Collaborative Research: PACE-Parallel Accelerated Cartesian Expansions with Application to Molecular Dynamics

合作研究：PACE 并行加速笛卡尔展开式及其在分子动力学中的应用

• 批准号: 0729157
• 负责人: Shanker Balasubramaniam
• 金额: $ 20.52万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-10-01 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0729157&HistoricalAwards=false
• 关键词: Collaborative; Research; PACE; Parallel; Accelerated

Computation of pairwise potential functions is crucial, albeit computationally expensive, to simulating the underlying physics in many fields. To mitigate this cost, fast and approximate potential computation methods have been developed for several potential functions; for example, particle-mesh methods, Fast Fourier Transforms, Fast Multipole Method (FMM), and limiting computation to neighborhoods. These methods differ in efficiency, accuracy, and applicability. Recent work by one of the PIs provides the foundation for the development of unified, robust, accurate and parallel methods for fast computation of non-oscillatory potentials using the Accelerated Cartesian Expansion framework. A two pronged approach undertaken herein involves the development of (i) translation operators to enable FMM based computation for different pairwise potentials, including Yukawa, Lennard Jones, Gauss, Morse, and Buckingham potentials, and (ii) parallel framework for computing individual and multiple potentials simultaneously. These techniques are to be applied to a set of practical systems involving the Poisson, diffusion, retarded and Helmholtz (sub-wavelength), and Klein-Gordon equations, and to computing van-der Waals (in mesoscopic systems). The underlying methodology requires that only translation operators change from potential to potential, and provides a mathematically exact formulation for traversal up and down the FMM tree. The unifying treatment for computing multiple potentials simplifies parallel code development, especially with regard to scalability. To ensure broad impact, portions of this research will be available as part of LAMMPS software package to ensure widespread dissemination. Graduate students will be trained across multiple disciplines, and will visit each other's institutions. Existing channels are utilized to recruit women and minorities and undergraduate students are involved through senior design projects and potential REU supplements.

成对电位函数的计算至关重要，尽管计算在计算上对于模拟许多领域的基础物理学而言是昂贵的。为了减轻这种成本，已经开发了几种潜在功能的快速而近似的潜在计算方法。例如，粒子网方法，快速傅立叶变换，快速多极方法（FMM）以及将计算限制为邻域。这些方法在效率，准确性和适用性方面有所不同。其中一项PI的最新工作为开发统一，健壮，准确和并行方法的开发为使用加速的笛卡尔扩张框架快速计算非振荡电势的基础。此处采用的两种规律的方法涉及（i）翻译运算符的开发，以使基于FMM的计算对不同的成对电势，包括Yukawa，Lennard Jones，Gauss，Gauss，Morse和Buckingham电位，以及（ii）同时计算个体和多个电位的并行框架。这些技术应应用于涉及泊松，扩散，智障和helmholtz（子波长）和klein-gordon方程的一组实用系统，以及计算Van-der van-der waals（介绍系统中）。潜在方法要求只有翻译运算符从电势转变为潜在，并为在FMM树上下的遍历提供了数学上精确的公式。计算多个电势的统一处理简化了并行代码的开发，尤其是在可伸缩性方面。为了确保广泛的影响，将作为LAMMPS软件包的一部分提供本研究的一部分，以确保广泛的传播。研究生将接受多个学科的培训，并将访问彼此的机构。现有的渠道用于招募妇女和少数民族，并且本科生通过高级设计项目和潜在的REU补充剂参与。