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Computation of Potential and Attraction Force of an Ellipsoid

The paper examines the problem of computing the potential and the attraction force of an ellipsoid, which requires taking a triple integral with an analytically integrable kernel. We consider the kernel as a weight function, while the inner integral is approximated by a quadrature for the product of functions, one of which has an integrable singularity. Such an approach makes it possible to obtain an integrand with only a weak logarithmic singularity before carrying out the next integration. This singularity can be overcome easily by changing a variable in the next outer integrals. Thus, to compute all the integrals, quadrature formulas without singularities are obtained. In addition, the functions to be computed do not have large values at the integration points. To carry out numerical experiments, complicated test functions are constructed. These functions are the exact potential and the exact force of attraction of an ellipsoid of rotation with an elliptic density distribution.