Riviere, Beatrice M.Warburton, Tim2013-03-082013-03-082011Tullius, Toni Kathleen. "Accelerated Discontinuous Galerkin Solvers with the Chebyshev Iterative Method on the Graphics Processing Unit." (2011) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/70478">https://hdl.handle.net/1911/70478</a>.https://hdl.handle.net/1911/70478This work demonstrates implementations of the discontinuous Galerkin (DG) method on graphics processing units (GPU), which deliver improved computational time compared to the conventional central processing unit (CPU). The linear system developed when applying the DG method to an elliptic problem is solved using the GPU. The conjugate gradient (CG) method and the Chebyshev iterative method are the linear system solvers that are compared, to see which is more efficient when computing with the CPU's parallel architecture. When applying both methods, computational times decreased for large problems executed on the GPU compared to CPU; however, CG is the more efficient method compared to the Chebyshev iterative method. In addition, a constant-free upper bound for the DC spectrum applied to the elliptic problem is developed. Few previous works combine the DG method and the GPU. This thesis will provide useful guidelines for the numerical solution of elliptic problems using DG on the GPU.76 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Applied sciencesApplied mathematicsComputer engineeringThesisTulliusTTHESIS MATH.SCI. 2011 TULLIUS