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Robust Schur complement method for strongly anisotropic elliptic equations
Author(s) -
Khoromskij Boris N.,
Wittum Gabriel
Publication year - 1999
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/(sici)1099-1506(199912)6:8<621::aid-nla164>3.0.co;2-f
Subject(s) - preconditioner , schur complement , mathematics , anisotropy , isotropy , degenerate energy levels , conformal map , mathematical analysis , robustness (evolution) , domain decomposition methods , finite element method , eigenvalues and eigenvectors , physics , linear system , biochemistry , chemistry , quantum mechanics , gene , thermodynamics
We present robust and asymptotically optimal iterative methods for solving 2D anisotropic elliptic equations with strongly jumping coefficients, where the direction of anisotropy may change sharply between adjacent subdomains. The idea of a stable preconditioning for the Schur complement matrix is based on the use of an exotic non‐conformal coarse mesh space and on a special clustering of the edge space components according to the anisotropy behavior. Our method extends the well known BPS interface preconditioner [2] to the case of anisotropic equations. The technique proposed also provides robust solvers for isotropic equations in the presence of degenerate geometries, in particular, in domains composed of thin substructures. Numerical experiments confirm efficiency and robustness of the algorithms for the complicated problems with strongly varying diffusion and anisotropy coefficients as well as for the isotropic diffusion equations in the ‘brick and mortar’ structures involving subdomains with high aspect ratios. Copyright © 1999 John Wiley & Sons, Ltd.