An acceleration technique for 2D method of characteristics based on Krylov subspace method and CUDA technique

The method of characteristics (MOC) with matrix form has more favorable performance compared with its standard application. And the linear algebraic solver affects heavily the computation efficiency. As a Krylov subspace technique, the preconditioned GMRES (PGMRES) algorithm was proposed to solve the resulting linear system in previous work. To accelerate the iteration process further, the current study utilizes the GPU-based CUDA technique to program the massively parallel PGMRES. The sparse matrix vector multiplication (SpMV), the most time-consuming operation, was optimized using the coherent visiting and shared memory, which improves the parallel computing performance significantly. Based on the analysis of the numerical feature of the coefficient matrix, two parallel optimization strategies are proposed to deal with the first part of the matrix equation, and the different schemes are utilized to the different parts of the matrix based on the size of row vector, which are expected to improve the throughput of the SpMV operation. Two benchmark problems (i.e. 2D C5G7 benchmark problem and 2D HTTR benchmark problem) have been simulated to verify the parallel code and measure the acceleration performance, and the numerical results demonstrate that the parallel strategies are efficient with or without CMFD method for the C5G7 problem, and the speedup can achieve more than 5.5 times with the optimal strategy for both the C5G7 and HTTR benchmark. (author)