Indexing GPU acceleration for solutions approximation of the Laplace equation

摘要

This paper presents the use of two-dimensional indexation existing in graphics processing units (GPU), to accelerate approximation algorithms of system solutions of partial differential equations. These approximation use recurrent equations where dependence of the near data plays an important role in the calculation speed. For these calculations large amount of data are involved, as well as frequently memory accesses. Therefore, using computational structures that allow you to realize operations in a parallel and concurrent way to process the information more quickly is convenient. Also the memory indexation capacity enables the generation of better acceleration. 3 different architectures are compared, and contrasted against the sequential process on CPU. The results shows how the accelerations up until 9x can be achieve on the case of the Laplace equation in two dimensions.