Comparison of treecodes for computing electrostatic potentials in charged particle systems with disjoint targets and sources

In molecular simulations, it is sometimes necessary to compute the electrostatic potential at M target sites due to a disjoint set of N charged source particles. Direct summation requires O(MN) operations, which is prohibitively expensive when M and N are large. Here, we consider two alternative tree-based methods that reduce the cost. The standard particle-cluster treecode partitions the N sources into an octree and applies a far-field approximation, whereas a recently developed cluster-particle treecode instead partitions the M targets into an octree and applies a near-field approximation. We compare the two treecodes with direct summation and document their accuracy, CPU run time, and memory usage. We find that the particle-cluster treecode is faster when N > M, that is, when the sources outnumber the targets, and conversely, the cluster-particle treecode is faster when M > N, that is, when the targets outnumber the sources. Hence, the two treecodes provide useful tools for computing electrostatic potentials in charged particle systems with disjoint targets and sources. (c) 2013 Wiley Periodicals, Inc.