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dc.contributor.authorHaslinger, Jaroslav
dc.contributor.authorKozubek, Tomáš
dc.contributor.authorKučera, Radek
dc.contributor.authorPeichl, Gunther
dc.identifier.citationNumerical Linear Algebra with Applications. 2007, vol. 14, issues 9, p. 713-739.en
dc.relation.ispartofseriesNumerical Linear Algebra with Applicationsen
dc.subjectsaddle-point systemen
dc.subjectfictitious domain methoden
dc.subjectSchur complementen
dc.subjectorthogonal projectorsen
dc.subjectBiCGSTAB algorithmen
dc.titleProjected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approachen
dc.identifier.locationNení ve fondu ÚKen
dc.description.abstract-enThis 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.en

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