Projected Krylov Methods for Solving Non-Symmetric Two-by-Two Block Linear Systems Arising from Fictitious Domain Formulations

Advances in Electrical and Electronic Engineering

Lukas Mocek¹  Alexandros Markopoulos¹  Tomas Kozubek¹  Jaroslav Haslinger¹  Radek Kucera² 

[1] ;Department of Mathematics and Descriptive GeometryVŠB - Technical University of Ostrava17. listopadu 15, CZ-70833 Ostrava-PorubaCzech RepublicRoom A826;

关键词: domain decomposition;    fictitious domain;    gmres;    krylov method;    null-space method;    orthogonal projector;    schur complement.;   

DOI  :  10.15598/aeee.v12i2.1045

来源: DOAJ

【 摘 要 】

The paper deals with the solution of large non-symmetric two-by-two block linear systems with a singular leading submatrix. Our algorithm consists of two levels. The outer level combines the Schur complement reduction with the orthogonal projectors that leads to the linear equation on subspaces. To solve this equation, we use a Krylov-type method representing the inner level of the algorithm. We propose a general technique how to get from the standard Krylov methods their projected variants generating iterations on subspaces. Then we derive the projected GMRES. The efficiency of our approach is illustrated by examples arising from the combination of the fictitious domain and FETI method.

【 授权许可】

Unknown