FFT-based homogenisation accelerated by low-rank approximation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F19%3A00334225" target="_blank" >RIV/68407700:21110/19:00334225 - 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

FFT-based homogenisation accelerated by low-rank approximation

Original language description

Fast Fourier transform (FFT) based methods has turned out to be an ef- fective computational approach for numerical homogenisation. Particularly, Fourier-Galerkin methods are computational methods for partial differential equations that are discretised with trigonometric polynomials. Its computa- tional effectiveness benefits from efficient FFT based algorithms as well as a favourable condition number. Here this kind of methods are accelerated by low-rank tensor approximation techniques for a solution field using canonical, Tucker, and tensor train formats. This reduced order model also allows to efficiently compute suboptimal global basis functions without solving the full problem. It significantly reduces computational and memory requirements 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 using numerical examples for the model homogenisation problem that consists of a scalar linear elliptic variational problem defined in two and three dimensional setting with continuous and discontinuous heterogeneous material coefficients. This approach opens up the potential of an efficient reduced order modelling of large scale engineering problems with heterogeneous material.

Czech name

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Czech description

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Type

O - Miscellaneous

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