二阶椭圆问题弱 Galerkin 方法的并行迭代程序

IF 1.3 4区数学 Q1 MATHEMATICS International Journal of Numerical Analysis and Modeling Pub Date : 2024-01-01 DOI:10.4208/ijnam2024-1001

Chunmei Wang,Junping Wang, Shangyou Zhang

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引用次数: 0

摘要

本文提出了一种基于域分解的可并行迭代程序，并对二阶椭圆方程的弱 Galerkin 有限元方法进行了分析。建立了将域分解为与弱 Galerkin 方法相关的单个元素或较大子域的收敛分析。通过一系列数值测试来验证本文所提出的理论。

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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A Parallel Iterative Procedure for Weak Galerkin Methods for Second Order Elliptic Problems

A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the domain into individual elements associated to the weak Galerkin methods or into larger subdomains. A series of numerical tests are illustrated to verify the theory developed in this paper.

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.