A CG–DG method for Maxwell’s equations in Cole–Cole dispersive media

The numerical approximation of Maxwell’s equations in Cole–Cole dispersive media is studied for two and three-dimensional cases. We construct a combined scheme using the standard continuous Galerkin (CG) finite element method in time and discontinuous Galerkin (DG) method in space to discretize the...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2021-09, Vol.393, p.113480, Article 113480
Main Authors: Wang, Jiangxing, Zhang, Jiwei, Zhang, Zhimin
Format: Article
Language:English
Subjects:
Cole–Cole dispersive media
Discontinuous Galerkin (DG) method
Fast algorithm
Finite element method
Maxwell equations
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Summary:The numerical approximation of Maxwell’s equations in Cole–Cole dispersive media is studied for two and three-dimensional cases. We construct a combined scheme using the standard continuous Galerkin (CG) finite element method in time and discontinuous Galerkin (DG) method in space to discretize the Cole–Cole dispersive model. The L2-stability and error estimate of the proposed scheme are analyzed. Furthermore, we use sum-of-exponential approximation for the convolution kernel to speed up the evaluation of the Caputo derivative. Numerical examples are provided to demonstrate the performance of the proposed numerical methods.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113480