Weight‐adjusted discontinuous Galerkin methods: Matrix‐valued weights and elastic wave propagation in heterogeneous media

机译：体重调整的不连续的Galerkin方法：异构介质中的矩阵重量和弹性波传播

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Summary > Weight‐adjusted inner products are easily invertible approximations to weighted <fi>L</fi> 2 inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time‐domain method for wave propagation which is low storage, energy stable, and high‐order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight‐adjusted DG methods to the case of matrix‐valued weights, with the linear elastic wave equation as an application. We present a DG formulation of the symmetric form of the linear elastic wave equation, with upwind‐like dissipation incorporated through simple penalty fluxes. A semidiscrete convergence analysis is given, and numerical results confirm the stability and high‐order accuracy of weight‐adjusted DG for several problems in elastic wave propagation. </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：lang =“en”xml：id =“nme5720-abs-abs-0001”> <标题类型=“main” >概要</标题> >体重调整的内部产品容易可逆近似为加权<fi> l </ fi> 2 </ sup>内部产品。这些近似可以与不连续的Galerkin（DG）离散化配对，以产生用于低存储，能量稳定的波传播的时域方法，以及任意异构介质和曲线网格的高阶精确。在这项工作中，我们将体重调整的DG方法扩展到矩阵值的重量的情况，用线性弹性波方程作为应用。我们介绍了线性弹性波方程的对称形式的DG配方，通过简单的惩罚助焊剂掺入了逆时间的耗散。给出了半机构收敛性分析，数值结果证实了重量调整DG的稳定性和高阶精度，在弹性波传播中的几个问题。 </ 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12期</span><b style="margin: 0 2px;">|</b><span>共31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=Chan Jesse&option=202" target="_blank" rel="nofollow">Chan Jesse;</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>Rice University6100 Main Street MS 134 Houston Texas USA;</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;"> </p> </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/0704022969962.html">Weight‐adjusted discontinuous Galerkin methods: 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href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=谢小碧&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,谢小碧</a> <span> <a href="/conference-cn-3927/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 2014年中国地球科学联合学术年会 </a> <span> <span> . 2014</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/02031638155.html">弹性材料及超弹性材料中波传播问题的间断Galerkin有限元方法</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=江金凤&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 江金凤</a> <span> . 2014</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120108713859.html">时域不连续Galerkin积分方程方法</a> <b>[P]</b> . <span> 中国专利： CN106202600A </span> <span> . 2016-12-07</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120979566.html">评价牛个体的胴体重量的基因标记及使用其的胴体重量评价方法</a> <b>[P]</b> . <span> 中国专利： CN101580880B </span> <span> . 2012.07.11</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130408406400.html">SYSTEM AND METHOD FOR ADJUSTING WEIGHTS VALUES ASSOCIATED WITH ERRORS OF A MOTOR'S ADJUSTMENT VALUES IF THE MOTOR IS CONTROLLED USING MODEL-PREDICTIVE CONTROL</a> <b>[P]</b> . <span> 外国专利：  DE102016120144A1 </span> <span> . 2017-05-04</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：如果使用模型预测控制来控制与电动机的调整值的误差相关的权重值的系统和方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130402371114.html">In order to quantize CNN parameters and feature values used for optimizing hardware applicable to mobile devices or high-precision small networks, FL (Fractional Length) values using weight quantization loss values are used. how to determine and apparatus {mETHOD aND dEVICE fOR dETERMINING FL VALUE BY USING WEIGHTED QUANTIZATION LOSS VALUES tO THEREBY QUANTIZE CNN PARAMETERS aND FEATURE VALUES tO bE USED fOR OPTIMIZING HARDWARE APPLICABLE tO MOBILE dEVICES oR COMPACT NETWORKS wITH HIGH PRECISION}</a> <b>[P]</b> . <span> 外国专利：  JP2020119528A </span> <span> . 2020-08-06</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：为了量化用于优化适用于移动设备或高精度小型网络的硬件的CNN参数和特征值，使用了使用权重量化损失值的FL（分数长度）值。如何通过使用加权量化丢失值来量化和确定CNN参数和特征值，并在优化移动设备使用的适用于移动设备的更早版本中使用，来确定FL值的方法和装置 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130446856725.html">Methods for designating parts of at least two downlink timeslots from a plurality of downlink timeslots of a frame for at least two units, to determine the encoding of 1d data bits, to determine the data modulation scheme a frame, and, to adjust the values of finite impulse response filter weights</a> <b>[P]</b> . <span> 外国专利：  BR0012910A </span> <span> . 2002-04-30</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：用于从至少两个单位的帧的多个下行链路时隙中指定至少两个下行链路时隙的部分，确定1d数据位的编码，确定帧的数据调制方案以及调整的值的方法有限脉冲响应滤波器权重 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704022969962','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div 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