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Multiscale computations for highly oscillatory problems
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). University of Texas at Austin, United States .
2009 (English)In: Multiscale Modeling and Simulation in Science, Springer Berlin/Heidelberg, 2009, 237-287 p.Conference paper (Refereed)
Abstract [en]

We review a selection of essential techniques for constructing computational multiscale methods for highly oscillatory ODEs. Contrary to the typical approaches that attempt to enlarge the stability region for specialized problems, these lecture notes emphasize how multiscale properties of highly oscillatory systems can be characterized and approximated in a truly multiscale fashion similar to the settings of averaging and homogenization. Essential concepts such as resonance, fast-slow scale interactions, averaging, and techniques for transformations to non-stiff forms are discussed in an elementary manner so that the materials can be easily accessible to beginning graduate students in applied mathematics or computational sciences.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2009. 237-287 p.
, Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 66
Keyword [en]
Applied mathematics, Computational science, Graduate students, Highly oscillatory problems, Lecture Notes, Multi-scale, Multi-scale methods, Multiscale computations, Oscillatory systems, Scale interactions, Stability regions
National Category
URN: urn:nbn:se:kth:diva-152460DOI: 10.1007/978-3-540-88857-4_5ScopusID: 2-s2.0-78651544535OAI: diva2:750051
Summer School on Multiscale Modeling and Simulation in Science; Stockholm; Sweden

QC 20140926

Available from: 2014-09-26 Created: 2014-09-26 Last updated: 2014-09-26Bibliographically approved

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Engquist, Björn
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Numerical Analysis, NA (closed 2012-06-30)

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