Overlapping domain decomposition methods for finite volume discretizations

被引：0
|
作者：
Zhang, Jinjin [1 ]
Su, Yanru [2 ]
Gao, Xinfeng [3 ]
Tu, Xuemin [2 ]
机构：
[1] Department of Mathematics, The Ohio State University, Columbus,OH,43210, United States
[2] Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence,KS,66045, United States
[3] Department of Mechanical and Aerospace Engineering, University of Virginia, 122 Engineer's Way, Charlottesville,VA,22904, United States
来源：
Computers and Mathematics with Applications | 2024年 / 174卷
关键词：
D O I：
10.1016/j.camwa.2024.10.018
中图分类号：
学科分类号：
摘要：
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. © 2024 Elsevier Ltd
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页码：510 / 529
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