Multi-dimensional filtering: Reducing the dimension through rotation

Docampo, Julia, Ryan, Jennifer K., Mirzargar, Mahsa and Kirby, Robert M. (2017) Multi-dimensional filtering: Reducing the dimension through rotation. SIAM Journal on Scientific Computing, 39 (5). A2179–A2200. ISSN 1064-8275

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Abstract

Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate of the DG solution through this post-processor. These advantages can be exploited during flow visualization, for example by applying the SIAC filter to the DG data before streamline computations [Steffan et al., IEEE-TVCG 14(3): 680-692]. However, introducing these filters in engineering applications can be challenging since a tensor product filter grows in support size as the field dimension increases, becoming computationally expensive. As an alternative, [Walfisch et al., JOMP 38(2);164-184] proposed a univariate filter implemented along the streamline curves. Until now, this technique remained a numerical experiment. In this paper we introduce the line SIAC filter and explore how the orientation, structure and filter size affect the order of accuracy and global errors. We present theoretical error estimates showing how line filtering preserves the properties of traditional tensor product filtering, including smoothness and improvement in the convergence rate. Furthermore, numerical experiments are included, exhibiting how these filters achieve the same accuracy at significantly lower computational costs, becoming an attractive tool for the scientific visualization community.

Item Type: Article
Uncontrolled Keywords: discontinuous galerkin,post-processing,siac filtering,accuracy enhancement,error reduction
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 12 May 2017 05:06
Last Modified: 05 Aug 2020 23:41
URI: https://ueaeprints.uea.ac.uk/id/eprint/63493
DOI: 10.1137/16M1097845

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