RPYFMM: Parallel adaptive fast multipole method for Rotne-Prager-Yamakawa tensor in biomolecular hydrodynamics simulations

RPYFMM is a software package for the efficient evaluation of the potential field governed by the Rotne-Prager-Yamakawa (RPY) tensor interactions in biomolecular hydrodynamics simulations. In our algorithm, the RPY tensor is decomposed as a linear combination of four Laplace interactions, each of which is evaluated using the adaptive fast multipole method (FMM) (Greengard and Rokhlin, 1997) where the exponential expansions are applied to diagonalize the multipole-to-local translation operators. RPYFMM offers a unified execution on both shared and distributed memory computers by leveraging the DASHMM library (DeBuhr et al., 2016, 2018). Preliminary numerical results show that the interactions for a molecular system of 15 million particles (beads) can be computed within one second on a Cray XC30 cluster using 12,288 cores, while achieving approximately 54% strong-scaling efficiency.RPYFMM是一款用于高效计算生物分子流体动力学模拟中由Rotne-Prager-Yamakawa（RPY）张量相互作用支配的势场的软件包。在本算法中，我们将RPY张量分解为四个拉普拉斯相互作用的线性组合，每个相互作用均通过自适应快速多极子方法（Adaptive Fast Multipole Method，FMM）（Greengard和Rokhlin，1997）进行计算，该方法采用指数展开来对角化多极到局部平移算子。RPYFMM借助DASHMM库（DeBuhr等人，2016、2018），可在共享内存与分布式内存计算机上实现统一执行。初步数值结果表明，在配备12288核心的Cray XC30集群上，可在一秒内完成包含1500万粒子（珠）的分子系统的相互作用计算，同时实现约54%的强缩放效率。