Integrating Singularities using Non-uniform Subdivision and Extrapolation

Abstract

A new approach to the computation of approximations to multidimensional integrals over an n-dimensional hyper-rectangular region, when the integrand is singular, is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. The strategy can be applied to vertex singularities, line singularities and more general subregion singularities. The technique turns out to have good numerical stability properties.