Nonlocal Optimized Schwarz Methods for time-harmonic electromagnetics

TL;DR

This paper presents a new domain decomposition method for time-harmonic Maxwell's equations that guarantees convergence even with complex subdomain partitions, supported by theoretical analysis and numerical results.

Contribution

It introduces a novel nonlocal optimized Schwarz method for Maxwell's equations with automatic subdomain partitioning and cross-point handling, including convergence guarantees and analysis.

Findings

Guaranteed convergence of the method.

Effective transmission matrices influence convergence.

Numerical results validate the approach.

Abstract

We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is guaranteed and we present a complete analysis of the matrix form of the method. The method involves transmission matrices responsible for imposing coupling between subdomains. We discuss the choice of such matrices, their construction and the impact of this choice on the convergence of the domain decomposition algorithm. Numerical results and algorithms are provided.