Preconditioning of the spectral Fourier method for homogenization of periodic media

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Preconditioning of the spectral Fourier method for homogenization of periodic media
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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