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Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods (2012.10304v1)
Published 18 Dec 2020 in math.NA and cs.NA
Abstract: We present simplified formulae for the analytic integration of the Newton potential of polynomials over boxes in two- and three-dimensional space. These are implemented in an easy-to-use C++ library that allows computations in arbitrary precision arithmetic which is also documented here. We describe how these results can be combined with fast multipole methods for general, non-polynomial data.