Oscillatory systems with three separated time scales: Analysis and computation

Gil Ariel; Björn Engquist; Yen Hsi Richard Tsai

doi:10.1007/978-3-642-21943-6_2

Oscillatory systems with three separated time scales: Analysis and computation

Gil Ariel, Björn Engquist, Yen Hsi Richard Tsai

Department of Mathematics

University of Texas at Austin

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

6 Scopus citations

Abstract

We study a few interesting issues that occur in multiscale modeling and computation for oscillatory dynamical systems that involve three or more separated scales. A new type of slow variables which do not formally have bounded derivatives emerge from averaging in the fastest time scale. We present a few systems which have such new slow variables and discuss their characterization. The examples motivate a numerical multiscale algorithm that uses nested tiers of integrators which numerically solve the oscillatory system on different time scales. The communication between the scales follows the framework of the Heterogeneous Multiscale Method. The method’s accuracy and efficiency are evaluated and its applicability is demonstrated by examples.

Original language	English
Title of host publication	Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009
Editors	Olof Runborg, Bjorn Engquist, Yen-Hsi R. Tsai
Publisher	Springer Verlag
Pages	23-45
Number of pages	23
ISBN (Print)	9783642219429
DOIs	https://doi.org/10.1007/978-3-642-21943-6_2
State	Published - 2012
Event	Workshop on Numerical Analysis and Multiscale Computations, 2009 - Banff, Canada Duration: 6 Dec 2009 → 11 Dec 2009

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	82
ISSN (Print)	1439-7358

Conference

Conference	Workshop on Numerical Analysis and Multiscale Computations, 2009
Country/Territory	Canada
City	Banff
Period	6/12/09 → 11/12/09

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.

Access to Document

10.1007/978-3-642-21943-6_2

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Ariel, G., Engquist, B., & Tsai, Y. H. R. (2012). Oscillatory systems with three separated time scales: Analysis and computation. In O. Runborg, B. Engquist, & Y.-H. R. Tsai (Eds.), Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009 (pp. 23-45). (Lecture Notes in Computational Science and Engineering; Vol. 82). Springer Verlag. https://doi.org/10.1007/978-3-642-21943-6_2

Ariel, Gil ; Engquist, Björn ; Tsai, Yen Hsi Richard. / Oscillatory systems with three separated time scales : Analysis and computation. Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. editor / Olof Runborg ; Bjorn Engquist ; Yen-Hsi R. Tsai. Springer Verlag, 2012. pp. 23-45 (Lecture Notes in Computational Science and Engineering).

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Ariel, G, Engquist, B & Tsai, YHR 2012, Oscillatory systems with three separated time scales: Analysis and computation. in O Runborg, B Engquist & Y-HR Tsai (eds), Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. Lecture Notes in Computational Science and Engineering, vol. 82, Springer Verlag, pp. 23-45, Workshop on Numerical Analysis and Multiscale Computations, 2009, Banff, Canada, 6/12/09. https://doi.org/10.1007/978-3-642-21943-6_2

Oscillatory systems with three separated time scales: Analysis and computation. / Ariel, Gil; Engquist, Björn; Tsai, Yen Hsi Richard.
Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. ed. / Olof Runborg; Bjorn Engquist; Yen-Hsi R. Tsai. Springer Verlag, 2012. p. 23-45 (Lecture Notes in Computational Science and Engineering; Vol. 82).

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

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Ariel G, Engquist B, Tsai YHR. Oscillatory systems with three separated time scales: Analysis and computation. In Runborg O, Engquist B, Tsai YHR, editors, Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. Springer Verlag. 2012. p. 23-45. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-642-21943-6_2

Oscillatory systems with three separated time scales: Analysis and computation

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