An Operator Preconditioned Combined Field Integral Equation for Electromagnetic Scattering

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-11-07 DOI:10.1137/23m1581674

Van Chien Le, Kristof Cools

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引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2484-2505, December 2024.
Abstract. This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned boundary element Galerkin discretization matrices on fine meshes and instability at spurious resonant frequencies. The remedy to ill-conditioned matrices is operator preconditioning, and resonant instability is eliminated by means of a combined field integral equation. Exterior traces of single and double layer potentials are complemented by their interior counterparts for a purely imaginary wave number. We derive the corresponding variational formulation in the natural trace space for electromagnetic fields and establish its well-posedness for all wave numbers. A Galerkin discretization scheme is employed using conforming edge boundary elements on dual meshes, which produces well-conditioned discrete linear systems of the variational formulation. Some numerical results are also provided to support the numerical analysis.

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电磁散射的算子预处理组合场积分方程

SIAM 数值分析期刊》，第 62 卷，第 6 期，第 2484-2505 页，2024 年 12 月。摘要本文旨在解决具有 Lipschitz 连续边界的完美电导体时谐电磁波散射积分方程的两个问题：细网格上边界元 Galerkin 离散矩阵条件不良和杂散共振频率下的不稳定性。解决矩阵条件不良问题的方法是算子预处理，通过组合场积分方程消除共振不稳定性。对于纯虚数波，单层和双层电势的外部迹线由其内部对应迹线补充。我们在电磁场的自然迹空间中推导出相应的变分公式，并确定了其对所有波数的良好求解性。我们采用了一种 Galerkin 离散化方案，在对偶网格上使用保边边界元素，从而产生了条件良好的离散线性变式系统。还提供了一些数值结果，以支持数值分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.