麦克斯韦方程组的完全辐射边界条件分析

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-05-28 DOI:10.1137/24m1663417

Seungil Kim

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第3期，第1183-1208页，2025年6月。摘要。本文研究了波导中时谐电磁波传播问题的高阶吸收边界条件，即完全辐射边界条件（CRBC）。基于对辐射条件的最优有理近似，设计了用于模拟由亥姆霍兹方程控制的波传播的吸收边界条件的CRBC。在本文中，我们开发了适用于麦克斯韦方程组的CRBC，并利用考虑源间分离和施加CRBC的虚拟边界的移位电-磁算子，证明了麦克斯韦方程组补充CRBC的适定性。这也导致满足CRBC的近似解相对于CRBC参数的数量呈指数收敛。数值实例验证了CRBC的高效性能。

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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Analysis of Complete Radiation Boundary Conditions for Maxwell’s Equations

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1183-1208, June 2025.
Abstract. We study a high order absorbing boundary condition, the so-called complete radiation boundary condition (CRBC), for a time-harmonic electromagnetic wave propagation problem in a waveguide in [math]. The CRBC has been designed for an absorbing boundary condition for simulating wave propagations governed by the Helmholtz equation based on an optimal rational approximation to the radiation condition. In this paper we develop CRBC suitable for Maxwell’s equations and show the well-posedness of Maxwell’s equations supplemented with CRBC by using a shifted electric-to-magnetic operator taking into account a separation between sources and the fictitious boundary on which CRBC is imposed. This also leads to the exponential convergence of approximate solutions satisfying CRBC with respect to the number of CRBC parameters. Numerical examples to validate the efficient performance of CRBC will be presented as well.

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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.