A CG-DG method for Maxwell's equations in Cole-Cole dispersive media

摘要

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.