +346,8 @@ def step(self,solution): state.q += self.b[j]*self._registers[j].q ### Linear multistep methods ### - elif self.time_integrator in ['SSPLMM32', 'SSPLMM43', 'SSPLMM53']: - num_steps = int(self.time_integrator[-2]) + elif self.time_integrator in ['SSPLMMk2', 'SSPLMMk3']: + num_steps = len(self._registers) if step_index < num_steps: # Use SSP22 Runge-Kutta method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] @@ -342,18 +358,18 @@ def step(self,solution): self.before_step(self,self._registers[0]) state.q = 0.5*(state.q + self._registers[0].q + self.dq(self._registers[0])) else: - self.sspcoeff0 = self._sspcoeff[self.time_integrator] + self.sspcoeff0 = self.sspcoeff self.set_dt() cfl = self.cfl.get_cached_max() self.cfl.set_global_max(self.dt / self.dt_old * cfl) - if self.time_integrator == 'SSPLMM32': + if self.time_integrator == 'SSPLMMk2': omega2 = sum(self.prev_dt_values[1:])/self.dt r = (omega2-1.)/omega2 # SSP coefficient delta = 1./omega2**2 beta = (omega2+1.)/omega2 - state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-3].q + state.q = beta*(r*state.q + self.dt*dq_dt) + delta*self._registers[-num_steps].q else: omega_k_minus_1 = sum(self.prev_dt_values[1:])/self.dt omega_k = omega_k_minus_1 + 1. @@ -367,9 +383,7 @@ def step(self,solution): (r*beta0 + delta0)*self._registers[-num_steps].q + beta0*self.dt*self.dq_dt[-num_steps] self.dt_old = self.dt - elif self.time_integrator == 'LMM': - assert self.dt_variable == False if step_index < len(self._registers): state.q = self.ssp104(state,dq_dt) # Use SSP104 for starting values else: @@ -429,18 +443,20 @@ def update_saved_values(self,state,dq_dt,step_index): """ if (self.prev_dt_values == []): # This only happens at the very beginning of the computation + self._registers[-1].q[:] = state.q + self._registers[-1].t = state.t self.dq_dt.append(dq_dt) self.prev_dt_values.append(0.) # Not used if 'SSPLMM' in self.time_integrator: cfl = self.cfl.get_cached_max() - dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] + dtFE = self.dt / cfl * self.cfl_max / self.sspcoeff self.prev_dtFE_values.append(dtFE) elif self.accept_step == True: # Previous step was accepted if 'SSPLMM' in self.time_integrator: cfl = self.cfl.get_cached_max() - dtFE = self.dt / cfl * self.cfl_max / self._sspcoeff[self.time_integrator] + dtFE = self.dt / cfl * self.cfl_max / self.sspcoeff - if (self.time_integrator in ['SSPLMM43','SSPLMM53']) and self.check_lmm_cond: + if self.time_integrator == 'SSPLMMk3' and self.check_lmm_cond: self.accept_step = self.check_3rd_ord_cond(state,step_index,dtFE) if not self.accept_step: state.q[:] = self._registers[-1].q @@ -449,12 +465,12 @@ def update_saved_values(self,state,dq_dt,step_index): return if step_index <= len(self._registers): # Startup - if (self.time_integrator in ['SSPLMM43','SSPLMM53']): + if self.time_integrator == 'SSPLMMk3': self.dq_dt.append(dq_dt) self.prev_dt_values.append(self.dt_old) self.prev_dtFE_values.append(dtFE) else: - if (self.time_integrator in ['SSPLMM43','SSPLMM53']): + if self.time_integrator == 'SSPLMMk3': self.dq_dt = self.dq_dt[1:] + self.dq_dt[:1] self.dq_dt[-1] = dq_dt @@ -488,11 +504,11 @@ def check_3rd_ord_cond(self,state,step_index,dtFE): accept_step = True if step_index <= len(self._registers): - rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 + rho = 0.6 if len(self._registers) == 4 else 0.57 if self.dt > rho * dtFE: accept_step = False - rhoFE = 0.9 if self.time_integrator == 'SSPLMM43' else 0.962 + rhoFE = 0.9 if len(self._registers) == 4 else 0.962 dtFEm1 = self.prev_dtFE_values[-1] if rhoFE * dtFEm1 > dtFE or dtFE > dtFEm1 / rhoFE: accept_step = False @@ -500,12 +516,6 @@ def check_3rd_ord_cond(self,state,step_index,dtFE): return accept_step - def save_init_sol(self,state): - r"""Save initial solution for SSPLMM methods.""" - self._registers[-1].q[:] = state.q - self._registers[-1].t = state.t - - def _set_mthlim(self): self._mthlim = self.limiters if not isinstance(self.limiters,list): self._mthlim=[self._mthlim] @@ -590,9 +600,8 @@ def _allocate_registers(self,solution): elif self.time_integrator == 'SSP33': nregisters=1 elif self.time_integrator == 'SSP104': nregisters=2 elif self.time_integrator == 'RK': nregisters=len(self.b)+1 - elif self.time_integrator == 'SSPLMM32': nregisters=3 - elif self.time_integrator == 'SSPLMM43': nregisters=4 - elif self.time_integrator == 'SSPLMM53': nregisters=5 + elif self.time_integrator == 'SSPLMMk2': nregisters=self.lmm_steps + elif self.time_integrator == 'SSPLMMk3': nregisters=self.lmm_steps elif self.time_integrator == 'LMM': nregisters=len(self.alpha) else: raise Exception('Unrecognized time integrator: '+self.time_integrator) @@ -623,7 +632,7 @@ def accept_reject_step(self,state): if self.time_integrator == 'LMM': sspcoeff_ratio = 1. else: - sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] + sspcoeff_ratio = self.sspcoeff0/self.sspcoeff if cfl > sspcoeff_ratio * self.cfl_max: accept_step = False @@ -647,7 +656,7 @@ def set_dt(self): mu = min([self.prev_dtFE_values[i] for i in range(s)]) H = sum(self.prev_dt_values[1:]) self.dt = H * mu / (H + (p-1)*mu) - elif self.time_integrator in ['SSPLMM43','SSPLMM53'] and self.check_lmm_cond: + elif self.time_integrator == 'SSPLMMk3' and self.check_lmm_cond: self.dt = 0.5*self.dt @@ -664,10 +673,10 @@ def get_dt_new(self): if step_index < len(self._registers): # Step-size update of starting methods - sspcoeff_ratio = self.sspcoeff0/self._sspcoeff[self.time_integrator] + sspcoeff_ratio = self.sspcoeff0/self.sspcoeff self.dt = sspcoeff_ratio * self.dt * self.cfl_desired / cfl - if (self.time_integrator in ['SSPLMM43','SSPLMM53']) and self.check_lmm_cond: - rho = 0.6 if self.time_integrator == 'SSPLMM43' else 0.57 + if self.time_integrator == 'SSPLMMk3' and self.check_lmm_cond: + rho = 0.6 if len(self._registers)== 4 else 0.57 self.dt = rho * self.dt # Step-size update for RK methods From deb71d0021c69b44d8f37df7d2f7335fb9464220 Mon Sep 17 00:00:00 2001 From: Yiannis Hadjimichael Date: Thu, 26 Mar 2015 11:29:56 +0300 Subject: [PATCH 45/46] Update nosetests: include tests for 3rd-order SSPLMM. --- examples/acoustics_1d_homogeneous/acoustics_1d.py | 8 ++++---- examples/acoustics_1d_homogeneous/test_acoustics.py | 4 ++-- examples/acoustics_2d_homogeneous/acoustics_2d.py | 3 ++- examples/acoustics_2d_homogeneous/test_2d_acoustics.py | 2 +- examples/acoustics_2d_variable/acoustics_2d_interface.py | 4 ++-- .../acoustics_2d_variable/test_acoustics_2d_variable.py | 2 +- examples/advection_1d/advection_1d.py | 3 +++ examples/advection_1d/test_advection.py | 4 ++-- 8 files changed, 17 insertions(+), 13 deletions(-) diff --git a/examples/acoustics_1d_homogeneous/acoustics_1d.py b/examples/acoustics_1d_homogeneous/acoustics_1d.py index e654d0019..edc6cb711 100644 --- a/examples/acoustics_1d_homogeneous/acoustics_1d.py +++ b/examples/acoustics_1d_homogeneous/acoustics_1d.py @@ -21,10 +21,8 @@ from numpy import sqrt, exp, cos from clawpack import riemann -def setup(use_petsc=False, kernel_language='Fortran', solver_type='classic', - outdir='./_output', ptwise=False, weno_order=5, - time_integrator='SSP104', - disable_output=False): +def setup(use_petsc=False, kernel_language='Fortran', solver_type='classic', outdir='./_output', ptwise=False, \ + weno_order=5, time_integrator='SSP104', disable_output=False): if use_petsc: import clawpack.petclaw as pyclaw @@ -47,6 +45,8 @@ def setup(use_petsc=False, kernel_language='Fortran', solver_type='classic', solver = pyclaw.SharpClawSolver1D(riemann_solver) solver.weno_order=weno_order solver.time_integrator=time_integrator + if time_integrator == 'SSPLMMk3': + solver.lmm_steps = 4 else: raise Exception('Unrecognized value of solver_type.') solver.kernel_language=kernel_language diff --git a/examples/acoustics_1d_homogeneous/test_acoustics.py b/examples/acoustics_1d_homogeneous/test_acoustics.py index 5f8508aa6..3bf139abb 100644 --- a/examples/acoustics_1d_homogeneous/test_acoustics.py +++ b/examples/acoustics_1d_homogeneous/test_acoustics.py @@ -40,9 +40,9 @@ def acoustics_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw', time_integrator='SSP104', disable_output=True) - sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.00169), + sharp_tests_lmm = gen_variants(acoustics_1d.setup, verify_expected(0.000231), kernel_languages=('Python','Fortran'), solver_type='sharpclaw', - time_integrator='SSPLMM32', disable_output=True) + time_integrator='SSPLMMk3', disable_output=True) weno_tests = gen_variants(acoustics_1d.setup, verify_expected(0.000153), kernel_languages=('Fortran',), solver_type='sharpclaw', diff --git a/examples/acoustics_2d_homogeneous/acoustics_2d.py b/examples/acoustics_2d_homogeneous/acoustics_2d.py index 6c62b3deb..0e30f3dd3 100755 --- a/examples/acoustics_2d_homogeneous/acoustics_2d.py +++ b/examples/acoustics_2d_homogeneous/acoustics_2d.py @@ -43,7 +43,8 @@ def setup(kernel_language='Fortran', use_petsc=False, outdir='./_output', if solver.time_integrator=='SSP104': solver.cfl_max = 0.5 solver.cfl_desired = 0.45 - elif solver.time_integrator=='SSPLMM32': + elif solver.time_integrator=='SSPLMMk2': + solver.lmm_steps = 3 solver.lim_type = 2 solver.cfl_max = 0.25 solver.cfl_desired = 0.24 diff --git a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py index 72b678760..0117dd430 100644 --- a/examples/acoustics_2d_homogeneous/test_2d_acoustics.py +++ b/examples/acoustics_2d_homogeneous/test_2d_acoustics.py @@ -37,7 +37,7 @@ def verify(claw): sharp_tests_lmm = gen_variants(acoustics_2d.setup, verify_data('verify_sharpclaw_lmm.txt'), kernel_languages=('Fortran',), solver_type='sharpclaw', - time_integrator='SSPLMM32', disable_output=True) + time_integrator='SSPLMMk2', disable_output=True) from itertools import chain for test in chain(classic_tests, ptwise_tests, sharp_tests_rk, sharp_tests_lmm): diff --git a/examples/acoustics_2d_variable/acoustics_2d_interface.py b/examples/acoustics_2d_variable/acoustics_2d_interface.py index 6184bd8af..110f8f99d 100755 --- a/examples/acoustics_2d_variable/acoustics_2d_interface.py +++ b/examples/acoustics_2d_variable/acoustics_2d_interface.py @@ -40,7 +40,8 @@ def setup(kernel_language='Fortran', use_petsc=False, outdir='./_output', elif solver_type=='sharpclaw': solver=pyclaw.SharpClawSolver2D(riemann.vc_acoustics_2D) solver.time_integrator=time_integrator - if time_integrator=='SSPLMM32': + if time_integrator=='SSPLMMk2': + solver.lmm_steps = 3 solver.cfl_max = 0.25 solver.cfl_desired = 0.24 @@ -149,6 +150,5 @@ def mark_interface(current_data): if __name__=="__main__": - import sys from clawpack.pyclaw.util import run_app_from_main output = run_app_from_main(setup,setplot) diff --git a/examples/acoustics_2d_variable/test_acoustics_2d_variable.py b/examples/acoustics_2d_variable/test_acoustics_2d_variable.py index 82d97bd92..1de0d0680 100644 --- a/examples/acoustics_2d_variable/test_acoustics_2d_variable.py +++ b/examples/acoustics_2d_variable/test_acoustics_2d_variable.py @@ -41,7 +41,7 @@ def verify_acoustics(controller, solver_type='classic'): sharp_tests_lmm = gen_variants(acoustics_2d_interface.setup, verify_func, lim_type=1, solver_type='sharpclaw', - time_integrator='SSPLMM32', + time_integrator='SSPLMMk2', disable_output=True, num_cells=(50, 50)) diff --git a/examples/advection_1d/advection_1d.py b/examples/advection_1d/advection_1d.py index 4f2bef408..35fa69736 100755 --- a/examples/advection_1d/advection_1d.py +++ b/examples/advection_1d/advection_1d.py @@ -38,6 +38,9 @@ def setup(nx=100, kernel_language='Python', use_petsc=False, solver_type='classi solver = pyclaw.SharpClawSolver1D(riemann_solver) solver.weno_order = weno_order solver.time_integrator = time_integrator + if time_integrator == 'SSPLMMk3': + solver.lmm_steps = 5 + solver.check_lmm_cond = True else: raise Exception('Unrecognized value of solver_type.') solver.kernel_language = kernel_language diff --git a/examples/advection_1d/test_advection.py b/examples/advection_1d/test_advection.py index 27ecd447f..0e8fb6d93 100644 --- a/examples/advection_1d/test_advection.py +++ b/examples/advection_1d/test_advection.py @@ -32,9 +32,9 @@ def advection_verify(claw): kernel_languages=('Python','Fortran'), solver_type='sharpclaw',time_integrator='SSP104', outdir=None) - sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(8.50256e-05), + sharp_tests_lmm = gen_variants(advection_1d.setup, verify_expected(1.500727e-05), kernel_languages=('Python','Fortran'), - solver_type='sharpclaw',time_integrator='SSPLMM32', outdir=None) + solver_type='sharpclaw',time_integrator='SSPLMMk3', outdir=None) weno_tests = gen_variants(advection_1d.setup, verify_expected(7.489618e-06), kernel_languages=('Fortran',), solver_type='sharpclaw', From 7dfd2eddd237df6075a02ede3d32b7098109c104 Mon Sep 17 00:00:00 2001 From: David Ketcheson Date: Thu, 26 Mar 2015 15:56:38 +0300 Subject: [PATCH 46/46] use solver.lmm_steps as definitive value --- src/pyclaw/sharpclaw/solver.py | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/src/pyclaw/sharpclaw/solver.py b/src/pyclaw/sharpclaw/solver.py index c24b84e46..eed874327 100644 --- a/src/pyclaw/sharpclaw/solver.py +++ b/src/pyclaw/sharpclaw/solver.py @@ -347,7 +347,7 @@ def step(self,solution): ### Linear multistep methods ### elif self.time_integrator in ['SSPLMMk2', 'SSPLMMk3']: - num_steps = len(self._registers) + num_steps = self.lmm_steps if step_index < num_steps: # Use SSP22 Runge-Kutta method for starting values self.sspcoeff0 = self._sspcoeff['SSP22'] @@ -389,8 +389,7 @@ def step(self,solution): else: # Update solution: alpha[-1] and beta[-1] correspond to solution at the previous step state.q = self.alpha[-1]*self._registers[-1].q + self.beta[-1]*self.dt*dq_dt - num_steps = len(self._registers) - for i in range(num_steps-1): + for i in range(self.lmm_steps-1): state.q += self.alpha[i]*self._registers[i].q + self.beta[i]*self.dt*self.dq_dt[i] else: