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

TL;DR

This paper introduces simplified formulas for analytically integrating the Newton potential over cuboids, implemented in a C++ library, and discusses their application within fast multipole methods for efficient computation of non-polynomial data.

Contribution

It provides new simplified formulas for Newton potential integration over cuboids and implements them in a versatile C++ library, enhancing fast multipole method applications.

Findings

Simplified formulas for Newton potential integration over cuboids.

Implementation of formulas in an arbitrary precision C++ library.

Application framework for fast multipole methods with non-polynomial data.

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.