Boundary integral multi-trace formulations and Optimised Schwarz Methods

This repository contains the code associated with:

Xavier Claeys and Pierre Marchand (2020). Boundary integral multi-trace formulations and Optimised Schwarz Methods. Computers & Mathematics with Applications, June 2020, Vol. 79, Issue 11, Pages 3241-3256.

Dependencies

C++:

1. CMake
2. Boost

Python:

1. scipy
2. pandas
3. matplotlib

For some reason, computing the spectrum with scipy did not always work and we used matlab in these cases.

Figures

To reproduce the results of the article:

1. Compile the code
   1. mkdir build & cd build
   2. cmake ../
   3. make
2. Create the input data
   1. cd ../scripts
   2. ./gen_meshes.zsh generates the meshes in meshes
   3. ./gen_mat.zsh generates the matrices in output/matrices
3. Create the results
   1. ./gen_iterations.zsh generate the data (number of iterations with number of interfaces )in output/csv
   2. ./gen_residus.zsh generate the data (residual with number of iterations in GMRes )in output/csv
4. Create the figures
   1. ./gen_plot_iterations.zsh generate the figures (number of iterations with number of interfaces )in output/figures
   2. ./gen_plot_residus.zsh generate the figures (residual with number of iterations in GMRes )in output/figures

Concerning the spectrum:

• For Configuration II, you can use
  • python3 compute_spectrum.py --ni 3 --geo non_emboite --type 1
  • python3 plot_spectrum.py --ni 3 --geo non_emboite --type 1

where ni is the number of interfaces and type the setting for $\kappa$

• For Configuration I, you need to
  • convert the matrices to matlab format with python3 to_matlab.py --ni 3 --geo emboite --type 1
  • run compute_spectrum.m with matlab
  • python3 plot_spectrum.py --ni 3 --geo emboite --type 1