Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media

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Dolbeau<span href=#aff_1></span></a><a class="author_link" href="#affiliation" data-bs-toggle="collapse" aria-controls="affiliation"><sup><span href=#aff_1>1</span></sup></a> ; <a class="author_link" href="/mecanique/search?"Jérémy Bleyer"-c">Jérémy Bleyer<span href=#aff_2></span></a><a class="author_link" href="#affiliation" data-bs-toggle="collapse" aria-controls="affiliation"><sup><span href=#aff_2>2</span></sup></a> ; <a class="author_link" href="/mecanique/search?"Karam Sab"-c">Karam Sab<span href=#aff_2></span></a><a class="author_link" href="#affiliation" data-bs-toggle="collapse" aria-controls="affiliation"><sup><span href=#aff_2>2</span></sup></a><sup><span class="glyphicon glyphicon-user" title="Auteur correspondant" style="color:#999999"></span></sup>  <a data-bs-toggle="collapse" href="#affiliation" aria-controls="affiliation"> <button id='house-affiliation' type="button" class="btn btn-link btn-xs" title="Affiliations des auteurs"> <span class="fa fa-home"></span><span id='house-caret' class="caret-icon fa fa-caret-down" style="margin-left:3px"></span> </button> </a> <div class="collapse" id="affiliation"> <div class="card card-body"> <div class="affiliation-authors"> <span id=aff_1> <sup>1</sup> Laboratoire Navier, IPParis ENPC, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France </span> <br> <span id=aff_2> <sup>2</sup> Laboratoire Navier, Ecole Nationale des Ponts et Chaussées, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France </span> <br> </div> </div> </div> </div> </div> <div style="margin-bottom:10px"> Comptes Rendus. Mécanique, Volume 352 (2024), pp. 251-267. </div> <div class="binary-file-icon" style="margin-top:20px;margin-bottom:10px"> <div class="wrapper-float"> <div class="d-flex flex-nowrap" style="margin-top:0px"> <a href="/mecanique/item/10.5802/crmeca.269.pdf" target="_blank"> <img src="/mecanique/static/ptf/img/pdf.gif"> </a> <a href="/mecanique/article/10.5802/crmeca.269/file/src/tex/CRMECA_2024__352_G1_251_0.tex"> <img src="/mecanique/static/ptf/img/tex.png"> </a> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:20px;margin-bottom:30px"> <ul class="nav nav-tabs article-tab"> <li class="nav-item active"> <a class="nav-link active" lang="fr" data-bs-toggle="tab" data-bs-target="#abstract-fr" href="#abstract-fr"><span title='Français '>Résumé</span></a> </li> <li class="nav-item"> <a class="nav-link" lang="en" data-bs-toggle="tab" data-bs-target="#abstract-en" href="#abstract-en"> <span title='Anglais '>Abstract</span> </a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div lang="fr" id="abstract-fr" class="tab-pane fade show active"> <p>Sab <span class="italique">et al.</span> (2024) ont récemment proposé un algorithme itératif basé sur la FFT, appelé Adaptive Eyre–Milton (AEM), pour résoudre l’équation de Lippmann–Schwinger dans le contexte de l’homogénéisation périodique de composites élastiques linéaires à double contraste infini (matériaux hétérogènes avec des lois constitutives linéaires contenant à la fois des pores et des inclusions rigides). Ils ont démontré la convergence linéaire inconditionnelle de ce schéma, quel que soit l’initialisation et le matériau de référence choisis. Cependant, les simulations numériques ont montré que la vitesse de convergence du schéma AEM dépend fortement du choix du matériau de référence. Dans cet article, nous introduisons une nouvelle version du schéma AEM, où le matériau de référence est mis à jour de manière itérative, aboutissant à un schéma rapide et polyvalent, appelé Accelerated Adaptive Eyre–Milton (A2EM). Des simulations numériques avec le schéma A2EM sur des composites élastiques linéaires avec des pores et des inclusions infiniment rigides montrent que, quel que soit le matériau de référence initial choisi, cet algorithme a la même vitesse de convergence que le schéma AEM avec le meilleur choix du matériau de référence.</p> </div> <div lang="en" id="abstract-en" class="tab-pane fade"> <p>Sab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitutive laws that contain both pores and rigid inclusions). They have demonstrated the unconditional linear convergence of this scheme, regardless of initialization and the chosen reference material. However, numerical simulations have shown that the rate of convergence of AEM strongly depends on the chosen reference material. In this paper, we introduce a new version of the AEM scheme where the reference material is updated iteratively, resulting in a fast and versatile scheme, termed Accelerated Adaptive Eyre–Milton (A2EM). Numerical simulations with A2EM on linear elastic composites with both pores and infinitely rigid inclusions show that, regardless of the initial chosen reference material, this algorithm has the same rate of convergence as AEM with the best choice of reference material.</p> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:10px;margin-bottom:10px"> <ul class="nav nav-tabs article-tab"> <li class="nav-item"><a class="nav-link active" data-bs-toggle="tab" data-bs-target="#info-tab" href="#info-tab">Détail</a></li> <li class="nav-item"><a class="nav-link" data-bs-toggle="tab"data-bs-target="#citation-tab" href="#citation-tab">Export</a></li> <li class="nav-item"> <a class="nav-link " data-bs-toggle="tab" data-toggle="tab" data-bs-target="#how-to-cite-tab" href="#how-to-cite-tab">Comment citer</a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div id="info-tab" class="tab-pane fade show active"> Reçu le : <time datetime="2024-07-11">2024-07-11</time><br> Accepté le : <time datetime="2024-09-26">2024-09-26</time><br> Publié le : <time datetime="2024-11-22">2024-11-22</time><br>  <div style="margin-top:5px"> </div> DOI : <a href="https://doi.org/10.5802/crmeca.269">10.5802/crmeca.269</a> <br> <div style="margin-top:5px"> Keywords: <span class="mathjax-formula"> computational homogenization, FFT-based method, iterative scheme, linear elasticity, composite materials </span> <br/> Mots-clés : <span class="mathjax-formula"> homogénéisation computationnelle, méthode basée sur la FFT, schéma itératif, élasticité linéaire, matériaux composites </span> <br/> </div> <div style="margin-top:5px"> </div> <div style="margin-top:5px"> <span id="affiliation-toggle" data-bs-toggle="collapse" href="#affiliation_details" role="button" aria-expanded="false" aria-controls="affiliation_details">Affiliations des auteurs : <span id="details-caret" class="caret-icon fa fa-caret-down" style="margin-left:3px"></span></span> <div class="collapse" id="affiliation_details" style="margin-top:10px;margin-left:10px"> <div class="card card-body"> <p> Martin Dolbeau&hairsp;<sup class="d-inline-block">1</sup> ; Jérémy Bleyer&hairsp;<sup class="d-inline-block">2</sup> ; Karam Sab&hairsp;<sup class="d-inline-block">2</sup> </p> <div class="affiliation-authors"> <span id=aff_1> <sup>1</sup> Laboratoire Navier, IPParis ENPC, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France </span> <br> <span id=aff_2> <sup>2</sup> Laboratoire Navier, Ecole Nationale des Ponts et Chaussées, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France </span> <br> </div> </div> </div> </div> <div style="margin-top:20px"> Licence : <img src="/mecanique/static/ptf/img/CC-BY%204.0.png" class="img-cc"> CC-BY 4.0 </div> <div style="margin-top:5px"> Droits d'auteur : Les auteurs conservent leurs droits </div> </div> <div id="citation-tab" class="tab-pane fade"> <div class="upper"> <ul class="nav nav-pills"> <li role="presentation" class="nav-item"><a class="nav-link active" data-bs-toggle="tab" data-bs-target="#bibtex" href="#bibtex">BibTeX</a></li> <li role="presentation" class="nav-item"><a class="nav-link" data-bs-toggle="tab" data-bs-target="#ris" href="#ris">RIS</a></li> <li role="presentation" class="nav-item"><a class="nav-link" data-bs-toggle="tab" data-bs-target="#enw" href="#enw">EndNote</a></li> </ul> <div class="tab-content"> <div id="bibtex" class="tab-pane fade show active"> <pre class="upper-right-content" id="bibtex-div">@article{CRMECA_2024__352_G1_251_0, author = {Martin Dolbeau and J\'er\'emy Bleyer and Karam Sab}, title = {Accelerating the {Adaptive} {Eyre{\textendash}Milton} {FFT-based} method for infinitely double contrasted media}, journal = {Comptes Rendus. M\'ecanique}, pages = {251--267}, publisher = {Acad\'emie des sciences, Paris}, volume = {352}, year = {2024}, doi = {10.5802/crmeca.269}, language = {en}, }</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#bibtex-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="Télécharger" href="/mecanique/export_citation/CRMECA_2024__352_G1_251_0/bib/"></a> </div> <div id="ris" class="tab-pane fade"> <pre class="upper-right-content" id="ris-div">TY - JOUR AU - Martin Dolbeau AU - Jérémy Bleyer AU - Karam Sab TI - Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media JO - Comptes Rendus. Mécanique PY - 2024 SP - 251 EP - 267 VL - 352 PB - Académie des sciences, Paris DO - 10.5802/crmeca.269 LA - en ID - CRMECA_2024__352_G1_251_0 ER - </pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#ris-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="Télécharger" href="/mecanique/export_citation/CRMECA_2024__352_G1_251_0/ris/"></a> </div> <div id="enw" class="tab-pane fade"> <pre class="upper-right-content" id="enw-div">%0 Journal Article %A Martin Dolbeau %A Jérémy Bleyer %A Karam Sab %T Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media %J Comptes Rendus. Mécanique %D 2024 %P 251-267 %V 352 %I Académie des sciences, Paris %R 10.5802/crmeca.269 %G en %F CRMECA_2024__352_G1_251_0</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#enw-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="Télécharger" href="/mecanique/export_citation/CRMECA_2024__352_G1_251_0/enw/"></a> </div> </div> </div> </div> <div id="how-to-cite-tab" class="tab-pane fade "> <div class="upper-right"> <pre class="upper-right-content" id="how-to-cite-div">Martin Dolbeau; Jérémy Bleyer; Karam Sab. Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 251-267. doi : 10.5802/crmeca.269. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.269/</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#how-to-cite-div" aria-hidden="true" title="Copier dans le presse-papier"></button> </div> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:30px;margin-bottom:10px"> <ul class="nav nav-tabs article-tab" > <li class="nav-item" id="main-citations-li" > <a class="nav-link active" data-bs-toggle="tab" data-bs-target="#references-tab" href="#references-tab">Bibliographie</a> </li> <li class="nav-item" id="citations-html" style="display:none"> <a class="nav-link" data-bs-toggle="tab" data-bs-target="#citations-tab" href="#citations-tab">Cité par</a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div id="references-tab" class="tab-pane fade show active"> <div style="margin-top:11px;margin-bottom: 0px"> <p class="bibitemcls " id="bris2010a"> [1] <span class="citation-author">S. 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Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media