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A multigrid method based on graph matching for convection–diffusion equations
Author(s) -
Kim HwanHo,
Xu Jinchao,
Zikatanov Ludmil
Publication year - 2002
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.317
Subject(s) - multigrid method , robustness (evolution) , mathematics , linear subspace , convection–diffusion equation , graph , algebraic number , convection , algorithm , mathematical analysis , geometry , partial differential equation , discrete mathematics , mechanics , biochemistry , chemistry , physics , gene
In this paper we propose a practical and robust multigrid method for convection–diffusion problems based on a new coarsening techniques for unstructured grids. The idea is to use a graph matching technique to define proper coarse subspaces. Such an approach is based on the graph corresponding to the stiffness matrix, and is purely algebraic. We prove that our coarsening technique preserves the M matrix property. We also give several numerical examples illustrating the robustness of the method with respect to the variations in both the diffusion and convection coefficients. Copyright © 2002 John Wiley & Sons, Ltd.