面向长程大规模分子动力学模拟的快速多极子算法研究

Molecular dynamics simulation has become an essential theoretical tool in many fields of research, for example, physics, chemistry, biology and material science. The efficient computation of the long-range interactions is the core component of the large-scale molecular dynamics simulations. The fast multipole method is the most promising algorithm that computes the long-range interactions in large-scale systems; however, due to the absence of the theoretical analysis of the efficiency, it has not achieved the optimal efficiency in real-world applications. In order to solve this problem, this project will establish the mathematical model for the algorithmic efficiency, and then propose a parameter optimization algorithm that minimizes the computational cost under a user-provided accuracy target. The crucial step toward the efficiency model is the error estimate of the algorithm. This project will estimate the error in both the inhomogeneous and correlated systems, not only for the original fast multipole method, but also for a group of improved fast multipole methods. Therefore, the error estimates developed by this project is more general and suitable for real-world applications. The error estimate and parameter optimization developed by this project will be verified in large-scale molecular systems, and implemented in software packages to support efficient large-scale simulations of long-range interacting molecular systems.

分子动力学模拟是物理、化学、生物和材料科学等学科中不可或缺的理论研究手段。其中高效能长程相互作用计算是进行大规模分子动力学模拟的关键。最有希望满足实际应用对大规模长程相互作用计算需求的算法是快速多极子算法。然而，由于缺乏算法效能的数学模型，快速多极子算法并未在分子动力学模拟中发挥最佳效能。为解决此问题，本项目对快速多级子算法的效能进行数学建模，并以此为基础开发自动化参数优化策略，使得在保证计算精确度的条件下极小化计算开销。其中，结合应用问题特征的算法误差模型是效能模型的核心。本项目在误差建模中不仅充分考虑实际模拟体系的非均匀性和相关性，而且考虑应用更广泛的改进型快速多极子方法，使误差模型更具普适性和实用性。本项目的研究成果将实现在分子动力学模拟软件中，并在大规模应用体系中进行检验，为高效分子动力学模拟提供算法支持。

分子动力学模拟是物理、化学、生物和材料科学等学科中不可或缺的理论研究手段。其中高效能长程相互作用计算是进行大规模分子动力学模拟的关键。本项目通过对长程相互作用计算算法效能建立数学模型，准确评估算法参数、改进策略等因素对算法误差和计算开销的影响，结合应用问题中电荷分布非均匀以及有相关性等特征，开发参数自动选取策略和交错网格、最优基底等改进精度的方法，使长程相互作用计算在实际应用中获得最优效能。