A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F16%3A00243029" target="_blank" >RIV/68407700:21110/16:00243029 - isvavai.cz</a>

Result on the web

<a href="http://www.sciencedirect.com/science/article/pii/S0021999116301863" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0021999116301863</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcp.2016.05.041" target="_blank" >10.1016/j.jcp.2016.05.041</a>

Result language

angličtina

Original language name

A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media

Original language description

In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is based on the Fourier–Galerkin method with exact and approximate integrations that has recently been shown to generalize the Lippmann–Schwinger setting of the original work by Moulinec and Suquet from 1994. It follows from this variational format that the ensuing system of linear equations can be solved by general-purpose iterative algorithms for symmetric positive-definite systems, such as the Richardson, the Conjugate gradient, and the Chebyshev algorithms, that are compared here to the Eyre–Milton scheme — the most efficient specialized method currently available. Our numerical experiments, carried out for two-dimensional elliptic problems, reveal that the Conjugate gradient algorithm is the most efficient option, while the Eyre–Milton method performs comparably to the Chebyshev semi-iteration. The Richardson algorithm, equivalent to the still widely used original Moulinec–Suquet solver, exhibits the slowest convergence. Besides this, we hope that our study highlights the potential of the well-established techniques of numerical linear algebra to further increase the efficiency of FFT-based homogenization methods.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

JI - Composite materials

OECD FORD branch

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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

2016

Confidentiality

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

Name of the periodical

Journal of Computational Physics

ISSN

0021-9991

e-ISSN

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Volume of the periodical

321

Issue of the periodical within the volume

September

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

18

Pages from-to

151-168

UT code for WoS article

000380750500008

EID of the result in the Scopus database

2-s2.0-84974555568