An accelerated surface discretization-based BEM approach for non-homogeneous linear problems in 3-D complex domains

For non-homogeneous or non-linear problems, a major difficulty in applying the boundary element method (BEM) is the treatment of the volume integrals that arise. An accurate scheme that requires no volume discretization is highly desirable. In this paper, we describe an efficient approach, based on the precorrected-FFT technique, for the evaluation of volume integrals resulting from non-homogeneous linear problems. In this approach, the 3-D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh for the evaluation of volume integrals. As such, no volume discretization of the interior problem domain is necessary. Moreover, with the uniform 3-D grid, the matrix sparsification techniques (such as the precorrected-FFT technique used in this work) can be extended to accelerate volume integration in addition to surface integration, thus greatly reducing the computational time. The accuracy and efficiency of our approach are demonstrated through several examples. A 3-D accelerated BEM solver for Poisson equations has been developed and has been applied to a 3-D multiply-connected problem with complex geometries. Good agreement between simulation results and analytical solutions has been obtained