The algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-07-25 DOI:10.1186/s13661-024-01900-z

Henda Ouertani, Mohamed Abdelwahed

引用次数: 0

Abstract

We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination method) is based on the Uzawa method by decoupling the linear system, while the second algorithm (Global inversion) is based on the overall resolution of the system by the GMRES method. A detailed implementation is proposed and some numerical tests are carried out in two and three dimensions and where the domain is multiply connected.

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时变斯托克斯问题的谱元离散化算法解析

我们考虑了用域分解谱元法解决具有非标准边界条件的时变斯托克斯问题的两种算法。第一种算法（消除法）基于解耦线性系统的乌泽法，而第二种算法（全局反演法）基于 GMRES 法对系统进行整体解析。我们提出了一个详细的实现方法，并在二维和三维以及域多连接的情况下进行了一些数值测试。

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

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.