Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Communications of the ACM
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
Mathematics of Computation
SIAM Journal on Scientific Computing
Postprocessing for the Discontinuous Galerkin Method over Nonuniform Meshes
SIAM Journal on Scientific Computing
IEEE Transactions on Visualization and Computer Graphics
Journal of Scientific Computing
Local derivative post-processing for the discontinuous Galerkin method
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A scalable, efficient scheme for evaluation of stencil computations over unstructured meshes
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many post-processing algorithms such as those used in visualization are based. Smoothness-increasing accuracy-conserving (SIAC) filters were proposed as a means of ameliorating the challenges introduced by the lack of regularity at element interfaces by eliminating the discontinuity between elements in a way that is consistent with the DG methodology; in particular, high-order accuracy is preserved and in many cases increased. The goal of this paper is to explicitly define the steps to efficient computation of this filtering technique as applied to both structured triangular and quadrilateral meshes. Furthermore, as the SIAC filter is a good candidate for parallelization, we provide, for the first time, results that confirm anticipated performance scaling when parallelized on a shared-memory multi-processor machine.