Wellposedness for Systems Arising in Time Domain Electromagnetics in Dielectrics

摘要

In this paper we present theoretical foundations (existence, uniqueness, continuous dependence) for a particular two dimensional Maxwell system This system is a multi-dimensional version of the one dimensional systems treated in 2, Chapter 31 The 2-D problem, carefully formulated and treated numerically in 11, arises from pulsed microwaves emanating from a semi- infinite strip of a finite antenna, producing obliquely incident waves on a dielectric material target as depicted in Figure 1 The problem is formulated with distributional (in space) input currents, a general convolution polarization relationship that includes most models for dielectrics currently found in the literature, and a finite computational domain with partially absorbing boundary conditions as well as perfectly matched layers (PMLs) to attenuate incident energy at the boundaries. The resulting system involves a second order (iii time) Maxwell's equation in variational form, coupled with the polarization convolution and PML constraint equations most conveniently formulated in terms of distributions and convolutions. While we follow the general approach to a theoretical framework developed in 21, the multi- dimensional aspects of the electric field as well as that of the computational domain with PML boundaries present new theoretical challenges. We provide arguments here to successfully overcome these difficulties and establish new wellposedness results.