Dirk schemes with high weak stage order

David I. Ketcheson; Benjamin Seibold; David Shirokoff; Dong Zhou

doi:10.1007/978-3-030-39647-3_36

Dirk schemes with high weak stage order

David I. Ketcheson, Benjamin Seibold, David Shirokoff, Dong Zhou

Mathematical Sciences

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

6 Scopus citations

Abstract

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

Original language	English (US)
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference
Editors	Spencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
Publisher	Springer
Pages	453-463
Number of pages	11
ISBN (Print)	9783030396466
DOIs	https://doi.org/10.1007/978-3-030-39647-3_36
State	Published - 2020
Event	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, United Kingdom Duration: Jul 9 2018 → Jul 13 2018

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	134
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
Country/Territory	United Kingdom
City	London
Period	7/9/18 → 7/13/18

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1007/978-3-030-39647-3_36

Cite this

Ketcheson, D. I., Seibold, B., Shirokoff, D., & Zhou, D. (2020). Dirk schemes with high weak stage order. In S. J. Sherwin, J. Peiró, P. E. Vincent, D. Moxey, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference (pp. 453-463). (Lecture Notes in Computational Science and Engineering; Vol. 134). Springer. https://doi.org/10.1007/978-3-030-39647-3_36

Ketcheson, David I. ; Seibold, Benjamin ; Shirokoff, David et al. / Dirk schemes with high weak stage order. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. editor / Spencer J. Sherwin ; Joaquim Peiró ; Peter E. Vincent ; David Moxey ; Christoph Schwab. Springer, 2020. pp. 453-463 (Lecture Notes in Computational Science and Engineering).

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abstract = "Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.",

author = "Ketcheson, {David I.} and Benjamin Seibold and David Shirokoff and Dong Zhou",

note = "Publisher Copyright: {\textcopyright} 2020, The Author(s).; 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2020",

doi = "10.1007/978-3-030-39647-3_36",

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

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booktitle = "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference",

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Ketcheson, DI, Seibold, B, Shirokoff, D & Zhou, D 2020, Dirk schemes with high weak stage order. in SJ Sherwin, J Peiró, PE Vincent, D Moxey & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. Lecture Notes in Computational Science and Engineering, vol. 134, Springer, pp. 453-463, 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018, London, United Kingdom, 7/9/18. https://doi.org/10.1007/978-3-030-39647-3_36

Dirk schemes with high weak stage order. / Ketcheson, David I.; Seibold, Benjamin; Shirokoff, David et al.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. ed. / Spencer J. Sherwin; Joaquim Peiró; Peter E. Vincent; David Moxey; Christoph Schwab. Springer, 2020. p. 453-463 (Lecture Notes in Computational Science and Engineering; Vol. 134).

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

TY - GEN

T1 - Dirk schemes with high weak stage order

AU - Ketcheson, David I.

AU - Seibold, Benjamin

AU - Shirokoff, David

AU - Zhou, Dong

PY - 2020

Y1 - 2020

N2 - Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

AB - Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

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T3 - Lecture Notes in Computational Science and Engineering

SP - 453

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BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference

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A2 - Peiró, Joaquim

A2 - Vincent, Peter E.

A2 - Moxey, David

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Ketcheson DI, Seibold B, Shirokoff D, Zhou D. Dirk schemes with high weak stage order. In Sherwin SJ, Peiró J, Vincent PE, Moxey D, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. Springer. 2020. p. 453-463. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-39647-3_36

Dirk schemes with high weak stage order

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