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. © 2013 Wiley Periodicals, Inc.