The Block-P3M algorithm

The Block-P3M algorithm is a new development of the P3M (particle–particle/particle–mesh) method [J. Eastwood, Optimal P3M algorithms for molecular dynamics simulations, in: M. Hooper (Ed.), Computational Methods in Classical and Quantum Physics, Advance Publications Ltd, 1976, pp. 206–228; R. Hockney, J. Eastwood, Computer Simulation using Particles, McGraw-Hill, 1981 (Student Ed., Adam-Hilger, 1988)] for boundary integral and N  -body calculations. It gives O(NlogN)O(NlogN) complexity and O(N)O(N) storage of action-at-a-distance convolution sums for non-uniform distributions of sources and for any displacement invariant Green's function. It gives optimal accuracy and, unlike the Fast Multipole Method, it does not suffer from low frequency breakdown problems.