Robust schur complement method for strongly anisotropic elliptic equations

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 b ased on the use of an exotic non-conformal coarse mesh space and on a speci al clustering of the edge space components according to the anisotropy beha vior. Our method extends the well known BPS interface preconditioner [2] to the case of anisotropic equations. The technique proposed also provides ro bust solvers for isotropic equations in the presence of degenerate geometri es, in particular, in domains composed of thin substructures. Numerical exp eriments confirm efficiency and robustness of the algorithms for the compli cated 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 (C) 1999 John Wiley Br Sons, Ltd.