Research On The Fast Multipole Boundary Element Method And Its Application For Scattering Of Elastic Waves

The fast multipole method(FMM) has been regarded as one of top10algorithmsin scientific computing that were developed in the20th century. Combined with theFMM,the boundary element method(BEM) can now solve large-scale problems withseveral million degrees of freedom on a desktop computer within hours. This openedup a wide range of applications for the BEM that has been hindered for many years bythe lack of efficiencies in the solution process, although it has been regarded as superbin the modeling stage. However, understanding the fast multipole BEM is even moredifficult as compared with the conventional BEM,because of the added complexitiesand different approaches in both FMM formulations and implementations. This paperis an introduction to the fast multipole BEM for scattering waves problems,which isaimed to overcome this hurdle for people who are familiar with the conventionalBEM and want to learn and adopt the fast multipole approach. The basic concept andmain procedures in the FMM for solving boundary integral equation are described indetail using the2D scattering waves problems as an example.Numerical examples arepresented to further demonstrate the efficiency of the fast multipole BEM for solvinglarge-scale problems.