Localized Implicit Time Stepping for the Wave Equation

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-07-15 DOI:10.1137/23m1582618

Dietmar Gallistl, Roland Maier

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1589-1608, August 2024.
Abstract. This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based on exponentially decaying entries of the global system matrices and an appropriate partition of unity, it is proved that the superposition of localized solutions is appropriately close to the solution of the (global) implicit scheme. It is thereby justified that the localized (and especially parallel) computation on multiple overlapping subdomains is reasonable. Moreover, a restart is introduced after a certain number of time steps to maintain a moderate overlap of the subdomains. Overall, the approach may be understood as a domain decomposition strategy in space on successive short time intervals that completely avoids inner iterations. Numerical examples are presented.

查看原文本刊更多论文

波方程的局部隐式时间步进

SIAM 数值分析期刊》第 62 卷第 4 期第 1589-1608 页，2024 年 8 月。摘要。本研究提出了一种声波方程的离散化方法，该方程具有可能的振荡系数，其基础是用隐式时间离散法计算的空间局部子问题的离散解的叠加。基于全局系统矩阵的指数衰减项和适当的统一分区，证明了局部解的叠加适当地接近于（全局）隐式方案的解。由此证明，在多个重叠子域上进行局部（尤其是并行）计算是合理的。此外，为了保持子域的适度重叠，在一定的时间步数后引入了重启。总的来说，这种方法可以理解为在连续的短时间间隔内完全避免内部迭代的空间域分解策略。本文介绍了一些数值示例。

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

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.