• Open Access

Performance comparison of three types of GPU-accelerated indirect boundary element method for voxel model analysis


Correspondence to: S. Hamada, Department of Electrical Engineering, Kyoto University, Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto 615–8510, Japan.

E-mail: shamada@kuee.kyoto-u.ac.jp


An indirect boundary element method that is geared to electrostatic field analysis in voxel models is accelerated by graphics processing units (GPUs). The method considers square walls on cubic voxels as boundary surface elements and uses the fast multipole method (FMM) to analyze large-scale models. On the basis of two conventional CPU codes, three GPU codes are programmed in search of higher computing performance. These GPU codes are designed as follows: In GPU code 1, direct and far fields in the FMM are simultaneously calculated on the GPU and the CPU, respectively; in GPU code 2, both fields are calculated on the GPU with a rotation-coaxial translation–rotation decomposition algorithm; and in GPU code 3, both fields are calculated on the GPU with a diagonal translation scheme. The electric fields in human models are generated by applying a 50-Hz magnetic field or by injecting direct-current (DC) current through two electrodes and they were calculated successfully using a personal computer with three GPUs and six CPU cores. An analysis with 3.9 million surface elements took 89.4 s to solve its governing linear system with double-precision floating-point arithmetic. GPU codes 1, 2, and 3 demonstrated the least memory usage, the greatest speed-up ratio, and the fastest calculation time, respectively. These results show an example of the trade-off relationships of computation performances on a heterogeneous CPU–GPU system. Copyright © 2013 John Wiley & Sons, Ltd.