Three-dimensional indexing in GPU for numerical approximation of solutions of the Laplace equation

This paper presents the use of three-dimensional indexing available in graphic processing units (GPU), to accelerate algorithms for the approximate solution of systems described by partial differential equations. These approximations use recurrent equations where dependence of the neighbor data plays an important role in the computation speed. For these calculations large amounts of data are involved, as well as frequently memory accesses. Therefore, using computational structures that allow to perform operations in a parallel and concurrent way is convenient to process the information faster. Also the memory indexing capacity enables the GPU to get better acceleration. Three different architectures are compared, and contrasted against the sequential process on CPU. The results show how accelerations up to 9x can be achieved for the Laplace equation in three dimensions