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

Liangyue Ji; Jennifer Ryan

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

Liangyue Ji, Jennifer Ryan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

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).

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
Publisher	Springer
Pages	415-423
Number of pages	9
Volume	106
ISBN (Electronic)	978-3-319-19800-2
ISBN (Print)	978-3-319-19799-9
Publication status	Published - Dec 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering

Keywords

discontinuous Galerkin
SIAC filtering
Spectral methods
filtering

Exploiting Superconvergence in Discontinuous Galerkin Methods for Improved Time-Stepping and Visualization
Ryan, J.
US Airforce
1/02/13 → 31/07/16
Project: Research

Cite this

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title = "Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space",

abstract = "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).",

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author = "Liangyue Ji and Jennifer Ryan",

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Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space. / Ji, Liangyue; Ryan, Jennifer.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Vol. 106 Springer, 2015. p. 415-423 (Lecture Notes in Computational Science and Engineering).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space

AU - Ji, Liangyue

AU - Ryan, Jennifer

PY - 2015/12

Y1 - 2015/12

N2 - 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).

AB - 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).

KW - discontinuous Galerkin

KW - SIAC filtering

KW - Spectral methods

KW - filtering

M3 - Conference contribution

SN - 978-3-319-19799-9

VL - 106

T3 - Lecture Notes in Computational Science and Engineering

SP - 415

EP - 423

BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

PB - Springer

ER -

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

Abstract

Publication series

Keywords

Projects

Exploiting Superconvergence in Discontinuous Galerkin Methods for Improved Time-Stepping and Visualization

Cite this