ANALYSIS OF THE PERFECTLY MATCHED LAYER PROBLEMS FOR TIME DEPENDENT MAXWELL EQUATIONS

Lung-An Ying (P. R. China)

Received January 6, 2008

Abstract

We study the perfectly matched layer method for electromagnetic scattering problems. Particularly we analyze the initial-boundary value problems of the transverse magnetic mode (TM) to Maxwell’s equation. An exterior domain in two spacial dimension is truncated by a square with a layer filled by a certain artificial medium. Using energy method we obtain some stability estimates for this initial-boundary value problem on the truncated domain. Then we define the weak formulation of this problem and prove existence and uniqueness. The results are extended to polar coordinates and three dimensional problems.

Keywords and phrases: Maxwell’s equation, perfectly matched layer, initial-boundary value problem, well posed.