# Analysis of Time-domain Electromagnetic Scattering Problem by Multiple Cavities

## TL;DR

This paper develops a new transparent boundary condition for the time-domain electromagnetic scattering problem involving multiple cavities, enabling stable and well-posed reformulation in a bounded domain for better analysis and simulation.

## Contribution

A novel time-domain transparent boundary condition is introduced for multiple cavity scattering problems, improving the mathematical formulation and analysis of the wave equation in bounded domains.

## Key findings

- Established well-posedness and stability of the reformulated problem
- Derived a priori estimates for the electric field with minimal data requirements
- Provided a rigorous mathematical framework for cavity scattering analysis

## Abstract

Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with inhomogeneous media characterized by variable dielectric permittivities and magnetic permeabilities. Corresponding to the transverse electric or magnetic polarization, the scattering problem can be studied for the Helmholtz equation in frequency domain and wave equation in time-domain, respectively. A novel transparent boundary condition in time-domain is developed to reformulate the cavity scattering problem into an initial-boundary value problem in a bounded domain. The well-posedness and stability are established for the reduced problem. Moreover, a priori estimates for the electric field is obtained with a minimum requirement for the data by directly studying the wave equation.