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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 12, Issue 4


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

Yalchin Efendiev
Juan Galvis
  • Departamento de Matemáticas, Universidad Nacional de Colombia, Carrera 30, calle 45, Ciudad Universitaria, Bogotá, Colombia.
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Raytcho Lazarov
Svetozar Margenov
  • Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Block 2, 1113 - Sofia, BULGARIA.
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Jun Ren


In 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.

Keywords: heterogeneous anisotropic media; domian decomposition; robust preconditioners; Schwarz method

About the article

Received: 2012-05-18

Revised: 2012-08-30

Accepted: 2012-08-31

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 12, Issue 4, Pages 415–436, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2012-0031.

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