Smoothness-Increasing Accuracy-Conserving SIAC Filtering for Discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order AccuracyReport as inadecuate




Smoothness-Increasing Accuracy-Conserving SIAC Filtering for Discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy - Download this document for free, or read online. Document in PDF available to download.

Journal of Scientific Computing

, Volume 53, Issue 1, pp 129–149

First Online: 20 April 2012Received: 27 December 2011Revised: 29 March 2012Accepted: 02 April 2012

Abstract

Smoothness-increasing accuracy-conserving SIAC filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order \k+\frac{1}{2}\ to order 2k+1 for specific types of translation invariant meshes Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 301:272–289, 2007; Mirzaee et al. in SIAM J. Numer. Anal. 49:1899–1920, 2011. Additionally, it improves the weak continuity in the discontinuous Galerkin method to k−1 continuity. Typically this improvement has a positive impact on the error quantity in the sense that it also reduces the absolute errors. However, not enough emphasis has been placed on the difference between superconvergent accuracy and improved errors. This distinction is particularly important when it comes to understanding the interplay introduced through meshing, between geometry and filtering. The underlying mesh over which the DG solution is built is important because the tool used in SIAC filtering—convolution—is scaled by the geometric mesh size. This heavily contributes to the effectiveness of the post-processor. In this paper, we present a study of this mesh scaling and how it factors into the theoretical errors. To accomplish the large volume of post-processing necessary for this study, commodity streaming multiprocessors were used; we demonstrate for structured meshes up to a 50× speed up in the computational time over traditional CPU implementations of the SIAC filter.

KeywordsHigh-order methods Discontinuous Galerkin SIAC filtering Accuracy enhancement Post-processing Hyperbolic equations  Download fulltext PDF



Author: James King - Hanieh Mirzaee - Jennifer K. Ryan - Robert M. Kirby

Source: https://link.springer.com/







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