Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space

Ji, Liangyue and Ryan, Jennifer (2015) Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space. In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, 106 . Springer, pp. 415-423. ISBN 978-3-319-19799-9

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It has been noted in the past that discontinuous Galerkin methods can be viewed as a low order multi-domain Spectral method with penalty term (Hesthaven et al., Spectral methods for time-dependent problems, Cambridge University Press, Cambridge, 2007). It is then logical to first ask how to relate filters in Spectral Methods to Smoothness-Increasing Accuracy-Conservin (SIAC) filters, which are typically applied to approximations obtained via the discontinuous Galerkin methods. In this article we make a first effort to relate Smoothness-Increasing Accuracy-Conserving filtering to filtering for Spectral Methods. We frame this discussion in the context of Vandeven (J Sci Comput 6:159–192, 1991).

Item Type: Book Section
Uncontrolled Keywords: discontinuous galerkin,siac filtering,spectral methods,filtering
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 05 Feb 2016 13:01
Last Modified: 21 Oct 2022 23:51

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