Multidomain spectral approach with Sommerfeld condition for the Maxwell equations

TL;DR

This paper introduces a multidomain spectral method with an exterior compactified domain for solving Maxwell's equations, accurately imposing Sommerfeld radiation conditions at infinity, demonstrated in axisymmetric spherical and spheroidal coordinate systems.

Contribution

It develops a novel spectral approach that exactly enforces Sommerfeld conditions at infinity using a compactified domain, applicable to axisymmetric electromagnetic problems.

Findings

Accurately imposes Sommerfeld condition at infinity

Demonstrates method in spherical and spheroidal coordinates

Provides a framework for efficient electromagnetic simulations

Abstract

We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.