Non-self adjoint impedance in Generalized Optimized Schwarz Methods

TL;DR

This paper develops a convergence theory for Generalized Optimized Schwarz Methods using non-self adjoint impedance operators, accommodating complex domain partitions and extending previous self-adjoint impedance results.

Contribution

It introduces a convergence framework for methods with non-local exchange operators and non-self-adjoint impedance, addressing arbitrary domain shapes and cross-points.

Findings

Convergence theory for non-self adjoint impedance operators

Extension of existing self-adjoint impedance results

Handles arbitrary domain partitions with cross-points

Abstract

We present a convergence theory for Optimized Schwarz Methods that rely on a non-local exchange operator and covers the case of coercive possibly non-self-adjoint impedance operators. This analysis also naturally deals with the presence of cross-points in subdomain partitions of arbitrary shape. In the particular case of self-adjoint impedance, we recover the theory proposed in [Claeys & Parolin, 2021].