Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 393, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2021.113480
Keywords
Maxwell equations; Cole-Cole dispersive media; Finite element method; Discontinuous Galerkin (DG) method; Fast algorithm
Categories
Funding
- National Natural Science Foundation of China [11801171, 11871092, 11771035, NSAF U1930402]
- Natural Science Foundation of Hubei Province [2019CFA007]
- Hunan Provincial Natural Science Foundation of China [2019JJ50384]
- Scientific Research Fund of Hunan Provincial Education Department, China [18B023]
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This study investigates the numerical approximation of Maxwell's equations in Cole-Cole dispersive media for both two and three-dimensional cases. A combined scheme using continuous Galerkin finite element method in time and discontinuous Galerkin method in space is constructed, with analysis on L-2-stability and error estimate. The use of sum-of-exponential approximation for the convolution kernel to speed up the evaluation of the Caputo derivative is also discussed, with numerical examples provided to demonstrate the performance of the proposed numerical methods.
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 L-2-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. (c) 2021 Elsevier B.V. All rights reserved.
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