FFT-based homogenisation accelerated by low-rank tensor approximations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F20%3A00342321" target="_blank" >RIV/68407700:21110/20:00342321 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.cma.2020.112890" target="_blank" >https://doi.org/10.1016/j.cma.2020.112890</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2020.112890" target="_blank" >10.1016/j.cma.2020.112890</a>

Result language

angličtina

Original language name

FFT-based homogenisation accelerated by low-rank tensor approximations

Original language description

Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier–Galerkin methods are computational methods for partial differential equations that are discretised with trigonometric polynomials. Their computational effectiveness benefits from efficient FFT based algorithms as well as a favourable condition number. Here these kinds of methods are accelerated by low-rank tensor approximation techniques for a solution field using canonical polyadic, 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 settings 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

J_imp - Article in a specialist periodical, which is included in the Web of Science database

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

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2020

Confidentiality

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

Name of the periodical

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

e-ISSN

1879-2138

Volume of the periodical

2020

Issue of the periodical within the volume

364

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

21

Pages from-to

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UT code for WoS article

000527574600024

EID of the result in the Scopus database

2-s2.0-85080072203