GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method
GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method
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DOI：
10.1016/j.cpc.2011.01.020
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发表时间：
2011-05
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影响因子：
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通讯作者：
S. Hamada
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作者：
S. Hamada
采用图形处理器（GPU）对采用快速多极子方法（FMM）的间接边界元法（BEM）进行加速，以减少计算三维静电场所需的时间。BEM被设计为处理立方体体素模型，并且专门考虑将方形体素壁作为边界表面元素。FMM处理表面电荷元素之间的相互作用，并直接输出每个单独元素上的场的表面积分。CPU代码最初开发用于从解剖图像导出的人体体素模型中的场分析。FMM过程使用NVIDIA计算统一设备架构（CUDA）进行编程，并基于共享的伪代码模板进行双精度浮点运算。通过在两个电极之间施加直流电流而感应的电场针对具有499，629（模型1）和1，458，813（模型2）表面单元的两个模型进行计算。计算时间是使用四个GPU配置（两个NVIDIA GTX 295卡）和四个CPU内核（Intel Core i7-975处理器）测量的。对于模型1和2，线性系统求解器所需的时间分别为31 s和186 s。FMM的加速比范围为5.9至8.2（模型1）和5.0至5.6（模型2）。在这种BEM分析中，元素相互作用的计算速度与在GPU上使用FMM的粒子相互作用的计算速度相当。
An indirect boundary element method (BEM) that uses the fast multipole method (FMM) was accelerated using graphics processing units (GPUs) to reduce the time required to calculate a three-dimensional electrostatic field. The BEM is designed to handle cubic voxel models and is specialized to consider square voxel walls as boundary surface elements. The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element. The CPU code was originally developed for field analysis in human voxel models derived from anatomical images. FMM processes are programmed using the NVIDIA Compute Unified Device Architecture (CUDA) with double-precision floating-point arithmetic on the basis of a shared pseudocode template. The electric field induced by DC-current application between two electrodes is calculated for two models with 499,629 (model 1) and 1,458,813 (model 2) surface elements. The calculation times were measured with a four-GPU configuration (two NVIDIA GTX295 cards) with four CPU cores (an Intel Core i7-975 processor). The times required by a linear system solver are 31 s and 186 s for models 1 and 2, respectively. The speed-up ratios of the FMM range from 5.9 to 8.2 for model 1 and from 5.0 to 5.6 for model 2. The calculation speed for element-interaction in this BEM analysis was comparable to that of particle-interaction using FMM on a GPU.