Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2024-03-29 DOI:10.1090/mcom/3958

M. Bernkopf, T. Chaumont-Frelet, J. Melenk

引用次数: 0

Abstract

We present a wavenumber-explicit convergence analysis of the h p hp Finite Element Method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber k k . Our analysis covers the heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann, and second order absorbing boundary conditions, as well as perfectly matched layers.

查看原文本刊更多论文

片状光滑介质中𝑝有限元离散化的亥姆霍兹问题的波长显式稳定性和收敛性分析

我们提出了对 h p hp 有限元方法的波数显式收敛性分析，该方法适用于一类在大波数 k k 下具有片断解析系数的异质亥姆霍兹问题。我们的分析涵盖了具有 Robin、精确 Dirichlet-to-Neumann、二阶吸收边界条件以及完全匹配层的异质 Helmholtz 方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.