A local multiple proper generalized decomposition based on the partition of unity

Ibá?ez Rubén; Abisset‐Chavanne Emmanuelle; Chinesta Francisco; Huerta Antonio; Cueto Elías

摘要

Summary > It is well known that model order reduction techniques that project the solution of the problem at hand onto a low‐dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required <fi>modes</fi> in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”XML：ID =“NME6128-Abs-0001”> <标题类型=“main”>摘要</ title> >众所周知，模型顺序减少当该解决方案位于非线性歧管上时，将问题解决问题解决问题的技术存在困难。为了克服这些困难（特别是，解决方案所需的所需数量的不希望的增加），已经提出了几种解决方案。其中，我们可以引用非线性维度降低技术的使用，或者，可选地，采用线性局部减少的订单方法。这些最后方法通常呈现难以确保这些本地模型之间的连续性。这里，提出了一种新方法，其通过诉诸单位分区的范式来确保这种连续性，同时在每个本地补丁处采用适当的广义分解。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20801/'>《International Journal for Numerical Methods in Engineering》</a> <b style="margin: 0 2px;">|</b><span>2019年第2期</span><b style="margin: 0 2px;">|</b><span>共14页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ibá?ez Rubén&option=202" target="_blank" rel="nofollow">Ibá?ez Rubén;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Abisset‐Chavanne Emmanuelle&option=202" target="_blank" rel="nofollow">Abisset‐Chavanne Emmanuelle;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Chinesta Francisco&option=202" target="_blank" rel="nofollow">Chinesta Francisco;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Huerta Antonio&option=202" target="_blank" rel="nofollow">Huerta Antonio;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Cueto Elías&option=202" target="_blank" rel="nofollow">Cueto Elías;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>ICI ‐ High Performance Computing InstituteEcole Centrale de NantesNantes France;</p> <p>ICI ‐ High Performance Computing InstituteEcole Centrale de NantesNantes France;</p> <p>ESI Group Chair @ PIMM ‐ Procédés et Ingénierie en Mécanique et MatériauxEnsam ParisTechParis France;</p> <p>Laboratori de Calcul NumericUniversitat Politecnica de Catalunya BarcelonaTechBarcelona Spain;</p> <p>Aragon Institute of Engineering ResearchUniversidad de ZaragozaZaragoza Spain;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/6940.html" title="工程数学">工程数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=local reduced order modeling&option=203" rel="nofollow">local reduced order modeling;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=model order reduction&option=203" rel="nofollow">model order reduction;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=partition of unity&option=203" rel="nofollow">partition of unity;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=proper generalized decomposition&option=203" rel="nofollow">proper generalized decomposition;</a> </p> <div class="translation"> 机译：局部减少秩序建模;减少模型顺序;单位分区;适当的广义分解; </div> </li> </ul> </div> </div> <div class="literature cardcommon" id="literaturereference" style="display:none"> <div class="similarity "> <h3 class="all_title" id="enpatent111">引文网络</h3> <div class="referencetab clearfix"> <ul id="referencedaohang"> <li dataid="referenceul">参考文献</li> <li dataid="citationul">引证文献</li> <li dataid="commonreferenceul">共引文献</li> <li dataid="commoncitationul">同被引文献</li> <li dataid="tworeferenceul">二级参考文献</li> <li dataid="twocitationul">二级引证文献</li> </ul> </div> <div class="reference_details" id="referenceList"> <ul id="referenceul"></ul> <ul id="citationul"></ul> <ul id="commonreferenceul"></ul> <ul id="commoncitationul"></ul> <ul id="tworeferenceul"></ul> <ul id="twocitationul"></ul> </div> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704022970190.html">A local multiple proper generalized decomposition based on the partition of unity</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ibá?ez Rubén&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Ibá?ez Rubén,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Abisset‐Chavanne Emmanuelle&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Abisset‐Chavanne Emmanuelle,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Chinesta Francisco&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Chinesta Francisco,</a> <a href="/journal-foreign-20801/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Journal for Numerical Methods in Engineering .</a> <span>2019</span><span>,第2期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于统一分区的本地多个适当的广义分解</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-foreign_computer-methods-applied-mechanics-and-engineering_thesis/02041306639.html">Linear dependence problems of partition of unity-based generalized FEMs</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Rong Tian&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Rong Tian,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Genki Yagawa&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Genki Yagawa,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Haruo Terasaka&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Haruo Terasaka </a> <a href="/journal-foreign-1047/" target="_blank" rel="nofollow" class="tuijian_authcolor">Computer Methods in Applied Mechanics and Engineering .</a> <span>2006</span><span>,第37a40期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于单位的广义有限元划分的线性依赖问题</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704023033748.html">A non-local void dynamics modeling and simulation using the Proper Generalized Decomposition</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> </a> <a href="/journal-foreign-21476/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Journal of Material Forming: Official Journal of the European Scientific Association for Material Forming - ESAFORM .</a> <span>2020</span><span>,第4期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用适当的广义分解的非本地void动态建模和仿真</span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-conference-foreign_meeting-284477_thesis/0705014157826.html">Local proper generalized decomposition</a> <b>[C]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=A. 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