Stability and convergence analysis of a domain decomposition FE/FD method for the Maxwell's equations in time domain

TL;DR

This paper presents a stability and convergence analysis of a domain decomposition FE/FD method tailored for time-dependent Maxwell's equations, supported by numerical validation of theoretical convergence rates.

Contribution

It introduces a novel stability and convergence framework for a semi-discrete FE/FD approach applied to Maxwell's equations with explicit schemes and domain decomposition.

Findings

Numerical examples confirm theoretical convergence rates.

The method demonstrates stability across various domain configurations.

Explicit schemes are effectively integrated within the domain decomposition framework.

Abstract

Stability and convergence analysis for the domain decomposition finite element/finite difference (FE/FD) method is presented. The analysis is designed for semi-discrete finite element scheme for the time-dependent Maxwell's equations. The explicit finite element schemes in different settings of the spatial domain are constructed and domain decomposition algorithm is formulated. Several numerical examples validate convergence rates obtained in the theoretical studies.