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

Data Analysis and Machine Learning

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

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
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

Conference

Conference	10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014
Country/Territory	United States
City	Salt Lake City
Period	06/23/14 → 06/27/14

Funding

The works of Dennis Denker and Anne Gelb are supported in part by grants NSF-DMS 1216559 and AFOSR FA9550-12-1-0393. 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.

Funders	Funder number
Air Force Office of Scientific Research
NSF-DMS	1216559
National Science Foundation	DMS 1216559
Office of Science
U.S. Department of Energy
U.S. Department of Energy
Air Force Office of Scientific Research	FA9550-12-1-0393
Office of Science
Advanced Scientific Computing Research	DE-AC05-00OR22725
Oak Ridge National Laboratory
UT-Battelle

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

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).

@inproceedings{2f73b3bf41924423be0ce2c56fdce9a9,

title = "An adaptive fourier filter for relaxing time stepping constraints for explicit solvers",

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.",

author = "Dennis Denker and Rick Archibald and Anne Gelb",

note = "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",

year = "2015",

doi = "10.1007/978-3-319-19800-2_12",

language = "English",

isbn = "9783319197999",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

pages = "157--166",

editor = "Kirby, {Robert M.} and Martin Berzins and Hesthaven, {Jan S.}",

booktitle = "Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM",

}

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, 06/23/14. 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 › peer-review

TY - GEN

T1 - An adaptive fourier filter for relaxing time stepping constraints for explicit solvers

AU - Denker, Dennis

AU - Archibald, Rick

AU - Gelb, Anne

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84952021441&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-19800-2_12

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

M3 - Conference contribution

AN - SCOPUS:84952021441

SN - 9783319197999

T3 - Lecture Notes in Computational Science and Engineering

SP - 157

EP - 166

BT - Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2014, Selected papers from the ICOSAHOM

A2 - Kirby, Robert M.

A2 - Berzins, Martin

A2 - Hesthaven, Jan S.

PB - Springer Verlag

T2 - 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014

Y2 - 23 June 2014 through 27 June 2014

ER -

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

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

Abstract

Publication series

Conference

Funding

Access to Document

Other files and links

Fingerprint

Cite this