Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods

12/18/2020

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by   Matthias Kirchhart, et al.

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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.