Novel Scalable Algorithms in Density Functional Theory Calculations

密度泛函理论计算中的新型可扩展算法

• 批准号: 0749074
• 负责人: Yunkai Zhou
• 金额: $ 7.39万
• 依托单位: Southern Methodist University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0749074&HistoricalAwards=false
• 关键词: Novel; Scalable; Algorithms; Density; Functional

Title: Novel Scalable Algorithms in Density Functional Theory CalculationsAbstract:Density functional theory (DFT) is one of the great scientific achievements of the 20th century. The fundamental importance of DFT originates from its much simplified description of the law of the fundamental building blocks of materials over the Schrodinger equation. DFT has had significant impact in a broad range of fields including condensed matter physics, quantum chemistry and materials science. However, first principals DFT calculations for complex materials often lead to computational problems of enormous dimension. Without efficient scalable algorithms, the sheer size of the problems can easily overwhelm even the most powerful supercomputers.One major computational bottleneck in DFT calculations is the repeated solution of large scale eigenproblems inside a self-consistent loop.Novel algorithms are needed in order to significantly reduce the computational cost without scarifying accuracy. We will investigate filtering approaches based on the recently developed Chebyshev filtered subspace iteration (CheFSI) method.CheFSI utilizes Chebyshev polynomials for adaptive subspace filtering, it is close to an eigenvector-free approach except that the first step of the self-consistent loop requires a diagonalization. The proposed research will further investigate and develop novel eigenvector-free algorithms based on polynomial filtering and preconditioning techniques for the nonlinear eigenvalue problems in DFT calculations. Emphasis will also be placed on extending the nonlinear subspace filtering techniques developed in the real-space setting to the widely used plane-wave setting. The goal is to make first principals DFT calculations more efficient and feasible for the study of increasingly more complex materials.Large scale eigenvalue related problems are ubiquitous in science and engineering and they often constitute the computational bottlenecks. Advances in scalable eigen-algorithms that can significantly reduce computational cost while maintaining accuracy will have broad and far-reaching intellectual impact. Besides materials science, the filtering and preconditioning techniques to be investigated also have potential applications in a broad range of areas such as pattern recognition, information retrieval and data mining, and other dimensionality reduction approaches for massive data sets.

标题：密度泛函理论计算中的新型可扩展算法摘要：密度泛函理论（DFT）是20世纪最伟大的科学成就之一。 DFT 的根本重要性源于它对薛定谔方程上材料基本构件定律的极其简化的描述。 DFT 在凝聚态物理、量子化学和材料科学等广泛领域产生了重大影响。然而，复杂材料的第一原理 DFT 计算通常会导致巨大维度的计算问题。如果没有高效的可扩展算法，问题的庞大规模甚至很容易压倒最强大的超级计算机。DFT 计算中的一个主要计算瓶颈是在自洽循环内重复求解大规模特征值问题。需要新的算法来显着降低计算成本而不牺牲精度。我们将研究基于最近开发的切比雪夫滤波子空间迭代（CheFSI）方法的滤波方法。CheFSI利用切比雪夫多项式进行自适应子空间滤波，它接近无特征向量方法，只是自洽循环的第一步需要对角化。所提出的研究将进一步研究和开发基于多项式滤波和预处理技术的新型无特征向量算法，用于 DFT 计算中的非线性特征值问题。重点还将放在将实空间设置中开发的非线性子空间滤波技术扩展到广泛使用的平面波设置上。目标是使第一原理 DFT 计算更加高效、可行，以研究日益复杂的材料。大规模特征值相关问题在科学和工程中普遍存在，并且常常构成计算瓶颈。可扩展的特征算法的进步可以显着降低计算成本，同时保持准确性，这将产生广泛而深远的智力影响。 除了材料科学之外，要研究的过滤和预处理技术在模式识别、信息检索和数据挖掘以及其他海量数据集的降维方法等广泛领域也具有潜在的应用。