Schwarz methods for domain decomposition using Isogeoemetric Analaysis:

** Three dimension for Poisson is avialable ** TODO:

Implement B-spline mapping
Handle complex geometries (single patch)
Extend to multipatch geometries

some papers

https://inria.hal.science/hal-02197673/file/paper.pdf

https://doi.org/10.1016/j.cma.2021.114017

https://sci-hub.se/https://doi.org/10.1016/j.cma.2019.07.010

https://arxiv.org/pdf/1502.03756

https://sci-hub.se/https://doi.org/10.1016/bs.hna.2020.09.002

https://www.sciencedirect.com/science/article/abs/pii/S0167839618300396

Please install pyccel and start enjoying your research with a simple implementation using simplines

For your analysis You can find and install the following packages from the url

For pyccel :

https://github.com/pyccel/pyccel

For simplines :

https://github.com/Bahari95/simplines

Some Examples:

The 1D Poisson equation using Dirichlet boundary conditions in DDM: solution evolution

The 2D Helmholtz equation with wave number K = 20 using Dirichlet in DDM

https://doi.org/10.1016/j.cma.2018.02.020

(left) real solution evolution (right) solution for the last iteration