An Optimized FFT-Based Direct Poisson Solver on CUDA GPUs

作者：Wu Jing^*; JaJa Joseph; Balaras Elias

来源：IEEE Transactions on Parallel and Distributed Systems, 2014, 25(3): 550-559.

DOI：10.1109/TPDS.2013.53

• Fast-Fourier transforms
• parallel and vector implementations
• elliptic equations

A highly multithreaded FFT-based direct Poisson solver that makes effective use of the capabilities of the current NVIDIA graphics processing units (GPUs) is presented. Our algorithms carefully manage the multiple layers of the memory hierarchy of the GPUs such that almost all the global memory accesses are coalesced into 128-byte device memory transactions, and all computations are carried out directly on the registers. A new strategy to interleave the FFT computation along each dimension with other computations is used to minimize the total number of accesses to the 3D grid. We illustrate the performance of our algorithms on the NVIDIA Tesla and Fermi architectures for a wide range of grid sizes, up to the largest size that can fit on the device memory (512 x 512 x 512 on the Tesla C1060/C2050 and 512 x 256 x 256 on the GeForce GTX 280/480). We achieve up to 140 GFLOPS and a bandwidth of 70 GB/s on the Tesla C1060, and up to 375 GFLOPS with a bandwidth of 120GB/s on the GTX 480. The performance of our algorithms is superior to what can be achieved using the CUDA FFT library in combination with well-known parallel algorithms for solving tridiagonal linear systems of equations.

• 出版日期2014-3