GPU Computing for Efficient Sedimentary Basin Simulations

Abstract: This paper presents PDEs that describes sedimentation by a system of diffusion and transportation equations. These PDEs are implemented with a semi-implicit scheme and solved on a Graphics Processing Unit (GPU). The equations are solved with the iterative solvers (conjugate gradient and biconjugate gradient stabilized method) provided by the software ViennaCL. The timings from these operations are compared with a CPU implementation. Before using the iterative solvers, a sparse matrix and a right hand side vector is set. The sparse matrix and the right hand side vector are efficiently updated on the GPU. The implicit terms of the PDEs are stored in the sparse matrix and the explicit terms in the right hand side vector. The sparse matrix is stored in the compressed sparse row (CSR) format. Algorithms to update the sparse matrix for the PDEs, which have Neumann or a mix of Neumann and Dirichlet boundary conditions, are presented. As the values in the sparse matrix depend on values from the previous results, the sparse matrix has to be updated frequently. Considerable time is saved by updating the sparse matrix on the GPU instead of on the CPU (slow data transfers between CPU and GPU are reduced). The speedup for the GPU implementation was found to be 8-10 and 12-18 for the GPUs GTX 590 and K20m respectively, depending on grid size. The high speedup is due to the CPU model of the CPUs used for timings being an older model. If a newer CPU model were used, the speedup would be lower. Due to limited access to newer hardware, a more accurate value for speedup comparison has not been acquired. Indications still prove that the GPU implementation is faster than the sequential CPU implementation.