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dc.contributor.authorFuhry, Martin 14:37:27 (GMT) 14:37:27 (GMT)
dc.description.abstractComputing 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 USD $500.00 NVIDIA GTX 580.en
dc.publisherUniversity of Waterlooen
dc.subjectnumerical PDEen
dc.titleAn Implementation of the Discontinuous Galerkin Method on Graphics Processing Unitsen
dc.typeMaster Thesisen
dc.subject.programApplied Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

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