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

Abstract

SUMMARYAn 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.

A voxel-based electrostatic field analysis for the virtual-human model Duke using the indirect boundary element method with a GPU-accelerated fast multipole method

“…The convergence performance of the linear equation solver was investigated to confirm the validity of eqns (6) and (7). The voxel side length, the number of fragment clusters, and the leaf-cell size were 5.0 mm, 3, and 7 3 voxels, respectively.…”

“…Gumerov and Duraiswami [10] and Yokota et al [11]). Details of GPU acceleration for the voxel-based FMM-IBEM were reported by Hamada [6,7]. The basic points used to estimate the performance of the GPU-accelerated FMM with CUDA (NVIDIA [8]) are summarised as follows.…”

“…These results demonstrated that eqn 7is effective in improving the convergence performance when a number of isolated voxel clusters exist. This implies that the use of eqn (7) ensures the quality of the solution even with a relatively high value for the convergence criterion.…”

“…However, a voxel-based indirect BEM (IBEM) was applied to relatively large-scale problems by Hamada and Kobayashi [4] using the Laplace-kernel fast multipole method (FMM) (Greengard and Rokhlin [5]). Furthermore, this IBEM was accelerated using graphics processing units (GPUs) (Hamada [6,7]) with NVIDIA's compute unified device architecture (CUDA) (NVIDIA [8]), thereby obtaining highperformance computation, even with a personal computer. This IBEM was used to analyse the electrostatic fields in human voxel models that describe the conductivities of biological tissues.…”

Step Ring-Based Three-Dimensional Path Planning Via Graphics Processing Unit Simulation for Subtractive Three-Dimensional Printing

“…[11] gives an idea of how to generate lookup table, block density, as well as index buffer for 2D and 3D textures via GPU with simple voxel and marching cube introduction. Hamada [12] introduced indirect fast multipole method-boundary element method for voxel model analysis and applied field for electrical field of biological samples via GPU acceleration and pseudocode template for CUDA kernels of the fast multipole method, along with multiple graphics processing unit execution. Crassin [13] introduced a system that achieves real-time rendering performance for several billion voxels and how the introduced prefiltered geometry model and approximate cone tracing method can achieve blurry effects and real-time indirect lighting.…”