Boundary Element Parallel Computation for 3D Elastostatics Using CUDA

Abstract

Finite Element Method (FEM) is pervasively used in most of 3D elastostatic numerical simulations, in which Computer Aided Design (CAD) models need to be converted into mesh models first and then enriched with semantic data (e.g. material parameters, boundary conditions). The interaction between CAD models and FEM models stated above is very intensive. Boundary Element Method (BEM) has been used gradually instead of FEM in recent years because of its advantage in meshing. BEM can reduce the dimensionality of the problem by one so that the complexity in mesh generation can be decreased greatly. In this paper, we present a Boundary Element parallel computation method for 3D elastostatics. The parallel computation runs on Graphics Processing Unit (GPU) using Computing Unified Device Architecture (CUDA). Three major components are included in such method: (1) BEM theory in 3D elastostatics and the boundary element coefficient integral methods, (2) the parallel BEM algorithm using CUDA, and (3) comparison the parallel BEM using CUDA with conventional BEM and FEM respectively by examples. The dimension reduction characteristics of BEM can dispose the 3D elastostatic problem by 2D meshes, therefore we develop a new faceting function to make the ACIS facet meshes suitable for Boundary Element Analysis (BEA). The examples show that the GPU parallel algorithm in this paper can accelerate BEM computation about 40 times.