| Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 857 - 880 | |
| DOI | https://doi.org/10.1051/m2an/2024022 | |
| Published online | 31 May 2024 | |
An exact in time Fourier pseudospectral method with multiple conservation laws for three-dimensional Maxwell’s equations
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shannxi 710049, P.R. China
* Corresponding author: yljiang@mail.xjtu.edu.cn
Received:
15
September
2023
Accepted:
20
March
2024
Maxwell’s equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an efficient fully discrete scheme for solving three-dimensional Maxwell’s equations. This is accomplished by combining Fourier pseudospectral methods in space and exact formulation in time. Fast computation is efficiently implemented in the scheme by using the matrix diagonalisation method and fast Fourier transform algorithm which are well known in scientific computations. An optimal error estimate which is not encumbered by the CFL condition is established and the resulting scheme is proved to be of spectral accuracy in space and exact in time. Furthermore, the scheme is shown to have multiple conservation laws including discrete energy, helicity, momentum, symplecticity, and divergence-free field conservations. All the theoretical results of the accuracy and conservations are numerically illustrated by two numerical tests.
Mathematics Subject Classification: 65M12 / 65M15 / 65M70
Key words: Maxwell’s equations / exact in time Fourier pseudospectral method / Duhamel’s formula / structure-preserving algorithms / convergence
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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