It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M x M y N 2). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
展开▼
机译：解决分数阶微分方程非常耗时。二维分数阶微分方程（2D-TFDE）的迭代隐式有限差分方法的计算复杂度为O（M x M y N 2 ）。在本文中，我们提出了一种用于2D-TFDE的并行算法，并对该算法进行了深入的讨论。为此并行算法设计了具有虚拟边界的任务分配模型和数据布局。实验结果表明，该并行算法与精确解具有很好的比较性。单个Intel Xeon X5540 CPU上的并行算法运行速度比单个CPU内核上的串行算法快3.16–4.17倍。与分布式内存群集系统上的9个进程相比，81个进程的并行效率高达88.24％。我们确实认为，在不久的将来，并行计算技术将成为计算密集型分数应用程序的一种非常基本的方法。
展开▼
