Title

Development and Analysis of Both Finite Element and Fourth-Order in Space Finite Difference Methods for an Equivalent Berenger's PML Model

Document Type

Article

Publication Date

11-29-2019

Publication Title

Journal of Computational Physics

Volume

405

First page number:

1

Last page number:

20

Abstract

This paper deals with an equivalent Berenger's Perfectly Matched Layer (PML) model. We first develop a finite element scheme using edge elements to solve this model. We prove a discrete stability of this method, which inherits the stability obtained in the continuous case. Then we propose a fourth-order in space finite difference scheme for solving this PML model. Numerical stability similar to the continuous stability and the optimal error estimate are established for the difference scheme. Here only second order time discretizations are considered for both schemes. Finally, numerical results are presented to justify our analysis and demonstrate the effectiveness of this PML model for absorbing impinging waves.

Keywords

Maxwell's equations; Perfectly Matched Layer; Finite difference method; Finite element method; Edge elements

Disciplines

Mathematics | Physical Sciences and Mathematics

Language

English

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