GPU accelerated simulation of elliptic partial differential equations

This paper assesses the performance improvements of a GPU based implementation of an elliptic equation (steady heat conduction) over the CPU based version. An iterative method based on a finite difference approach has been used for the numerical solution (red black point successive over relaxation). The main idea is to move the computationally intensive parts of the algorithm onto the GPU. Because of the lack of communication between the blocks of the GPU grid, the computations have been included in two separate kernels. An important improvement to the GPU implementation has been the padding of the memory buffers which has led to fewer global memory transactions and faster kernel execution times. The performances of the two versions of the algorithm (CPU and CPU-GPU) have been compared on three different grained grids. The results indicate a speed-up which varies from around two for the coarsest grid up to over one order of magnitude for the finest grid.