极点条件、吸收边界条件与完全匹配层的关系

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-05-28 DOI:10.1137/24m1690916

M. Gander, A. Schädle

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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1209-1231页，2025年6月。摘要。透明（或精确或不反射）边界条件对于截断无限计算域是必不可少的。由于透明边界条件通常是非局部且昂贵的，因此必须对其进行近似。本文基于极点条件，研究了无限条上亥姆霍兹方程的近似。我们证明了极点条件的离散化既可以解释为高阶吸收边界条件，也可以解释为完美匹配层，这是另外两种众所周知的近似透明边界条件的方法。在没有Wood异常的情况下给出了指数收敛的误差估计。

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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On the Relationship Between the Pole Condition, Absorbing Boundary Conditions, and Perfectly Matched Layers

SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1209-1231, June 2025.
Abstract. Transparent (or exact or nonreflecting) boundary conditions are essential to truncate infinite computational domains. Since transparent boundary conditions are usually nonlocal and expensive, they must be approximated. In this paper, we study such an approximation for the Helmholtz equation on an infinite strip, based on the pole condition. We show that a discretization of the pole condition can be interpreted both as a high order absorbing boundary condition and as a perfectly matched layer, two other well-known methods for approximating a transparent boundary condition. We give an error estimate which shows exponential convergence in the absence of Wood anomalies.

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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.