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.

成对势函数的计算对于模拟许多领域的基础物理至关重要，尽管计算成本很高。为了减轻这种成本，已经为多个势函数开发了快速且近似的势计算方法；例如，粒子网格方法、快速傅立叶变换、快速多极子方法 (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。一位 PI 最近的工作为开发统一、稳健、准确和并行的方法奠定了基础，以便使用加速笛卡尔展开框架快速计算非振荡势。这里采用的双管齐下的方法涉及开发（i）平移算子，以便能够对不同的成对势进行基于 FMM 的计算，包括 Yukawa、Lennard Jones、Gauss、Morse 和 Buckingham 势，以及（ii）用于同时计算单个和多个势的并行框架。这些技术将应用于一组涉及泊松、扩散、延迟和亥姆霍兹（亚波长）方程以及克莱因-戈登方程的实际系统，以及计算范德华（在介观系统中）。底层方法要求只有翻译算子从潜在到潜在的变化，并为 FMM 树的上下遍历提供了数学上精确的公式。计算多个势的统一处理简化了并行代码开发，特别是在可扩展性方面。为了确保广泛的影响，本研究的部分内容将作为 LAMMPS 软件包的一部分提供，以确保广泛传播。研究生将接受跨学科的培训，并将参观彼此的院校。利用现有渠道招募女性和少数族裔，本科生通过高级设计项目和潜在的 REU 补充参与其中。