Robust Two-level Domain Decomposition Preconditioners for High-contrast Anisotropic Flows in Multiscale Media

Author:

Efendiev Yalchin1,Galvis Juan12,Lazarov Raytcho1,Margenov Svetozar3,Ren Jun1

Affiliation:

1. 1Department of Mathematics, TAMU, College Station, TX 77843-3368, USA.

2. 2Departamento de Matemáticas, Universidad Nacional de Colombia, Carrera 30, calle 45, Ciudad Universitaria, Bogotá, Colombia.

3. 3Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Block 2, 1113 - Sofia, BULGARIA.

Abstract

AbstractIn this paper we discuss robust two-level domain decomposition preconditioners for highly anisotropic heterogeneous multiscale problems. We present a construction of several coarse spaces that employ standard finite element and multiscale basis functions and discuss techniques to reduce the dimensions of coarse spaces without sacrificing the robustness. We experimentally study the performance of the preconditioner on a variety two-dimensional test problems with channels of high anisotropy. The numerical tests confirm the robustness of the perconditioner with respect to the underlying physical parameters.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference1 articles.

1. References and Generalized Finite Element Methods : Their Performance and Their Relation to Mixed Methods SIAM Numer pp;Babusˇka;Anal,1983

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