Acceleration of FFT-based homogenisation by low-rank tensors approximations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F19%3A00334171" target="_blank" >RIV/68407700:21110/19:00334171 - isvavai.cz</a>
Result on the web
<a href="http://www.ugn.cas.cz/actually/event/2019/sna/sna-sbornik.pdf" target="_blank" >http://www.ugn.cas.cz/actually/event/2019/sna/sna-sbornik.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Acceleration of FFT-based homogenisation by low-rank tensors approximations
Original language description
Fast Fourier transform (FFT) based methods has turned out to be an effective computationalapproach for numerical homogenisation. Particularly, Fourier-Galerkin methods are computa-tional methods for partial differential equations that are discretised with trigonometric polyno-mials. Its computational effectiveness benefits from efficient FFT based algorithms as well asa favourable condition number. Here this kind of methods are accelerated by low-rank tensorapproximation techniques for a solution field using canonical, Tucker, and tensor train formats.This reduced order model also allows to efficiently compute suboptimal global basis functionswithout solving the full problem. It significantly reduces computational and memory require-ments for problems with a material coefficient field that admits a moderate rank approximation.The advantages of this approach against those using full material tensors are demonstrated usingnumerical examples for the model homogenisation problem that consists of a scalar linear ellipticvariational problem defined in two and three dimensional setting with continuous and discontin-uous heterogeneous material coefficients. This approach opens up the potential of an efficientreduced order modelling of large scale engineering problems with heterogeneous material.
Czech name
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Czech description
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Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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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