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| Description
| - Práce pojednává o rychlé metodě k řešení rozsáhlých algebraických sedlo-bodových soustav vznikajících z fiktivně oblastní formulace eliptických okrajových úloh. Nová metoda fiktivních oblastí je představena a analyzována. Okrajové podmínky jsou vynuceny pomocí kontrolních proměnných definovaných na pomocné hranici umístěné vně původní oblasti. Tento přístup podstatně zvyšuje řády konvergence, ikdyž výsledná algebraická soustava plynoucí z konečně prvkové diskretizace je obvykle nesymetrická. Představená metoda je založena na redukci na Schurův doplněk. Pokud je matice tuhosti singulární, redukovaná soustava může být opět formulována jako jiná sedlo-bodová soustava. Její modifikace pomocí ortogonálních projektorů může být efektivně řešena pomocí Krylovovi metody s projekcemi pro nesymetrické operátory. Z tohoto důvodu je odvozena varianta algoritmu BiCGSTAB s projekcemi ze standardní verze. Chování metody je ilustrováno na příkladech, ve kterých jsou počty iterací metody BICGSTAB redukovány pomocí mult (cs)
- The 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 of 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 by 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 e
- The 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 of 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 by 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 e (en)
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| Title
| - Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approach
- Metoda Schurova doplňku s projekcemi k řešení nesymetrických soustav vznikajících z hladké varianty metody fiktivních oblastí (cs)
- Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approach (en)
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| skos:prefLabel
| - Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approach
- Metoda Schurova doplňku s projekcemi k řešení nesymetrických soustav vznikajících z hladké varianty metody fiktivních oblastí (cs)
- Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain approach (en)
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| skos:notation
| - RIV/61989100:27240/07:00014978!RIV08-AV0-27240___
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| http://linked.open.../vavai/riv/strany
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(1ET400300415), P(IAA1075402), Z(MSM6198910027)
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/61989100:27240/07:00014978
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - Saddle-point system; fictitious domain method; Schur complement; orthogonal projectors; BiCGSTAB algorithm; multigrid. (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
| - GB - Spojené království Velké Británie a Severního Irska
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - Numerical Linear Algebra with Applications
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
| - Haslinger, Jaroslav
- Kozubek, Tomáš
- Kučera, Radek
- Peichl, G.
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| http://linked.open...n/vavai/riv/zamer
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| issn
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| number of pages
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| http://localhost/t...ganizacniJednotka
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| is http://linked.open...avai/riv/vysledek
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