"[642BB9C8B72D]" . . "Applied Numerical Mathematics" . . . "finite volume methods; update preconditioning; Krylov subspace methods; Euler equations; conservation laws"@en . "T\u016Fma, Miroslav" . "Preconditioner Updates Applied to CFD Model Problems"@en . "P(1ET400300415), P(KJB100300703), Z(AV0Z10300504)" . "Aktualizace p\u0159edpodm\u00EDn\u011Bn\u00ED pro modelov\u00E1n\u00ED v dynamice tekutin"@cs . "Meister, A." . "Duintjer Tebbens, Jurjen" . "This paper deals with solving sequences of nonsymmetric linear systems with a block structure arising from compressible flow problems. The systems are solved by a preconditioned iterative method. We attempt to improve the overall solution process by sharing a part of the computational effort throughout the sequence. Our approach is fully algebraic and it is based on updating preconditioners by a block triangular update. A particular update is computed in a black-box fashion from the known preconditioner of some of the previous matrices, and from the difference of involved matrices. Results of our test compressible flow problems show, that the strategy speeds up the entire computation. The acceleration is particularly important in phases of instationary behavior where we saved about half of the computational time in the supersonic and moderate Mach number cases. In the low Mach number case the updated decompositions were similarly effective as the frozen preconditioners." . . "14"^^ . . . "Birken, P." . "Duintjer Tebbens, Jurjen" . "000260268600003" . "RIV/67985807:_____/08:00089231" . . . . . . . . "Preconditioner Updates Applied to CFD Model Problems"@en . "Aktualizace p\u0159edpodm\u00EDn\u011Bn\u00ED pro modelov\u00E1n\u00ED v dynamice tekutin"@cs . . "58" . "11" . "RIV/67985807:_____/08:00089231!RIV09-AV0-67985807" . "4"^^ . "This paper deals with solving sequences of nonsymmetric linear systems with a block structure arising from compressible flow problems. The systems are solved by a preconditioned iterative method. We attempt to improve the overall solution process by sharing a part of the computational effort throughout the sequence. Our approach is fully algebraic and it is based on updating preconditioners by a block triangular update. A particular update is computed in a black-box fashion from the known preconditioner of some of the previous matrices, and from the difference of involved matrices. Results of our test compressible flow problems show, that the strategy speeds up the entire computation. The acceleration is particularly important in phases of instationary behavior where we saved about half of the computational time in the supersonic and moderate Mach number cases. In the low Mach number case the updated decompositions were similarly effective as the frozen preconditioners."@en . "Preconditioner Updates Applied to CFD Model Problems" . . "NL - Nizozemsko" . "\u010Cl\u00E1nek je praktickou uk\u00E1zkou \u00FA\u010Dinnosti aktualizace p\u0159epodm\u00EDn\u011Bn\u00ED itera\u010Dn\u00EDch metod pro \u0159e\u0161en\u00ED sekvenci rozs\u00E1hl\u00FDch a \u0159\u00EDdk\u00FDch soustav line\u00E1rn\u00EDch algebraick\u00FDch rovnic. Konkr\u00E9tn\u011B se zab\u00FDv\u00E1 \u0159e\u0161en\u00EDm blokov\u00FDch syst\u00E9m\u016F, kter\u00E9 v mechanice tekutin \u010Dasto vznikaj\u00ED. Aktualizace je pln\u011B algebraick\u00E1 a cely postup se sna\u017E\u00ED vyu\u017E\u00EDt vlastnosti konkr\u00E9tn\u00ED aplikace.Porovn\u00E1van\u00ED zahrnuje nejenom novy postup, ale i \u0159e\u0161en\u00ED v p\u0159\u00EDpad\u011B, kdy p\u0159edpodm\u00EDn\u011Bn\u00ED nen\u00ED aktualizov\u00E1no, nebo je p\u0159epo\u010D\u00EDt\u00E1v\u00E1no v ka\u017Ed\u00E9 iteraci. V\u00FDsledky v p\u0159\u00EDpad\u011B \u0159e\u0161en\u00ED probl\u00E9mu stla\u010Diteln\u00E9ho proud\u011Bn\u00ED se zdaj\u00ED byt velmi povzbudiv\u00E9."@cs . . "2"^^ . . . "0168-9274" . "388716" . . "Preconditioner Updates Applied to CFD Model Problems" . .