An adaptive fourier filter for relaxing time stepping constraints for explicit solvers

Dennis Denker; Rick Archibald; Anne Gelb

doi:10.1007/978-3-319-19800-2_12

An adaptive fourier filter for relaxing time stepping constraints for explicit solvers

Dennis Denker, Rick Archibald, Anne Gelb

Mathematical and Statistical Sciences, School of (SoMSS)

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

Abstract

Filtering is necessary to stabilize piecewise smooth solutions. The resulting diffusion stabilizes the method, but may fail to resolve the solution near discontinuities. Moreover, high order filtering still requires cost prohibitive time stepping. This paper introduces an adaptive filter that controls spurious modes of the solution, but is not unnecessarily diffusive. Consequently we are able to stabilize the solution with larger time steps, but also take advantage of the accuracy of a high order filter.

Original language	English (US)
Title of host publication	Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM
Editors	Robert M. Kirby, Martin Berzins, Jan S. Hesthaven
Publisher	Springer Verlag
Pages	157-166
Number of pages	10
ISBN (Print)	9783319197999
DOIs	https://doi.org/10.1007/978-3-319-19800-2_12
State	Published - 2015
Event	10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 - Salt Lake City, United States Duration: Jun 23 2014 → Jun 27 2014

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	106
ISSN (Print)	1439-7358

Other

Other	10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014
Country/Territory	United States
City	Salt Lake City
Period	6/23/14 → 6/27/14

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-319-19800-2_12

Cite this

Denker, D., Archibald, R., & Gelb, A. (2015). An adaptive fourier filter for relaxing time stepping constraints for explicit solvers. In R. M. Kirby, M. Berzins, & J. S. Hesthaven (Eds.), Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM (pp. 157-166). (Lecture Notes in Computational Science and Engineering; Vol. 106). Springer Verlag. https://doi.org/10.1007/978-3-319-19800-2_12

An adaptive fourier filter for relaxing time stepping constraints for explicit solvers. / Denker, Dennis; Archibald, Rick; Gelb, Anne.
Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM. ed. / Robert M. Kirby; Martin Berzins; Jan S. Hesthaven. Springer Verlag, 2015. p. 157-166 (Lecture Notes in Computational Science and Engineering; Vol. 106).

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

Denker, D, Archibald, R & Gelb, A 2015, An adaptive fourier filter for relaxing time stepping constraints for explicit solvers. in RM Kirby, M Berzins & JS Hesthaven (eds), Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM. Lecture Notes in Computational Science and Engineering, vol. 106, Springer Verlag, pp. 157-166, 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014, Salt Lake City, United States, 6/23/14. https://doi.org/10.1007/978-3-319-19800-2_12

Denker D, Archibald R, Gelb A. An adaptive fourier filter for relaxing time stepping constraints for explicit solvers. In Kirby RM, Berzins M, Hesthaven JS, editors, Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM. Springer Verlag. 2015. p. 157-166. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-19800-2_12

Denker, Dennis ; Archibald, Rick ; Gelb, Anne. / An adaptive fourier filter for relaxing time stepping constraints for explicit solvers. Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM. editor / Robert M. Kirby ; Martin Berzins ; Jan S. Hesthaven. Springer Verlag, 2015. pp. 157-166 (Lecture Notes in Computational Science and Engineering).

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abstract = "Filtering is necessary to stabilize piecewise smooth solutions. The resulting diffusion stabilizes the method, but may fail to resolve the solution near discontinuities. Moreover, high order filtering still requires cost prohibitive time stepping. This paper introduces an adaptive filter that controls spurious modes of the solution, but is not unnecessarily diffusive. Consequently we are able to stabilize the solution with larger time steps, but also take advantage of the accuracy of a high order filter.",

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note = "Funding Information: The works of Dennis Denker and Anne Gelb are supported in part by grants NSF-DMS 1216559 and AFOSR FA9550-12-1-0393. Funding Information: The submitted manuscript is based upon work of Rick Archibald, authored in part by contractors [UT-Battelle LLC, manager of Oak Ridge National Laboratory (ORNL)], and supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract No. DE-AC05-00OR22725. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 ; Conference date: 23-06-2014 Through 27-06-2014",

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An adaptive fourier filter for relaxing time stepping constraints for explicit solvers

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