A new sweeping domain decomposition method for elliptic problems

par Bastien Chaudet (Université de Genève)

mardi 12 déc. 2023, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier, La Doua)

In the context of partial differential equations, domain decompositions methods constitute an effective way to build efficient iterative solvers. Among other advantages, they are naturally adapted to run in parallel, and their convergence properties do not depend on the chosen discretization method, nor on the mesh size, since they can be applied at the continuous level. However, in order for these iterative methods to be truly efficient, we must be able to have some control over the number of iterations necessary to reach convergence.

In this presentation, we introduce a new domain decompositon method that converges in a finite number of iterations. For a given set of subdomains, the method relies on a corresponding decomposition of the solution into pseudo-even/odd components (one for each dimension variable). Thanks to this decomposition, we are able to compute exactly the solution in boundary subdomains, and then we can propagate the information step by step towards the center of the domain. For a simple elliptic problem, we prove that the method converges in 1D and 2D for generic sets of regular subdomains. Finally, we illustrate our results with numerical experiments.