Preconditioners for domain decomposition methods

Robust Domain Decomposition Preconditioners For

An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into “local” subspaces and a global “coarse” space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function for...

Low-rank correction methods for algebraic domain decomposition preconditioners

This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain decomposition method and low-rank corrections. The domain decomposition approach decouples the matrix and once inverted, a low-rank approximation is applied by e...

Local preconditioners for two-level non-overlapping domain decomposition methods

Schwarz Domain Decomposition Preconditioners for Plane Wave Discontinuous Galerkin Methods

We construct Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods for Helmholtz boundary value problems. In particular, we consider additive and multiplicative non-overlapping Schwarz methods. Numerical tests show good performance of these preconditioners when solving the linear system of equations with GMRES.

Domain decomposition preconditioners for multiscale problems

In this paper, we study domain decomposition preconditioners for multiscale elliptic problems in high contrast media. We construct preconditioners such that the condition number of the preconditioned system is independent of media contrast. For this purpose, multiscale spaces for the interpolation on the coarse grid is developed using a local weighted spectral problem. A main observation is tha...