Solution of time-harmonic Maxwell's equations by a domain decomposition method based on PML transmission conditions

TL;DR

This paper introduces a domain decomposition method for solving time-harmonic Maxwell's equations using PML as transmission conditions, improving solver efficiency and convergence over traditional absorbing boundary conditions.

Contribution

It presents a novel application of PML as interface transmission conditions in domain decomposition for Maxwell's equations, enhancing computational efficiency.

Findings

PML-based transmission conditions improve convergence rates.

The method outperforms traditional ABC-based approaches.

Efficient solver for large-scale Maxwell's equations.

Abstract

Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In this work we use Perfectly Matched Layers (PML) to increase this efficiency. PML have been widely used to truncate numerical simulations of wave equations due to improving the accuracy of the solution instead of using absorbing boundary conditions (ABCs). Here, we will develop an efficient solver by providing an alternative use of PML as transmission conditions at the interfaces between subdomains in our domain decomposition method. We solve Maxwell's equations and assess the convergence rate of our solutions compared to the situation where absorbing boundary conditions are chosen as transmission conditions.