**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Wednesday, April 10, 2013 10:00 AM EDT

MC 5158

Marty Fuhry, Applied Mathematics, University of Waterloo

An Implementation of the Discontinuous Galerkin Method on Graphics Processing Units

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.

Location

University of Waterloo

MC 5158

,

Canada

,

Canada

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.