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NOVEL CONCEPTS FOR DIFFERENTIAL EQUATION BASED ELECTROMAGNETIC FIELD SIMULATIONS

By Fernando Lisboa Teixeira

Abstract

This thesis presents novel concepts for electromagetic field simulations via partial differential equation (PDE) solvers. A vital a.::~pect for any successful general implementation of a POE solver is the use of an efficient absorbing boundary condition (ABC). The perfectly matched layer (PML) is a recently introduced ABC in Cartesian coordinates which provides reflection errors orders of magnitude smaller than previously employed ABCs. In this work, a new interpretation of the PML as an analytic continuation of the coordinate space is used to extend the PML to other coordinate systems. Modified equations replace the original Maxwell's equations, mapping propagating solutions into exponentially decaying solutions. Alternative (Maxwellian) formulations are also put forth, where the PML is represented as an artificial media with complex constitutive tensors, and the form of Maxwell's equations is retained. The causality and dynamic stability of the PML is characterized through a spectral analysis. In addition, a rationale is presented to extend the PML to complex media, e.g., dispersive and/or (bi-)anisotropic. For the Maxwellian formulation, the general expressions for the PML tensors matched to any interio

Year: 1999
OAI identifier: oai:CiteSeerX.psu:10.1.1.309.231
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