Treatment of Complex Interfaces for Maxwell’s Equations with Continuous Coefficients Using the Correction Function Method
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10915_2020_1148_ReferencePDF.pdf
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Author(s)
Law, Yann-Meing
Marques, Alexandre N
Nave, Jean-Christophe
Date Issued
February 17, 2020
Publisher
Springer US
Citation
Journal of Scientific Computing. 2020 Feb 17;82(3):56
Version
Author's final manuscript
Abstract
Abstract
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without significantly increasing the complexity of the numerical approach for constant coefficients. Correction functions are modeled by a system of PDEs based on Maxwell’s equations with interface conditions. To be able to compute approximations of correction functions, a functional that is a square measure of the error associated with the correction functions’ system of PDEs is minimized in a divergence-free discrete functional space. Afterward, approximations of correction functions are used to correct a FDTD scheme in the vicinity of an interface where it is needed. We perform a perturbation analysis on the correction functions’ system of PDEs. The discrete divergence constraint and the consistency of resulting schemes are studied. Numerical experiments are performed for problems with different geometries of the interface. A second-order convergence is obtained for a second-order FDTD scheme corrected using the CFM. High-order convergence is obtained with a corrected fourth-order FDTD scheme. The discontinuities within solutions are accurately captured without spurious oscillations.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10915-020-01148-6
