Title

An Adaptive P1 Finite Element Method for Two-Dimensional Transverse Magnetic Time Harmonic Maxwell’s Equations with General Material Properties and General Boundary Conditions

Document Type

Article

Publication Date

8-1-2016

Abstract

We present an adaptive P finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions. It is based on reducing the boundary value problems for Maxwell’s equations to standard second order scalar elliptic problems through the Hodge decomposition. We allow inhomogeneous and anisotropic electric permittivity, sign changing magnetic permeability, and both the perfectly conducting boundary condition and the impedance boundary condition. The optimal convergence of the adaptive finite element method is demonstrated by numerical experiments. We also present results for a semiconductor simulation, a cloaking simulation and a flat lens simulation that illustrate the robustness of the method. 1

Publication Source (Journal or Book title)

Journal of Scientific Computing

First Page

848

Last Page

863

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