GPU-based acceleration of a water wave model

A two-dimensional water wave model based on potential flow is investigated with the intention of simulating marine water on the large scale. The transformed linearized Laplace problem, which arises in the model is solved by the Multigrid method on the GPU using CUDA. Full Multigrid cycle is extended by an additional sequence of V-cycles to achieve desired accuracy. The algorithm is terminated after the iterative method error becomes insignificant compared to the discretization error of the finite difference method. Multigrid is completely parallelized to fit the GPU architecture. Every step of the algorithm is designed in such a way, that no communication between GPU threads is necessary. Jacobi method is used as the smoothing step in the Multigrid. A discretization scheme using an additional layer of grid points lying outside the fluid domain, described in [A.P. Engsig-Karup, H.B. Bingham, O. Lindberg, An efficient flexible-order model for 3D nonlinear water waves], is used. All GPU computations are performed using double-precision. For devices, which do not support double-precision operations, single-precision mode is also available. Experiments performed on NVIDIA Tesla C1060 show linear growth of execution time with the problem size. The method is robust enough for available memory to be the limiting factor, rather than required execution time. Problem sizes with over 67 millions of unknowns were tested. Experiments show monotonic convergence and rate o