On Domain Decomposition Methods with optimized transmission conditions and cross-points

Bruno Després (1) , Anouk Nicolopoulos (1) , Bertrand Thierry (2, 1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CNRS - Centre National de la Recherche Scientifique

We study a mathematical framework for the construction of domain decomposition methods (DDM) for the model Helmholtz equation with high order transmission conditions (TC) and cross-points. A compatibility condition is formulated for cross-points matrices so that the DDM is proved to be convergent under general conditions. The proof is based on a new global energy formulated on the skeleton of the DDM decomposition. It allows to use transmission operators which have a non trivial anti-symmetric part.

Domaines: Analyse numérique [math.NA]

Bruno Després, Anouk Nicolopoulos, Bertrand Thierry. On Domain Decomposition Methods with optimized transmission conditions and cross-points. SIAM Journal on Numerical Analysis, 2022, 60 (5), pp.2482-2507. ⟨hal-03230250⟩