+ Geometric predicates for unconditionally robust elastodynamics simulation
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+ Daniele Panozzo, Courant Institute of Mathematical Sciences in New York University
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+ The numerical solution of partial differential equations (PDE) is
+ ubiquitously used for physical simulation in scientific computing and
+ engineering. Ideally, a PDE solver should be opaque: the user provides
+ as input the domain boundary, boundary conditions, and the governing
+ equations, and the code returns an evaluator that can compute the
+ value of the solution at any point of the input domain. This is
+ surprisingly far from being the case for all existing open-source or
+ commercial software, despite the research efforts in this direction
+ and the large academic and industrial interest. To a large extent,
+ this is due to lack of robustness in geometric algorithms used to
+ create the discretization, detect collisions, and evaluate element
+ validity.
+ I will present the incremental potential contact simulation paradigm,
+ which provides strong robustness guarantees in simulation codes,
+ ensuring, for the first time, validity of the trajectories accounting
+ for floating point rounding errors over an entire elastodynamic
+ simulation with contact. A core part of this approach is the use of a
+ conservative line-search to check for collisions between geometric
+ primitives and for ensuring validity of the deforming elements over
+ linear trajectories.
+ I will discuss both problems in depth, showing that SOTA approaches
+ favor numerical efficiency but are unfortunately not robust to
+ floating point rounding, leading to major failures in simulation. I
+ will then present an alternative approach based on judiciously using
+ rational and interval types to ensure provable correctness, while
+ keeping a running time comparable with non-conservative methods.
+ To conclude, I will discuss a set of applications enabled by this
+ approach in microscopy and biomechanics, including traction force
+ estimation on a live zebrafish and efficient modeling and simulation
+ of fibrous materials.
+