Boundary-field formulation for transient electromagnetic scattering by dielectric scatterers and coated conductors

TL;DR

This paper introduces a boundary-field formulation for analyzing transient electromagnetic scattering by dielectric objects and coated conductors, providing a new approach to solve and estimate solutions in the time domain.

Contribution

It develops a boundary-field equation method in the Laplace domain, establishing existence, uniqueness, and stability of solutions, and translating these into time-domain estimates for numerical analysis.

Findings

Proves well-posedness of the boundary value problem.

Derives stability bounds and regularity estimates.

Facilitates error estimation for numerical discretization.

Abstract

We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method, we reformulate the problem in the Laplace domain using the electric field equation inside the scatterer and a system of boundary integral equations for the scattered electric field in free space. To analyze this nonlocal boundary problem, we replace it by an equivalent boundary value problem. Existence, uniqueness and stability of the weak solution to the equivalent BVP are established in appropriate function spaces in terms of the Laplace transformed variable. The stability bounds are translated into time-domain estimates which determine the regularity of the solution in terms of the regularity of the problem data. These estimates can be easily converted into error estimates for a numerical discretization on the convolution quadrature for time evolution.