Schur Complement Preconditioners for Anisotropic Problems

We present two new variants of Schur complement domain decomposition preconditioners suitable for 2D anisotropic problems. These variants are based on adaptations of the probing idea 5] used in conjunction with a coarse grid approximation 3]. The new methods are speciically designed for situations when the coupling between neighboring interfaces is stronger than the coupling within an interface. Taking into account this strong coupling, one variant uses a multicolor probing technique to avoid distortion in the probe approximations that appears when using the method proposed in 5]. The second technique uses additional probe matrices to approximate not only coupling within the interfaces but also coupling between interface points across the subdomains. This latter procedure looks somewhat-like an alternating line relaxation procedure and was motivated by the success of line relaxation within multigrid methods for anisotropic problems 4]. To assess the relevance of the new precon-ditioners, we compare their numerical behavior with well-known robust preconditioners such as the balanced Neumann-Neumann method 14].