The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement

de?Borst R.; Chen L.

摘要

Summary >We present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element‐wise point of view is adopted, exploiting Bézier extraction, which facilitates the implementation of adaptive refinement in isogeometric analysis. Locally refined and hierarchical T‐splines are used for the description of the geometry as well as for the approximation of the solution space in the analysis. The refinement is conducted with the aid of a subdivision operator, which is computed by again exploiting the Bézier extraction operator. The concept and algorithm of an element‐based adaptive isogeometric analysis are illustrated. Numerical examples are given to examine the accuracy, the convergence, and the condition number. </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 XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：id =“nme5696-abs-abs-0001”xml：lang =“en”> <title type =“main” >摘要</ title> >我们提供了2个自适应细化技术，即适应性本地细化和自适应分层改进，用于异诊断分析。采用元素明智的观点，利用Bézier提取，促进了在异步分析中实施自适应细化。本地精制和分层T样曲面用于几何形状的描述以及分析中解决方案空间的近似值。该细分算法进行了细节，通过再次利用Bézier提取操作员来计算。示出了基于元素的自适应异步分析的概念和算法。给出了数值例子来检查精度，收敛和条件号。</ 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>2018年第6期</span><b style="margin: 0 2px;">|</b><span>共21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=de?Borst R.&option=202" target="_blank" rel="nofollow">de?Borst R.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Chen L.&option=202" target="_blank" rel="nofollow">Chen L.;</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>Department of Civil and Structural EngineeringUniversity of SheffieldSheffield S1 3JD UK;</p> <p>Department of Civil and Structural EngineeringUniversity of SheffieldSheffield S1 3JD UK;</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=isogeometric analysis&option=203" rel="nofollow">isogeometric analysis;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bézier extraction&option=203" rel="nofollow">Bézier extraction;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=adaptive refinement&option=203" rel="nofollow">adaptive refinement;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=LR T‐splines&option=203" rel="nofollow">LR T‐splines;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=hierarchical T‐splines&option=203" rel="nofollow">hierarchical T‐splines;</a> </p> <div class="translation"> 机译：异步测定分析;Bézier提取;自适应细化;LR T样曲线;分层T样曲面; </div> </li> </ul> </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/0704022969939.html">The role of Bézier extraction in adaptive isogeometric analysis: 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