A new variant of the Optimised Schwarz Method for arbitrary non-overlapping subdomain partitions

Xavier Claeys (1, 2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations

We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new variant of the Optimized Schwarz Method (OSM) that can accomodate the presence of cross-points in the subdomain partition. This leads to the derivation of a strongly coercive formulation of our Helmholtz problem posed on the union of all interfaces. The corresponding operator takes the form "identity + contraction".

Domaines: Analyse numérique [math.NA]

Xavier Claeys. A new variant of the Optimised Schwarz Method for arbitrary non-overlapping subdomain partitions. ESAIM: Mathematical Modelling and Numerical Analysis, 2020. ⟨hal-03137210⟩