Investigating GPU parallelism for discontinuous Petrov-Galerkin methods with optimal test functions

Abstract

We study the application of the naturally stable class of numerical methods called discontinuous Petrov-Galerkin methods with optimal test spaces, or DPG methods, focusing on their inherent complexity and potential for massive parallelism. We develop a numerical DPG solver for the Poisson equation using Python and analyze and test its complexity. Using PyCUDA we port essential numerical DPG computations to a graphics processing unit. We find that much of the cost introduced by the use of discontinuous optimal test spaces can be greatly alleviated through the use of a GPU.