A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries

Document Type

Article

Publication Date

2-1-2016

Abstract

We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain. The forcing, or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter, which then allows for higher order numerical methods. We present an efficient numerical method for constructing the penalty term, and discretize the resulting equations using a Fourier spectral method. We demonstrate convergence orders of up to 3.5 for the one-dimensional Maxwell's equations, and show that the numerical method does not suffer from dispersion (or pollution) errors. We also illustrate the approach in two dimensions and demonstrate convergence orders of 2.5 for transverse magnetic modes and 1.5 for the transverse electric modes. We conclude the paper with numerous test cases in dimensions two and three including waves traveling in a bent waveguide, and scattering off of a windmill-like geometry.

Identifier

84949034163 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/j.jcp.2015.11.031

e-ISSN

10902716

ISSN

00219991

First Page

167

Last Page

198

Volume

306

Grant

359610

Fund Ref

Simons Foundation

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