Electromagnetic Scattering for Time-Domain Maxwell's Equations in an Unbounded Structure

TL;DR

This paper develops an exact transparent boundary condition for time-domain Maxwell's equations in unbounded structures, transforming the scattering problem into a well-posed initial-boundary value problem with explicit time-dependent estimates.

Contribution

It introduces a novel boundary condition and proves well-posedness and stability for the reformulated scattering problem in unbounded structures.

Findings

Established well-posedness and stability of the reformulated problem.

Derived explicit a priori estimates with time dependence.

Developed an exact transparent boundary condition for the problem.

Abstract

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary value problem in an infinite rectangular slab. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax--Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the electric field by directly studying the time-domain Maxwell equations.