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Wavelets and wavelet based numerical homogenization
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).ORCID iD: 0000-0002-6321-8619
2009 (English)In: Multiscale Modeling and Simulation in Science, Springer Berlin/Heidelberg, 2009, 195-235 p.Conference paper (Refereed)
Abstract [en]

Wavelets is a tool for describing functions on different scales or level of detail. In mathematical terms, wavelets are functions that form a basis for with special properties; the basis functions are spatially localized and correspond to different scale levels. Finding the representation of a function in this basis amounts to making a multiresolution decomposition of the function. Such a wavelet representation lends itself naturally to analyzing the fine and coarse scales as well as the localization properties of a function.Wavelets have been used in many applications, from image and signal analysis to numerical methods for partial differential equations (PDEs). In this tutorial we first go through the basic wavelet theory and then show a more specific application where wavelets are used for numerical homogenization.We will mostly give references to the original sources of ideas presented. There are also a large number of books and review articles that cover the topic of wavelets, where the interested reader can find further information, e.g. [25, 51, 48, 7, 39, 26, 23], just to mention a few.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2009. 195-235 p.
, Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 66
Keyword [en]
Basis functions, Different scale, Different scale levels, Level of details, Localization properties, Multi-resolution decompositions, Numerical homogenizations, Special properties, Wavelet representations, Wavelet theories, Describing functions, Reviews, Signal analysis, Numerical methods
National Category
URN: urn:nbn:se:kth:diva-152461DOI: 10.1007/978-3-540-88857-4_4ScopusID: 2-s2.0-78651548355ISBN: 978-3-540-88856-7OAI: diva2:750047
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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Runborg, Olof
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Numerical Analysis, NA (closed 2012-06-30)

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