A Multipole-Based Algorithm for Efficient Calculation of Forces and Potentials in Macroscopic Period
A Multipole-Based Algorithm for Efficient Calculation of Forces and Potentials in Macroscopic Period
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一种基于多极子的宏观周期力和势的高效计算算法
DOI：
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发表时间：
1996
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通讯作者：
T. Darden
中科院分区：
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作者：
Christophe Gerard Lambert;J. Board;T. Darden
提出了一种基于多极技术的新的有效算法，用于计算宏观周期性粒子集合中的静电力和静电势。快速多极子算法（FMA）可以在O（n）时间内计算n个粒子单元胞内的力。对于立方晶格，由3k× 3k× 3k晶格的单胞图像产生的力，包含33knparticles，可以在O（nk 2 +k3logk）时间内计算到任意精度。该算法很容易添加到现有的FMA实现，并给出了计算结果。精确的静电计算是在一个38 × 38× 38的区域上进行的，该区域由10万个粒子组成，给出了28个四次方个粒子的体积，而计算力和势的成本不到单胞中的两倍。实际上，ak= 4？6模拟近似真正的无限晶格埃瓦尔德总和力（包括形状依赖偶极校正），以高精度，采取25？计算时间比只计算单元格多30%。该方法扩展到非立方晶胞形状和非立方宏观形状。简单的代码修改允许计算宏观球体和椭球体内的力，以及由沿沿着两个轴复制的单元立方体形成的近无限正方形、圆形和椭圆形表面内的力。除了有效的周期性模拟，该方法提供了一个强大的工具来研究各种有限晶体形状的限制行为，以及在分子动力学模拟的表面现象。
A new and efficient algorithm based on multipole techniques is presented which calculates the electrostatic forces and potentials in macroscopic periodic assemblies of particles. The fast multipole algorithm (FMA) can be used to compute forces within then-particle unit cell inO(n) time. For the cubic lattice, forces due to a 3k× 3k× 3klattice of images of the unit cell, containing 33knparticles, can be computed inO(nk2+k3logk) time to arbitrary precision. The algorithm was readily added onto an existing FMA implementation, and computational results are presented. Accurate electrostatic computations were done on a 38× 38× 38region of 100000-particle unit cells, giving a volume of 28 quadrillion particles at less than a twofold cost over computing the forces and potentials in the unit cell alone. In practice, ak= 4?6 simulation approximates the true infinite lattice Ewald sum forces (including the shape-dependent dipole correction) to high accuracy, taking 25?30 % more time to compute than only the unit cell. The method extends to noncubic unit cell shapes, and noncubic macroscopic shapes. Simple code modifications allowed computation of forces within macroscopic spheres and ellipsoids, and within near-infinite square, circular, and elliptical surfaces formed of unit cubes replicated along two of the three axes. In addition to efficient periodic simulations, the method provides a powerful tool to study limiting behavior of various finite crystal shapes, as well as surface phenomena in molecular dynamics simulations.