An O(N) algorithm for Stokes and Laplace interactions of particles
An O(N) algorithm for Stokes and Laplace interactions of particles
复制标题
粒子斯托克斯和拉普拉斯相互作用的 O(N) 算法
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Guobiao Mo
中科院分区：
文献类型：
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作者：
A. Sangani;Guobiao Mo
本文描述了一种计算任意放置在周期阵列单元格中的N个球形粒子之间的拉普拉斯和斯托克斯相互作用的方法。该方法基于Greengard和Rokhlin的算法[J]。第一版。[物理学报，73,325(1987)]通过将粒子组织成若干不同大小的不同组来快速地求和粒子之间的拉普拉斯相互作用。用多极展开技术将每组粒子所产生的远场表示成一个在群中心有奇点的等效场。由此产生的计算量仅随n线性增加。该方法被应用于悬架力学中的许多问题，目的是评估该方法在研究大型系统动力学方面的效率和潜在的有用性。结果表明，在大多数情况下，即使采用相对低阶的多极展开，也能得到相当准确的相互作用力计算结果。
A method for computing Laplace and Stokes interactions among N spherical particles arbitrarily placed in a unit cell of a periodic array is described. The method is based on an algorithm by Greengard and Rokhlin [J. Comput. Phys. 73, 325 (1987)] for rapidly summing the Laplace interactions among particles by organizing the particles into a number of different groups of varying sizes. The far‐field induced by each group of particles is expressed by a multipole expansion technique into an equivalent field with its singularities at the center of the group. The resulting computational effort increases only linearly with N. The method is applied to a number of problems in suspension mechanics with the goal of assessing the efficiency and the potential usefulness of the method in studying dynamics of large systems. It is shown that reasonably accurate results for the interaction forces are obtained in most cases even with relatively low‐order multipole expansions.