A preconditioner for the Schur complement matrix

A preconditioner for the Schur complement matrix

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

A preconditioner for the Schur complement domain decomposition method

SchurRAS: A Restricted Version of the Overlapping Schur Complement Preconditioner

This paper presents a preconditioner based on solving approximate Schur complement systems with overlapping restricted additive Schwarz methods (RAS). The construction of the preconditoner, called SchurRAS, is as simple as in the standard RAS. The communication requirements for each application of the preconditioning operation are similar with those of the standard RAS approach. In the particul...

SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR COMPLEMENT WHEN COEFFICIENT MATRIX IS AN M-MATRIX

This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...

A Hierarchical Low-rank Schur Complement Preconditioner for Indefinite Linear Systems

Nonsymmetric and highly indefinite linear systems can be quite difficult to solve via iterative methods. This paper combines ideas from the Multilevel Schur Low-Rank preconditioner developed by Y. Xi, R. Li, and Y. Saad [SIAM J. Matrix Anal., 37 (2016), pp. 235–259] with classic block preconditioning strategies in order to handle this case. The method to be described generates a tree structure ...