A Time-Domain Finite Element Scheme and Its Analysis for Nonlinear Maxwell's Equations in Kerr Media

Document Type

Article

Publication Date

3-4-2021

Publication Title

Journal of Computational Physics

Volume

435

First page number:

1

Last page number:

18

Abstract

The purpose of this paper is to develop and analyze a finite element method for solving the time-dependent Maxwell's equations in nonlinear Kerr media. The proposed fully-discrete scheme is proved to be conditionally stable and optimally convergent in the spatial variable and second order in time. Numerical results are presented to support our theoretical analysis and also to demonstrate the practical soliton propagation phenomena in Kerr media.

Keywords

Kerr media; Maxwell's equations; Nonlinear media; Soliton propagation; Time-domain finite element method

Disciplines

Numerical Analysis and Computation

Language

English

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