Master's defences | Marty Fuhry, An Implementation of the Discontinuous Galerkin Method on Graphics Processing Units

MC 5158

Candidate

Marty Fuhry, Applied Mathematics, University of Waterloo

Title

An Implementation of the Discontinuous Galerkin Method on Graphics Processing Units

Abstract

Computing highly-accurate approximate solutions to partial differential equations (PDEs) requires both a robust numerical method and a powerful machine. We present a parallel implementation of the discontinuous Galerkin (DG) method on graphics processing units (GPUs). In addition to being flexible and highly accurate, DG methods accommodate parallel architectures well, as their discontinuous nature produces entirely  element-local approximations.

While GPUs were originally intended to compute and display computer graphics, they have recently become a popular general purpose computing device. These cheap and extremely powerful devices have a massively parallel structure. With the recent addition of double precision floating point number support, GPUs have matured as serious platforms for parallel scientific computing.

In this thesis, we present an implementation of the DG method applied to systems of hyperbolic conservation laws in two dimensions on a GPU using NVIDIA’s Compute Unified Device Architecture (CUDA). Numerous computed examples from linear advection to the Euler equations demonstrate the modularity and usefulness of our implementation. Benchmarking our method against a single core, serial implementation of  the DG method reveals a speedup of a factor of over fifty times using a $500 USD NVIDIA GTX 580.