大规模声学边界元法的GPU并行计算

提出一种大规模声学边界元法的高效率、高精度GPU并行计算方法.基于Burton-Miller边界积分方程,推导适于GPU的并行计算格式并实现了传统边界元法的GPU加速算法.为提高原型算法的效率,研究GPU数据缓存优化方法.由于GPU的双精度浮点运算能力较低,为了降低数值误差,研究基于单精度浮点运算实现的doublesingle精度算法.数值算例表明,改进的算法实现了最高89.8%的GPU使用效率,且数值精度与直接使用双精度数相当,而计算时间仅为其1/28,显存消耗也仅为其一半.该方法可在普通PC机(8GB内存,NVIDIA Ge Force 660 Ti显卡)上快速完成自由度超过300万的大规模声学边界元分析,计算速度和内存消耗均优于快速边界元法.

GPU-accelerated Boundary Element Method for Large-scale Problems in Acoustics

A boundary element method (BEM) for large-scale acoustic analysis is accelerated efficiently and precisely with Graphics Processing Units (GPUs). Based on Burton-Miller boundary integral equation, an implementation scheme that can be handled efficiently in GPU is derived and applied to accelerate conventional BEM. Data caching techniques in GPU are introduced to improve efficiency of the prototype algorithm. A double-single precision algorithm implemented with single-precision floating-point numbers is employed to reduce numerical errors. It shows that the improved algorithm sustained a highest GPU efficiency of 89.8% for large-scale problems, and its accuracy was almost the same as that with double-precision numerals directly while costing only 1/28 in time and half in GPU memory consumption of the latter. The largest problem size up to 3 million unknowns was solved rapidly on a desktop PC (8GB RAM, NVIDIA GeForce 660 Ti) by the method. Its performance was better than the fast BEM algorithms in both time and memory consumption.