The ([math], [math])-HDG Method for the Helmholtz Equation with Large Wave Number

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-06-12 DOI:10.1137/23m1562639

Bingxin Zhu, Haijun Wu

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1394-1419, June 2024.
Abstract. In this paper, we analyze a hybridizable discontinuous Galerkin method for the Helmholtz equation with large wave number, which uses piecewise polynomials of degree of [math] to approximate the potential [math] and its traces and piecewise polynomials of degree of [math] for the flux [math]. It is proved that [math] and [math] hold under the conditions that [math] is sufficiently small and that the penalty parameter [math], where [math] is the mesh size. Numerical experiments are proposed to verify our theoretical findings and to show that the pollution error may be greatly reduced by tuning the penalty parameter.

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大波数亥姆霍兹方程的（[math], [math]）-HDG 方法

SIAM 数值分析期刊》第 62 卷第 3 期第 1394-1419 页，2024 年 6 月。摘要本文分析了大波数 Helmholtz 方程的可混合非连续 Galerkin 方法，该方法用[math]度的分片多项式逼近势[math]及其迹，用[math]度的分片多项式逼近通量[math]。证明[math]和[math]在[math]足够小、惩罚参数[math]（其中[math]为网格大小）足够大的条件下成立。我们提出了数值实验来验证我们的理论发现，并表明通过调整惩罚参数可以大大减少污染误差。

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.