Optimizations for Elastodynamic Simulation Analysis with FMM-DRBEM and CUDA

Abstract

In this study, we propose a novel method to accelerate the process of elastodynamic analysis in 3D problems with BEM (boundary element method). With applying the DRBEM (dual reciprocity boundary element method) to form new integral equations for reducing complexity;the modified FMM (fast multipole method)is introduced to simplify the computation process and save storage space by avoiding intermediate coefficientmatrices. At the same time, FMM-DRBEM is reprogrammed in parallel byapplying GPU with CUDA (Compute Unified Device Architecture)for improving efficiency further.The main features in this paper are: (1)with respect to defects of classical method for elastodynamic, modified FMM- DRBEM algorithm is introduced; (2)optimal algorithms of translationsin FMM are discussed in parallel for improving the effect of GPU with CUDA;(4) PLE (Posi- tion Location Equation) and GHST (Global Hierarchy Substitution Transferring) methods are proposedfor improving efficiency, saving storage space requirement and optimizing data transforming process between host and device, respectively. The effect has been tested by numerical examples in the last section, and signifi- cantoptimal results both in efficiency and accuracy have been observed.