The fast multipole is a powerful algorithm for modelling on a simple desktop computer problems with many millions of degrees of freedom. Its combination with the collocation boundary element method, which is based on fundamental solutions with global support, leads to a scheme whose efficiency or sometimes just simulation feasibility cannot be matched by any other numerical tool. The basic goal of this research work is the consolidation of computer algorithms previously developed at PUC-Rio in language C++ for the analysis of threedimensional potential problems. An analytic, thus machine-precision, evaluation scheme of integrals for the case of close distances between boundary elements and source points is implemented for the specific case of three-node triangle elements. For larger distances an adaptative quadrature scheme is applied for the sake of saving computational effort. For very large distances a reverse fast multipole scheme previously implemented by M.Sc. and Ph.D. works is implemented – also making use of machine-precision boundary integral evaluations. This has ultimately led to a complete revisiting of the recent fast multipole developments carried out at PUC-Rio. The implemented code is validated by means of a few elucidative numerical examples.