Robust Schur Complement Method for Strongly Anisotropic Elliptic Equations

Boris N. Khoromskij*, Gabriel Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)621-653
Number of pages33
JournalNumerical Linear Algebra with Applications
Issue number8
StatePublished - 1999
Externally publishedYes


  • Anisotropic elliptic equations
  • Iterative substructuring methods
  • Multilevel interface preconditioning
  • Schur complement methods

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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