Direct Schur complement method by domain decomposition based on H-matrix approximation

Direct Schur Complement Method by Domain Decomposition Based on H-Matrix Approximation

The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O(NΓ log NΓ) is almost linear in NΓ – the number of de...

Direct Schur Complement Method by Hierarchical Matrix Techniques

The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O(NΓ log q NΓ ) is almost linear in NΓ – the number of...

A preconditioner for the Schur complement domain decomposition method

Auxiliary space multigrid method based on additive Schur complement approximation

In this paper the idea of auxiliary space multigrid (ASMG) methods is introduced. The construction is based on a two-level block factorization of local (finite element stiffness) matrices associated with a partitioning of the domain into overlapping or non-overlapping subdomains. The two-level method utilizes a coarse-grid operator obtained from additive Schur complement approximation (ASCA). I...

Schur Complement based domain decomposition preconditioners with Low-rank corrections

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this “Schur Low Rank” (SLR) preconditioning approach, the coefficient matrix is first decoupled by DD, and then a low-rank correction is exploited to compute an approximate inverse of the Schur compleme...