Constant Boundary Elements on graphics hardware: a GPU-CPU complementary implementation

Abstract

Numerical simulation of engineering problems has reached such a large scale that the use of a parallel computing approach is required to obtain solutions within a reasonable time. Recent efforts have been made to implement these large scale computational tasks on general-purpose programmable graphics hardware (GPGPU). The Graphics Processing Unit (GPU) is specially well-suited to address problems that can be formulated in form of data-parallel computations with high arithmetic intensity. This work addresses the implementation of the direct version of the Boundary Element Method (DBEM) on a complementary GPU-CPU system. In this article, constant elements were used for the solution of 2D potential problems. A serial implementation of the BEM was rewritten under the SIMT (Single Instruction Multiple Thread) parallel programming paradigm. The code was developed on an NVidiaTM CUDA programming environment. The efficiency of the implemented strategies is investigated by solving a representative 2D potential problem. The paper reviews in detail the classical BEM formulation in order to be able to address the possible parallelization steps in the numerical implementation. The article reports the performance of the GPU-CPU system compared to the classical CPU-based system for an increasing number of boundary elements.