Generalized summation by parts operators: Second derivative and time-marching methods

David C. Del Rey Fernández; Pieter D. Boom; David W. Zingg

doi:10.1007/978-3-319-19800-2_17

Generalized summation by parts operators: Second derivative and time-marching methods

David C. Del Rey Fernández^*, Pieter D. Boom, David W. Zingg

^*Corresponding author for this work

University of Toronto

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

Abstract

This paper describes extensions of the generalized summation-by-parts (GSBP) framework to the approximation of the second derivative with a variable coefficient and to time integration. GSBP operators for the second derivative lead to more efficient discretizations, relative to the classical finite-difference SBP approach, as they can require fewer nodes for a given order of accuracy. Similarly, for time integration, time-marching methods based on GSBP operators can be more efficient than those based on classical SBP operators, as they minimize the number of solution points which must be solved simultaneously. Furthermore, we demonstrate the link between GSBP operators and Runge-Kutta time-marching methods.

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 Nature
Pages	207-215
Number of pages	9
ISBN (Print)	9783319197999
DOIs	https://doi.org/10.1007/978-3-319-19800-2_17
Publication status	Published - 1 Jan 2015
Event	10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 - Salt Lake City, United States Duration: 23 Jun 2014 → 27 Jun 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	23/06/14 → 27/06/14

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10.1007/978-3-319-19800-2_17

Cite this

Del Rey Fernández, D. C., Boom, P. D., & Zingg, D. W. (2015). Generalized summation by parts operators: Second derivative and time-marching methods. 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. 207-215). (Lecture Notes in Computational Science and Engineering; Vol. 106). Springer Nature. https://doi.org/10.1007/978-3-319-19800-2_17

Del Rey Fernández, David C. ; Boom, Pieter D. ; Zingg, David W. / Generalized summation by parts operators : Second derivative and time-marching methods. 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 Nature, 2015. pp. 207-215 (Lecture Notes in Computational Science and Engineering).

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abstract = "This paper describes extensions of the generalized summation-by-parts (GSBP) framework to the approximation of the second derivative with a variable coefficient and to time integration. GSBP operators for the second derivative lead to more efficient discretizations, relative to the classical finite-difference SBP approach, as they can require fewer nodes for a given order of accuracy. Similarly, for time integration, time-marching methods based on GSBP operators can be more efficient than those based on classical SBP operators, as they minimize the number of solution points which must be solved simultaneously. Furthermore, we demonstrate the link between GSBP operators and Runge-Kutta time-marching methods.",

author = "{Del Rey Fern{\'a}ndez}, {David C.} and Boom, {Pieter D.} and Zingg, {David W.}",

year = "2015",

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

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Del Rey Fernández, DC, Boom, PD & Zingg, DW 2015, Generalized summation by parts operators: Second derivative and time-marching methods. 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 Nature, pp. 207-215, 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014, Salt Lake City, United States, 23/06/14. https://doi.org/10.1007/978-3-319-19800-2_17

Generalized summation by parts operators: Second derivative and time-marching methods. / Del Rey Fernández, David C.; Boom, Pieter D.; Zingg, David W.
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 Nature, 2015. p. 207-215 (Lecture Notes in Computational Science and Engineering; Vol. 106).

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

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N2 - This paper describes extensions of the generalized summation-by-parts (GSBP) framework to the approximation of the second derivative with a variable coefficient and to time integration. GSBP operators for the second derivative lead to more efficient discretizations, relative to the classical finite-difference SBP approach, as they can require fewer nodes for a given order of accuracy. Similarly, for time integration, time-marching methods based on GSBP operators can be more efficient than those based on classical SBP operators, as they minimize the number of solution points which must be solved simultaneously. Furthermore, we demonstrate the link between GSBP operators and Runge-Kutta time-marching methods.

AB - This paper describes extensions of the generalized summation-by-parts (GSBP) framework to the approximation of the second derivative with a variable coefficient and to time integration. GSBP operators for the second derivative lead to more efficient discretizations, relative to the classical finite-difference SBP approach, as they can require fewer nodes for a given order of accuracy. Similarly, for time integration, time-marching methods based on GSBP operators can be more efficient than those based on classical SBP operators, as they minimize the number of solution points which must be solved simultaneously. Furthermore, we demonstrate the link between GSBP operators and Runge-Kutta time-marching methods.

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Del Rey Fernández DC, Boom PD, Zingg DW. Generalized summation by parts operators: Second derivative and time-marching methods. 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 Nature. 2015. p. 207-215. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-19800-2_17

Generalized summation by parts operators: Second derivative and time-marching methods

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