分数阶微分方程的一种细粒度数据级并行算法

A fine-grain data-level parallel algorithm for fractional differential equations

在GPU上基于CUDA编程模型提出针对Riesz空间分数阶扩散方程显式有限差分法的细粒度数据级并行算法。对算术逻辑操作的基本CUDA核心的细节及网格点值的计算优化进行了描述。实验结果表明,本文提出的并行算法与精确解符合得很好,在NVIDIA Quadro FX 5800GPU上的运行速度超过多核Intel Xeon E5540CPU并行算法的运行速度四倍有余。

The paper proposes a fine-grain data-level parallel algorithm for Riesz space fractional dif- fusion equation with explicit finite difference method and implements it with CUDA parallel program- ming model on GPU. The details of basic CUDA kernels for these operations and optimization of the production of grid points are described. The experimental results show that the parallel algorithm com- pares well with the exact analytic solution and runs more than four times faster on NVIDIA Quadro FX 5800 GPU than the parallel CPU solution on multi-core Intel Xeon E5540 CPU