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KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The standard numerical methods developed for handling evolutions of fronts use a set of marker points as a discrete representation of the interface on its path in a velocity field. In this study a multi resolution representation will be introduced, replacing the markers. The interface will be described by a set of marker related wavelet vectors. Like the markers the vectors satisfy ordinary dffierential equations. In much the same way as the markers, the vectors are traced in the same velocity field with the same properties. In addition, the vectors evolve slower for the finer spatial scaled vectors. The intent is to exploit this property by increasing the time step for finer scales in order to reduce computational cost without compromising accuracy. Two multi resolution ODE algorithms will be developed and examined with respect to computational cost and accuracy, both theoretical and empirical for comparison with their marker point representation.

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URN: urn:nbn:se:kth:diva-168955OAI: diva2:818905
Available from: 2015-06-09 Created: 2015-06-09 Last updated: 2015-06-09Bibliographically approved

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