2 research outputs found
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 complement associated with the interface points. The method avoids
explicit formation of the Schur complement matrix. We show the feasibility of
this strategy for a model problem, and conduct a detailed spectral analysis for
the relationship between the low-rank correction and the quality of the
preconditioning. Numerical experiments on general matrices illustrate the
robustness and efficiency of the proposed approach
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 exploiting the Sherman-Morrison-Woodbury formula, which yields two
variants of the preconditioning methods. The low-rank expansion is computed by
the Lanczos procedure with reorthogonalizations. Numerical experiments indicate
that, when combined with Krylov subspace accelerators, this preconditioner can
be efficient and robust for solving symmetric sparse linear systems.
Comparisons with other distributed-memory preconditioning methods are
presented