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

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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

Název statě ve sborníku

Proceedings of the conference SNA'19

ISBN

978-80-86407-73-9

ISSN

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e-ISSN

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Počet stran výsledku

4

Strana od-do

134-137

Název nakladatele

Ústav geoniky AV ČR, v. v. i.

Místo vydání

Ostrava

Místo konání akce

Ostrava

Datum konání akce

20. 1. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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