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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:306

Article

Galagusz, Ryan¹  Shirokoff, David²  Nave, Jean-Christophe³ 

[1] McGill Univ, Dept Elect & Comp Engn, Montreal, PQ H3A 0E9, Canada

[2] NJIT, Dept Math Sci, Newark, NJ 07102 USA

[3] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada

关键词: Active penalty method;    Sharp mask function;    Fourier methods;    Maxwell equations;    Fourier continuation;   

DOI  :  10.1016/j.jcp.2015.11.031

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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