On the achievement of high fidelity and scalability for large‐scale diagonalizations in grid‐based DFT simulations

Choi Sunghwan; Kim Woo Youn; Yeom Min Sun; Ryu Hoon

摘要

Abstract >Recent advance in high performance computing (HPC) resources has opened the possibility to expand the scope of density functional theory (DFT) simulations toward large and complex molecular systems. This work proposes a numerically robust method that enables scalable diagonalizations of large DFT Hamiltonian matrices, particularly with thousands of computing CPUs (cores) that are usual these days in terms of sizes of HPC resources. The well‐known Lanczos method is extensively refactorized to overcome its weakness for evaluation of multiple degenerate eigenpairs that is the substance of DFT simulations, where a multilevel parallelization is adopted for scalable simulations in as many cores as possible. With solid benchmark tests for realistic molecular systems, the fidelity of our method are validated against the locally optimal block preconditioned conjugated gradient (LOBPCG) method that is widely used to simulate electronic structures. Our method may waste computing resources for simulations of molecules whose degeneracy cannot be reasonably estimated. But, compared to LOBPCG method, it is fairly excellent in perspectives of both speed and scalability, and particularly has remarkably less ( 10%) sensitivity of performance to the random nature of initial basis vectors. As a promising candidate for solving electronic structures of highly degenerate systems, the proposed method can make a meaningful contribution to migrating DFT simulations toward extremely large computing environments that normally have more than several tens of thousands of computing cores. </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”> <标题类型=“main”>抽象</ title> >最近的高性能计算（HPC）资源开辟了扩展密度泛函理论（DFT）模拟范围的可能性朝大型和复杂的分子系统。这项工作提出了一种数值鲁棒的方法，可以实现大型DFT HAMILTONIAN矩阵的可扩展对角线，特别是在HPC资源的大小方面是通常的数千个计算的CPU（核心）。众所周知的Lanczos方法被广泛重新设计，以克服其对DFT仿真的多个简并分段的评估的弱点，其中采用多级并行化以尽可能多的核心可扩展模拟。利用实际分子系统的固体基准测试，我们的方法的保真度针对广泛用于模拟电子结构的局部最佳块预先说明的共轭梯度（LOBCG）方法验证。我们的方法可以浪费计算资源，用于模拟其退化不能合理地估计的分子。但是，与Lobpcg方法相比，速度和可扩展性的观点相当优异，并且特别少（＆lt 19％）对初始基载体的随机性的性能的敏感性。作为解决高度简并系统的电子结构的有希望的候选者，该方法可以对迁移DFT模拟迁移到极大的计算环境的有意义的贡献，这些环境通常具有超过数万个计算核心。</ 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-21753/'>《International Journal of Quantum Chemistry》</a> <b style="margin: 0 2px;">|</b><span>2018年第16期</span><b style="margin: 0 2px;">|</b><span>共12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=Choi Sunghwan&option=202" target="_blank" rel="nofollow">Choi Sunghwan;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kim Woo Youn&option=202" target="_blank" rel="nofollow">Kim Woo Youn;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Yeom Min Sun&option=202" target="_blank" rel="nofollow">Yeom Min Sun;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ryu Hoon&option=202" target="_blank" rel="nofollow">Ryu Hoon;</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>National Institute of Supercomputing and Networking Korea Institute of Science and Technology InformationDaejeon 34141 Republic of Korea;</p> <p>Department of ChemistryKorea Advanced Institute of Science and TechnologyDaejeon 34141 Republic of Korea;</p> <p>National Institute of Supercomputing and Networking Korea Institute of Science and Technology InformationDaejeon 34141 Republic of Korea;</p> <p>National Institute of Supercomputing and Networking Korea Institute of Science and Technology InformationDaejeon 34141 Republic of Korea;</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/1186.html" title="物理化学（理论化学）、化学物理学">物理化学（理论化学）、化学物理学;</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=degenerate eigenpairs&option=203" rel="nofollow">degenerate eigenpairs;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=density functional theory&option=203" rel="nofollow">density functional theory;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=high performance computing&option=203" rel="nofollow">high performance computing;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Lanczos iterations&option=203" rel="nofollow">Lanczos iterations;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=large‐scale electronic structures&option=203" rel="nofollow">large‐scale electronic structures;</a> </p> <div class="translation"> 机译：脱义特征;密度函数理论;高性能计算;Lanczos迭代;大型电子结构; </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/0704019755736.html">On the achievement of 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