MC 5158
Candidate
Marty Fuhry, Applied Mathematics, University of À¶Ý®ÊÓƵ
Title
An Implementation of the Discontinuous Galerkin Method on Graphics Processing Units
Abstract
Computing highly-accurate approximate solutions to partial differential equations (PDEs)Ìýrequires both a robust numerical method and a powerful machine. We present a parallelÌýimplementation of the discontinuous Galerkin (DG) method on graphics processing unitsÌý(GPUs). In addition to being flexible and highly accurate, DG methods accommodateÌýparallel architectures well, as their discontinuous nature produces entirely Ìýelement-localÌýapproximations.
While GPUs were originally intended to compute and display computer graphics, theyÌýhave recently become a popular general purpose computing device. These cheap andÌýextremely powerful devices have a massively parallel structure. With the recent additionÌýof double precision floating point number support, GPUs have matured as serious platformsÌýfor parallel scientific computing.
In this thesis, we present an implementation of the DG method applied to systemsÌýof hyperbolic conservation laws in two dimensions on a GPU using NVIDIA’s ComputeÌýUnified Device Architecture (CUDA). Numerous computed examples from linear advectionÌýto the Euler equations demonstrate the modularity and usefulness of our implementation.ÌýBenchmarking our method against a single core, serial implementation of Ìýthe DG methodÌýreveals a speedup of a factor of over fifty times using a $500 USD NVIDIA GTX 580.