A note on true desingularisation of boundary integral methods for three-dimensional potential problems

A desingularized boundary element formulation for the three-dimensional potential problem will be presented. It is based on integral identities for the fundamental solution. The shown approach has the advantage that the singular terms on both influence matrices can be directly calculated by replacing it with a special summation of the other off-diagonal elements. It is an extension of the so-called 4π rule in which the strongest singularity is removed by replacing the terms of one of the influence matrices by 4π minus the sum of the off-diagonal terms of the same row. It is shown here that a similar method can also be applied to the weakest singularity, thereby completely desingularizing the method. Both integral equations and their corresponding matrix–vector notation will be presented.