Interlaced P3M algorithm with analytical and ik-differentiation.

The interlacing technique of Hockney and Eastwood is extended to the particle-particle, particle-mesh (P3M) algorithm with analytical and ik-differentiation that computes the approximate Coulomb forces between N point particles in a periodic box. Interlacing means that one makes two separate computations of the reciprocal-space Ewald force, using two grids shifted with respect to each other by half of the diagonal of the grid subcell, and then takes the average of the two forces. The resulting algorithms compare favorably against their own noninterlaced versions and against the interlaced smooth particle-mesh Ewald algorithm. In our tests, the accuracy of the interlaced P3M methods was usually more than an order of magnitude higher than that of the other particle-mesh algorithms with the same parameter values. This accuracy gain can be converted into a speedup if the parameters of the algorithm are changed. Interlacing allows one to increase the grid spacing by up to a factor of 2 while keeping the same accuracy. A priori error estimates for the new algorithms are constructed, and the removal of the spurious self-force term is discussed. The success of interlacing is shown to be due to the fact that it suppresses the aliasing effects in the forces. It should be easy to incorporate the interlaced P3M algorithms into an existing simulation package, since this only requires a minor modification of the particle-mesh Ewald part of the code.