A fast multipole implementation of the simplified hybrid boundary element method: application to 2D potential problems

The ultimate subject of this work is the implementation and testing of a novel numerical tool that can simulate on a personal computer and only in a few minutes a problem with many millions of degrees of freedom. The authors have already successfully developed and tested a technique that turned out to be a modified, reverse fast-multipole implementation for the conventional BEM. The variationally based hybrid BEM leads to a computationally less intensive formulation than in the conventional BEM for large-scale 2D and 3D problems of potential and elasticity. This formulation is especially advantageous for problems of complicated geometry and topology or requiring complicated fundamental solutions. The proposed implementation of the fast multipole method (FMM)for the simplified, hybrid BEM deals with the transpose of the double-layer potential matrix as well as with the nodal matrix expression of the potential fundamental solution. The basic aspects of the FMM are firstly introduced for the conventional BEM as well as for its expedite version. This takes most part of the present paper, which ends up with some validating numerical results. The FMM outline for the simplified hybrid BEM is shown in a separate section, as its numerical implementation is still in progress.