Preconditioning of the spectral Fourier method for homogenization of periodic media

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F19%3A00332802" target="_blank" >RIV/68407700:21110/19:00332802 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Preconditioning of the spectral Fourier method for homogenization of periodic media

Popis výsledku v původním jazyce

We consider a homogenization problem over a rectangular domain with periodic boundary conditions. For numerical solution, we use the Galerkin or collocation method employing the spectral Fourier basis. The purpose of our presentation is to show that the matrix of the associated system of linear equations can be preconditioned by a matrix arising from a problem corresponding to the data of the original homogenization problem which are simplified in a certain manner. The matrix associated to this simplified problem is sparse (diagonal or multi-diagonal). This kind of preconditioning can avoid influence of anizotropy and of some oscillatory components of the data. We introduce sharp guaranteed theoretical upper bound to the condition number of the preconditioned problem. Some relevant numerical experiments are presented.

Název v anglickém jazyce

Preconditioning of the spectral Fourier method for homogenization of periodic media

Popis výsledku anglicky

We consider a homogenization problem over a rectangular domain with periodic boundary conditions. For numerical solution, we use the Galerkin or collocation method employing the spectral Fourier basis. The purpose of our presentation is to show that the matrix of the associated system of linear equations can be preconditioned by a matrix arising from a problem corresponding to the data of the original homogenization problem which are simplified in a certain manner. The matrix associated to this simplified problem is sparse (diagonal or multi-diagonal). This kind of preconditioning can avoid influence of anizotropy and of some oscillatory components of the data. We introduce sharp guaranteed theoretical upper bound to the condition number of the preconditioned problem. Some relevant numerical experiments are presented.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GC17-04150J" target="_blank" >GC17-04150J: Robustní dvojúrovňové simulace založené na Fourierově metodě a metodě konečných prvků: Odhady chyb, redukované modely a stochastika</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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