Cyclically parallelized treecode for fast computations of electrostatic interactions on molecular surfaces

Abstract

We study the parallelization of a flexible order Cartesian treecode algorithm for evaluating electrostatic potentials of charged particle systems in which N particles are located on the molecular surfaces of biomolecules such as proteins. When the well-separated condition is satisfied, the treecode algorithm uses a far-field Taylor expansion to compute O(NlogN) particle–cluster interactions to replace the O(N2) particle–particle interactions. The algorithm is implemented using the Message Passing Interface (MPI) standard by creating identical tree structures in the memory of each task for concurrent computing. We design a cyclic order scheme to uniformly distribute spatially-closed target particles to all available tasks, which significantly improves parallel load balancing. We also investigate the parallel efficiency subject to treecode parameters such as Taylor expansion order p, maximum particles per leaf N0, and maximum acceptance criterion θ. This cyclically parallelized treecode can solve interactions among up to tens of millions of particles. However, if the problem size exceeds the memory limit of each task, a scalable domain decomposition (DD) parallelized treecode using an orthogonal recursive bisection (ORB) tree can be used instead In addition to efficiently computing the N-body problem of charged particles, our approach can potentially accelerate GMRES iterations for solving the boundary integral Poisson–Boltzmann equation.