An algorithmically consistent macroscopic tangent operator for FFT‐based computational homogenization

机译：一种算法一致的宏观切线操作员，用于基于FFT的计算均质化

获取原文

获取原文并翻译 | 示例

掌桥外文数据库（机构版） >>

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相似文献
相关主题

摘要

Summary > The present work addresses a multiscale framework for fast‐Fourier‐transform–based computational homogenization. The framework considers the scale bridging between microscopic and macroscopic scales. While the macroscopic problem is discretized with finite elements, the microscopic problems are solved by means of fast‐Fourier‐transforms (FFTs) on periodic representative volume elements (RVEs). In such multiscale scenario, the computation of the <fi>effective properties</fi> of the microstructure is crucial. While effective quantities in terms of stresses and deformations can be computed from surface integrals along the boundary of the RVE, the computation of the associated moduli is not straightforward. The key contribution of the present paper is the derivation and implementation of an <fi>algorithmically consistent macroscopic tangent operator</fi> which directly resembles the effective moduli of the microstructure. The macroscopic tangent is derived by means of the classical Lippmann‐Schwinger equation and can be computed from a simple system of linear equations. This is performed through an efficient FFT‐based approach along with a conjugate gradient solver. The viability and efficiency of the method is demonstrated for a number of two‐ and three‐dimensional boundary value problems incorporating linear and nonlinear elasticity as well as viscoelastic material response. </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 =“nme5627-abs-abs-0001”xml：lang =“en”> <title type =“main” >摘要</ title> >本工作解决了基于快速傅里叶变换的计算均匀化的多尺度框架。该框架考虑了显微镜和宏观尺度之间的缩放桥接。虽然具有有限元素的宏观问题被离散化，但是通过在周期性代表体积元素（rves）上通过快速傅里叶变换（FFT）来解决微观问题。在这种多尺度场景中，微结构的<fi>有效性质</ fi>的计算至关重要。虽然可以从RVE边界的表面积分计算应力和变形方面的有效量，但是相关模子的计算并不简单。本文的主要贡献是<fi>算法一致的宏观切线操作员</ fi的衍生和实施，其直接类似于微观结构的有效模量。宏观切线通过经典的Lippmann-Schwinger方程来源，并且可以从简单的线性方程系统计算。这是通过高效的基于FFT的方法以及共轭梯度求解器进行的。该方法的可行性和效率用于许多包括线性和非线性弹性的两维边界值问题以及粘弹性材料响应。 </ 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4期</span><b style="margin: 0 2px;">|</b><span>共20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=G?küzüm Felix Selim&option=202" target="_blank" rel="nofollow">G?küzüm Felix Selim;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Keip Marc‐André&option=202" target="_blank" rel="nofollow">Keip Marc‐André;</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>Institute of Applied Mechanics (CE)University of StuttgartPfaffenwaldring 7 70569 Stuttgart Germany;</p> <p>Institute of Applied Mechanics (CE)University of StuttgartPfaffenwaldring 7 70569 Stuttgart Germany;</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=computational homogenization&option=203" rel="nofollow">computational homogenization;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=effective properties&option=203" rel="nofollow">effective properties;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=fast Fourier transforms&option=203" rel="nofollow">fast Fourier transforms;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=finite element method&option=203" rel="nofollow">finite element method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=nonlinear elasticity&option=203" rel="nofollow">nonlinear elasticity;</a> </p> <div class="translation"> 机译：计算均匀化;有效的性能;快速傅里叶变换;有限元法;非线性弹性; </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/0704022969894.html">An algorithmically consistent macroscopic tangent operator for FFT‐based computational homogenization</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=G?küzüm Felix Selim&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">G?küzüm Felix Selim,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Keip Marc‐André&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Keip Marc‐André </a> <a href="/journal-foreign-20801/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Journal for Numerical Methods in Engineering .</a> <span>2018</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：一种算法一致的宏观切线操作员，用于基于FFT的计算均质化</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070401788312.html">Study of efficient homogenization algorithms for nonlinear problems: Approximation of a homogenized tangent stiffness to reduce computational cost</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Okada J.-I.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Okada J.-I.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Washio T.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Washio T.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hisada T.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Hisada T. </a> <a href="/journal-foreign-16989/" target="_blank" rel="nofollow" class="tuijian_authcolor">Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods .</a> <span>2010</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：研究非线性问题的有效均化算法：均切正切刚度的近似值以减少计算成本</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/academic-journal-foreign_computational-mechanics_thesis/020419835742.html">Study of efficient homogenization algorithms for nonlinear problems Approximation of a homogenized tangent stiffness to reduce computational cost</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Jun-ichi Okada&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Jun-ichi Okada,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Takumi Washio&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Takumi Washio,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Toshiaki Hisada&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Toshiaki Hisada </a> <a href="/journal-foreign-7947/" target="_blank" rel="nofollow" class="tuijian_authcolor">Computational Mechanics .</a> <span>2010</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：求解非线性问题的有效均化算法的研究均化切线刚度的近似值以减少计算成本</span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-conference-foreign_meeting-282216_thesis/0705013703701.html">An Efficient Algorithm to Include Sub-Voxel Data in FFT-Based Homogenization for Heat Conductivity</a> <b>[C]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Dennis Merkert&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Dennis Merkert,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Heiko Andrae&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Heiko Andrae,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Matthias Kabel&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Matthias Kabel,</a> <a href="/conference-foreign-282216/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Workshop on Computational Engineering .</a> <span>2015</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：一种有效的算法，包括基于FFT的均质化的子体素数据进行导热率</span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/academic-degree-foreign_mphd_thesis/02061826995.html">Consistent asymptotic homogenization method for lattice structures based on the virtual power principle</a> <b>[D] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bracho, David.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Bracho, David. </a> <span>2016</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：基于虚拟动力原理的晶格结构一致的渐近均化方法</span> </p> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-journal-foreign-pmc_detail_thesis/040005399216.html">Computational Analysis of Distance Operators for the Iterative Closest Point Algorithm</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Higinio Mora&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Higinio Mora,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Jerónimo M. Mora-Pascual&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Jerónimo M. Mora-Pascual,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Alberto García-García&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Alberto García-García,</a> <span>-1</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：迭代最近点算法的距离算子计算分析</span> </p> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/open-access_resources_thesis/0100018681431.html ">Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Nguyen, Van Dung&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Nguyen, Van Dung,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu, Ling&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Wu, Ling,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Noels, Ludovic&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Noels, Ludovic </a> <span>2017</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：计算均质化方法中边界条件的统一处理和用于估计均质化行为的切线算符的有效算法</span> </p> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/academic-journal-cn_journal-test-measurement-technology_thesis/0201212064034.html">一种用于FFT计算倒位序的新算法</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘微&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 刘微</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=朱明&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,朱明</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=姚志军&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,姚志军</a> <span> <a href="/journal-cn-7666/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 测试技术学报 </a> </span> <span> . 2004</span><span>,第0z1期</span> </span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-cn_digital-communication-world_thesis/0201236809952.html">一种基于FFT的快速高精度的频偏估计算法</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=蔡青&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 蔡青</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=陈海腾&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,陈海腾</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=徐勇&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,徐勇</a> <span> <a href="/journal-cn-8773/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 数字通信世界 </a> </span> <span> . 2017</span><span>,第005期</span> </span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/academic-journal-cn_electronic-science-technology_thesis/0201235051119.html">一种基于FFT的高精度频率估计算法</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=万灵达&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 万灵达</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=杨晓光&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,杨晓光</a> <span> <a href="/journal-cn-8717/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 电子科技 </a> </span> <span> . 2010</span><span>,第010期</span> </span> </div> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-journal-cn_techniques-automation-applications_thesis/0201240452210.html">基于FFT计算线性离散卷积的一种算法</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=田秀华&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 田秀华</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘文进&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,刘文进</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=裴晓敏&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,裴晓敏</a> <span> <a href="/journal-cn-8885/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 自动化技术与应用 </a> </span> <span> . 2009</span><span>,第002期</span> </span> </div> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/academic-journal-cn_journal-harbin-engineering-university_thesis/020129388101.html">一种基于FFT变换的超宽带信道盲估计算法</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=窦峥&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 窦峥</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=郭黎利&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,郭黎利</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张雅彬&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,张雅彬</a> <span> <a href="/journal-cn-7530/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 哈尔滨工程大学学报 </a> </span> <span> . 2007</span><span>,第009期</span> </span> </div> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-conference-cn_meeting-28130_thesis/020221953030.html">一种用于FFT计算倒位序的新算法</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘微&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 刘微</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=朱明&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,朱明</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=姚志军&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,姚志军</a> <span> <a href="/conference-cn-28130/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 中国兵工学会第十二届测试技术学术年会 </a> <span> <span> . 2004</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020315043561.html">用于设计灵敏度分析的一致切线算子弹粘塑性边界元方法</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=梁利华&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 梁利华</a> <span> . 2006</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120103476435.html">一种基于FFT的GMSK信号频偏估计算法</a> <b>[P]</b> . <span> 中国专利： CN110691051A </span> <span> . 2020-01-14</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/061203085759.html">一种基于一致性哈希算法的分布式计算和储存方法</a> <b>[P]</b> . <span> 中国专利： CN105282045B </span> <span> . 2018.11.16</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130444701731.html">System and method for testing an integrated circuit device using FFT analysis based on a non-iterative FFT coherency analysis algorithm</a> <b>[P]</b> . <span> 外国专利：  US6545454B1 </span> <span> . 2003-04-08</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：使用基于非迭代FFT相干分析算法的FFT分析测试集成电路器件的系统和方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130414690735.html">PROCESSOR FOR PROCESSING DIGITAL DATA HAVING A BUTTERFLY OPERATOR CONFIGURABLE BETWEEN A FFT/IFFT COMPUTATION AND A CHANNEL DECODING AND CORRESPONDING TELECOMMUNICATION DEVICE</a> <b>[P]</b> . <span> 外国专利：  WO2015033080A1 </span> <span> . 2015-03-12</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：具有可在FFT / IFFT计算与信道解码和对应的电信设备之间配置的蝶形运算符的处理数字数据的处理器 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130435948618.html">FFT arithmetic and FFT computation method</a> <b>[P]</b> . <span> 外国专利：  JP3951066B2 </span> <span> . 2007-08-01</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：FFT算法和FFT计算方法 </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('0704022969894','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 class="journalsub-pop-up" style="display: none"> <div class="journal-sub"> <h2>期刊订阅</h2> <img src="https://cdn.zhangqiaokeyan.com/img/loginclose.png" alt="" onclick="$('.journalsub-pop-up').hide()"> <p class="pardon">抱歉，该期刊暂不可订阅，敬请期待！</p> <p class="current">目前支持订阅全部北京大学中文核心（2020）期刊目录。</p> <div style="display: flex;margin-top: 69px;justify-content: space-between;"> <div class="no-sub" onclick="$('.journalsub-pop-up').hide()">暂不订阅</div> <div class="other-sub" onclick="continueSub('from=pc-detail')">继续订阅其他期刊</div> </div> </div> </div> <div class="right_btn"> <ul> <li class="gouwuche">  </li> <li class="yijian"> <a href="javascript:void(0);" onclick="link_analysis('/mycenter/auth/complaint.html',this)">意见反馈</a> </li> <li class="top"> <a href="javascript:scrollTo(0,0);">回到顶部</a> </li> <li class="shouye"> <a href="/">回到首页</a> </li> </ul> </div> <div class="xllindexfooter"> <div class="xllindexfootercenter"> <div class="xllindexfooterleft left" > <div class="xllindexfooterleftli"> <ul> <li><a href="/about.html">关于掌桥</a></li> <li><a href="/help/helpmap.html">资源导航</a></li> <li><a href="/help/helpguide.html">新手指南</a></li> <li><a href="/help/helpcenter.html">常见问题</a></li> <li><a href="/sitemap.html">网站地图</a></li> <li><a href="/help/helpcenter.html?type=9">版权声明</a></li> </ul> </div> <div class="xllindexfooterleft"> <p class="xllindexfooterlefteamil">客服邮箱：kefu@zhangqiaokeyan.com</p> <div class="xllindexfooterlefttcp"> <div class="xllindexfooterpoliceiimg"></div> <div class="xllindexfooterpoliceispan"> <span>京公网安备：11010802029741号 </span> <span>ICP备案号：<a href="https://beian.miit.gov.cn" rel="nofollow" target="_blank">京ICP备15016152号-6</a></span> <span>六维联合信息科技 (北京) 有限公司©版权所有</span> </div> </div> </div> </div> <div class="xllindexfooterright left"> <ul> <li> <p style="font-weight: bold;">客服微信</p> <div></div> </li> <li> <p style="font-weight: bold;">服务号</p> <div></div> </li> </ul> </div> </div> </div> <span id="0704022969894down" data-source="7," data-out-id="FE0W1WWlR7Y6cXrXvSfqQw==," data-f-source-id="7" data-title="An algorithmically consistent macroscopic tangent operator for FFT‐based computational homogenization" data-price="20" data-site-name="" data-transnum="24" style="display:none;"></span> <input type="hidden" value="4" id="sourcetype"> <input type="hidden" value="20801" id="journalid"> <input type="hidden" value="1" id="inyn_provide_service_level"> <input type="hidden" value="https://cdn.zhangqiaokeyan.com" id="imgcdn"> <input type="hidden" value="1" id="isdeatail"> <input type="hidden" value="" id="syyn_indexed_database"> <input type="hidden" value="" id="servicetype"> <input type="hidden" id="pagename" value="An algorithmically consistent macroscopic tangent operator for FFT‐based computational homogenization"/> <input type="hidden" value="thesis_get_original" id="pageIdentification"> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/jquery-1.12.4.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/lwlh_ajax.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zq.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/common.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/jquery.cookie.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/top.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/tip.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/login.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/down.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/search.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/searchtype.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/user/regist.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zxs_solor/detail.js?v=5.7.7"></script> <script type="text/javascript" src="https://www.zhangqiaokeyan.com/statistics/static/pagecollection.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/tj.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/pushbaidu.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/history.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/util/cookie.js?v=5.7.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/weipu/weipu.js?v=5.7.7"></script> </body> <script> $(function(){ var weiPuStatus = getCookie('WeiPuStatus'); if(weiPuStatus){ tipWeiPuStatus(weiPuStatus); delCookie('WeiPuStatus'); } getFacetKeywordVoInId(); var sourcetype = $("#sourcetype").val(); var inyn_provide_service_level = $("#inyn_provide_service_level").val(); if((sourcetype ==1||sourcetype==4)&&inyn_provide_service_level!=4){ getJournal(); } }) </script> </html>