Multiscale computations for highly oscillatory problems

Gil Ariel; Björn Engquist; Heinz Otto Kreiss; Richard Tsai

doi:10.1007/978-3-540-88857-4_5

Multiscale computations for highly oscillatory problems

Gil Ariel
, Björn Engquist
, Heinz Otto Kreiss
, Richard Tsai

University of Texas at Austin
KTH Royal Institute of Technology
Träskö Storö Institute of Mathematics

Research output: Contribution to journal › Conference article › peer-review

11 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	237-287
Number of pages	51
Journal	Lecture Notes in Computational Science and Engineering
Volume	66 LNCSE
DOIs	https://doi.org/10.1007/978-3-540-88857-4_5
State	Published - 2009
Externally published	Yes

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Multiscale computations for highly oscillatory problems

Abstract

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