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Titel
Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approach
Verfasser/ VerfasserinHaslinger, J. ; Kozubek, T. ; Kučera, R. ; Peichl, G.
Erschienen in
Numerical Linear Algebra with Applications, 2007, Jg. 14, H. 9, S. 713-739
ErschienenWiley, 2007
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)saddle-point system / fictitious domain method / Schur complement / orthogonal projectors / BiCGSTAB algorithm / multigrid
ISSN1099-1506
URNurn:nbn:at:at-ubg:3-4153 Persistent Identifier (URN)
DOI10.1002/nla.550 
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Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approach [1.35 mb]
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This paper deals with a fast method for solving large-scale algebraic saddle-point systems arising from fictitious domain formulations of elliptic boundary value problems. A new variant of the fictitious domain approach is analyzed. Boundary conditions are enforced by control variables introduced on an auxiliary boundary located outside the original domain. This approach has a significantly higher convergence rate; however, the algebraic systems resulting from finite element discretizations are typically non-symmetric. The presented method is based on the Schur complement reduction. If the stiffness matrix is singular, the reduced system can be formulated again as another saddle-point problem. Its modification by orthogonal projectors leads to an equation that can be efficiently solved using a projected Krylov subspace method for non-symmetric operators. For this purpose, the projected variant of the BiCGSTAB algorithm is derived from the non-projected one. The behavior of the method is illustrated by examples, in which the BiCGSTAB iterations are accelerated by a multigrid strategy.

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