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frosty

Author: Minah Oh Date: 04/27/2020 Program Description:By using multigrid, this program solves the matrix system Ax=b arising from the Fourier-FEMs applied to the H(div) problem on an axisymmetric domain for Fourier modes not equal to zero.

Details can be found in the following paper: https://doi.org/10.1016/j.jmaa.2020.124209

How to run main.m:

Input:

  1. Make mesh1.mat, mesh2.mat, ... , through the final mesh corresponding to your domain that contains variables [p,e,t,BdyEdges,new_ele] (1) p,e,t has the same format as those created by using Matlab's "initmesh" (2) BdyEdges is a vector of length the same as the number of edges in the mesh. If the i-th edge is on the boundary then BdyEdges(i)=1 and zero otherwise. (3) new_ele is a matrix of size Number of Elements by 3. The i-th row of new_ele saves the three edge numbers that makes the i-th triangle.
  2. Save RHS_r.m, RHS_theta.m, RHS_z.m where F(r,z)=(RHS_r(r,z), RHS_theta(r,z), RHS_z(r,z)) is the input function
  3. n: Fourier_mode of interest not equal to zero.
  4. mesh_level: The final mesh level to solve the Ax=b system.

Output: The soltuion vector x to Ax=b. (x=main(mesh_level,n))

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