Element-by-Element schur complement approximations for general nonsymmetric matrices of two-by-two block form

Authors:
Maya Neytcheva;Minh Do-Quang;He Xin
Affiliations:
Department of Information Technology, Uppsala University, Sweden;Department of Mechanics, Royal University of Technology, Stockholm, Sweden;Department of Information Technology, Uppsala University, Sweden
Venue:
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Year:
2009

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Abstract

We consider element-by-element Schur complement approximations for indefinite and general nonsymmetric matrices of two-by-two block form, as arising in finite element discretized systems of PDEs The paper provides some analysis of the so-obtained approximation and attempts to quantify the quality of the underlying two-by-two matrix splitting in a way similar to that used for symmetric positive definite matrices The quality of the approximation is illustrated numerically.