Total FETI method and singular matrices in engineering problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F12%3A86084325" target="_blank" >RIV/61989100:27240/12:86084325 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/12:86084325

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Total FETI method and singular matrices in engineering problems

Popis výsledku v původním jazyce

Scalable implementation of FETI methods applied to engineering problems requires an efficient application of a direct method for solving a system of linear equations with a symmetric positive semidefinite matrix A. The direct solver is usually based on triangular decomposition of a nonsingular diagonal block AJJ of the stiffness matrix A of a subdomain and an effective evaluation of the action of a generalized inverse of the corresponding Schur complement. Here we review our results which address both problems. We present a procedure which first identifies a well-conditioned positive definite diagonal block AJJ of A, then decomposes AJJ by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S of AJJ. The Schur complement S is typically very small, so the generalized inverse can be effectively evaluated by the SVD. If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any "epsilon"

Název v anglickém jazyce

Total FETI method and singular matrices in engineering problems

Popis výsledku anglicky

Scalable implementation of FETI methods applied to engineering problems requires an efficient application of a direct method for solving a system of linear equations with a symmetric positive semidefinite matrix A. The direct solver is usually based on triangular decomposition of a nonsingular diagonal block AJJ of the stiffness matrix A of a subdomain and an effective evaluation of the action of a generalized inverse of the corresponding Schur complement. Here we review our results which address both problems. We present a procedure which first identifies a well-conditioned positive definite diagonal block AJJ of A, then decomposes AJJ by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S of AJJ. The Schur complement S is typically very small, so the generalized inverse can be effectively evaluated by the SVD. If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any "epsilon"

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

ISBN

978-3-9503537-0-9

ISSN

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e-ISSN

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Počet stran výsledku

8

Strana od-do

5411-5419

Název nakladatele

Vienna University of Technology

Místo vydání

Vienna

Místo konání akce

Vídeň

Datum konání akce

10. 9. 2012

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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