James King

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Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order k + 1 2 to order 2k + 1 for specific types of translation invariant meshes (Cockburn et al. improves the weak continuity in the discontinuous Galerkin method to k − 1 continuity.(More)
The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromag-netics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with conventional(More)
Sparse matrices are a core component in many numerical simulations, and their efficiency is essential to achieving high performance. Dynamic sparse-matrix allocation (insertion) can benefit a number of problems such as sparse-matrix factorization, sparse-matrix-matrix addition, static analysis (e.g., points-to analysis), computing transitive closure, and(More)
Numerical methods for elliptic partial differential equations (PDEs) within both continuous (CG) and hybridized discontinuous Galerkin (HDG) frameworks share the same general structure: local (elemental) matrix generation followed by a global linear system assembly and solve. The lack of inter-element communication and easily parallelizable nature of the(More)
Stencil computations are a common class of operations that appear in many computational scientific and engineering applications. Stencil computations often benefit from compile-time analysis, exploiting data-locality, and parallelism. Post-processing of discontinuous Galerkin (dG) simulation solutions with B-spline kernels is an example of a numerical(More)
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