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Fast Coulomb Solvers

There is an ever-growing demand for efficient algorithms to overcome the bottleneck posed by long-range interactions in N-body problems which are found in a broad range of strategic areas in physics, chemistry and electrical engineering. At JSC, a number of these so-called fast Coulomb solvers are being pursued to speed up the Coulomb force calculation in such N-body systems. These algorithms reduce the computational effort from O(N2), to O(N log N) or O(N), enabling system sizes to be considered which would otherwise be simply intractable.

Since different physical systems have widely varying precision and geometry requirements, a priority of this work is to establish a library where fast electrostatic solvers can be linked to existing programs. This includes a standardised interface, provide a choice of parallel algorithms with good processor scaling, and aims to allow for different boundary conditions (e.g. periodic, open, mixed).

Several Coulomb solvers currently being developed at JSC form the core of the library: the Barnes-Hut tree algorithm (PEPC), the Fast Multipole Method, a Multigrid Poisson solver and a Wavelet based method. Other algorithms based on lattice sums are also currently being investigated.