有限体积离散的重叠域分解方法

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Jinjin Zhang , Yanru Su , Xinfeng Gao , Xuemin Tu
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引用次数: 0

摘要

两级加性重叠域分解方法用于求解椭圆问题的单元中心有限体积离散化方法(FVMs)所产生的线性系统。共轭梯度(CG)方法用于加速收敛。为了分析有前提条件的 CG 算法,引入了离散 L2 准则、H1 准则和 H1 半准则来连接 FVM 和相关双线性方程组的矩阵。研究证明,在少量重叠的情况下,预处理系统的条件数并不取决于子域的数量。这一结果与符合有限元的结果类似。数值实验证实了这一理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Overlapping domain decomposition methods for finite volume discretizations
Two-level additive overlapping domain decomposition methods are applied to solve the linear system arising from the cell-centered finite volume discretization methods (FVMs) for the elliptic problems. The conjugate gradient (CG) methods are used to accelerate the convergence. To analyze the preconditioned CG algorithm, a discrete L2 norm, an H1 norm, and an H1 semi-norm are introduced to connect the matrices resulting from the FVMs and related bilinear forms. It has been proved that, with a small overlap, the condition number of the preconditioned systems does not depend on the number of the subdomains. The result is similar to that for the conforming finite element. Numerical experiments confirm the theory.
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来源期刊
Computers & Mathematics with Applications
Computers & Mathematics with Applications 工程技术-计算机:跨学科应用
CiteScore
5.10
自引率
10.30%
发文量
396
审稿时长
9.9 weeks
期刊介绍: Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
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