PARALLELIZATION OF A FINITE VOLUMES DISCRETIZATION FOR ANISOTROPIC DIFFUSION PROBLEMS USING AN IMPROVED SCHUR COMPLEMENT TECHNIQUE

被引：0

作者：

Belhadj, Hassan ^{[1
]}

Khallouq, Samir ^{[2
]}

Rhoudaf, Mohamed ^{[3
]}

机构：

[1] Abdelmalek Essaadi Univ, Fac Sci & Tech Tangier, Lab Math & Applicat, Dept Math, BP 416, Tangier 90000, Morocco

[2] Moulay Ismail Univ Meknes, Fac Sci & Tech Errachidia, Dept Math, BP 509, Boutalamine Errachidia 57000, Morocco

[3] Moulay Ismail Univ Meknes, Fac Sci Meknes, Dept Math & Informat, BP 11201, Zitoune Meknes, Morocco

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2021年 / 14卷 / 07期

关键词：

Anisotropic diffusion problems; discrete duality finite volume (DDFV); convergence; domain decomposition methods; Schur complement method; parallel computing; CONVERGENCE; SCHEMES;

D O I：

10.3934/dcdss.2020260

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present in this paper a new algorithm combining a finite volume method with an improved Schur complement technique to solve 2D anisotropic diffusion problems on general meshes. After having proved the convergence of the finite volume method, we have given a description of the proposed algorithm in the case of two nonoverlapping subdomains. Several numerical tests are achieved which illustrate the theoretical results of convergence of the finite volume method and show the advantages of the proposed algorithm.

引用

页码：2075 / 2099

页数：25

共 50 条

[1] Schur complement preconditioners for anisotropic problems
Giraud, L
Tuminaro, RS
IMA JOURNAL OF NUMERICAL ANALYSIS, 1999, 19 (01) : 1 - 18
[2] A matching Schur complement preconditioning technique for inverse source problems
Lin, Xuelei
Ng, Michael K.
APPLIED NUMERICAL MATHEMATICS, 2024, 201 : 404 - 418
[3] Discontinuous Galerkin finite element discretization of a strongly anisotropic diffusion operator
Pestiaux, A.
Melchior, S. A.
Remacle, J. F.
Karna, T.
Fichefet, T.
Lambrechts, J.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2014, 75 (05) : 365 - 384
[4] A finite volume scheme for anisotropic diffusion problems
Eymard, R
Gallouët, T
Herbin, R
COMPTES RENDUS MATHEMATIQUE, 2004, 339 (04) : 299 - 302
[5] Application of the iterative solution method with Schur complement reduction to mixed finite elements based in a tetrahedral discretization
Naff, Richard L.
ADVANCES IN WATER RESOURCES, 2014, 65 : 9 - 17
[6] A Schur-complement model-order-reduction technique for the finite element solution of transient elastohydrodynamic lubrication problems
Habchi, W.
ADVANCES IN ENGINEERING SOFTWARE, 2019, 127 : 28 - 37
[7] A linearity-preserving technique for finite volume schemes of anisotropic diffusion problems on polygonal meshes
Dong, Cheng
Kang, Tong
MATHEMATICS AND COMPUTERS IN SIMULATION, 2022, 201 : 141 - 162
[8] Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems
Chen, Xingding
Yuan, Guangwei
Yu, Yunlong
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2014, 6 (06) : 849 - 866
[9] Nonlinear finite volume discretization for transient diffusion problems on general meshes
Quenjel, El Houssaine
APPLIED NUMERICAL MATHEMATICS, 2021, 161 : 148 - 168
[10] Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
Eymard, R.
Gallouet, T.
Herbin, R.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2010, 30 (04) : 1009 - 1043

← 1 2 3 4 5 →