Handle URI:
http://hdl.handle.net/10754/623515
Title:
Anisotropy in wavelet-based phase field models
Authors:
Korzec, Maciek; Münch, Andreas; Süli, Endre; Wagner, Barbara
Abstract:
When describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and linear. The paper focuses on the classical coupled temperature/Ginzburg--Landau type phase-field model for dendritic growth. For the model based on the wavelet analogue, existence, uniqueness and continuous dependence on initial data are proved for weak solutions. Numerical studies of the wavelet based phase-field model show dendritic growth similar to the results obtained for classical phase-field models.
Citation:
Korzec M, Münch A, Süli E, Wagner B (2016) Anisotropy in wavelet-based phase field models. Discrete and Continuous Dynamical Systems - Series B 21: 1167–1187. Available: http://dx.doi.org/10.3934/dcdsb.2016.21.1167.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Discrete and Continuous Dynamical Systems - Series B
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
1-Apr-2016
DOI:
10.3934/dcdsb.2016.21.1167
Type:
Article
ISSN:
1531-3492
Sponsors:
The first author acknowledges the support by the DFG Matheon research centre, within the project C10, SENBWF in the framework of the program Spitzenforschung und Innovation in den Neuen Landern, Grant Number 03IS2151 and KAUST, award No. KUK-C1-013-04, and the hospitality of the Mathematical Institute at the University of Oxford during his Visiting Postdoctoral Fellowship.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorKorzec, Macieken
dc.contributor.authorMünch, Andreasen
dc.contributor.authorSüli, Endreen
dc.contributor.authorWagner, Barbaraen
dc.date.accessioned2017-05-15T10:35:05Z-
dc.date.available2017-05-15T10:35:05Z-
dc.date.issued2016-04-01en
dc.identifier.citationKorzec M, Münch A, Süli E, Wagner B (2016) Anisotropy in wavelet-based phase field models. Discrete and Continuous Dynamical Systems - Series B 21: 1167–1187. Available: http://dx.doi.org/10.3934/dcdsb.2016.21.1167.en
dc.identifier.issn1531-3492en
dc.identifier.doi10.3934/dcdsb.2016.21.1167en
dc.identifier.urihttp://hdl.handle.net/10754/623515-
dc.description.abstractWhen describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and linear. The paper focuses on the classical coupled temperature/Ginzburg--Landau type phase-field model for dendritic growth. For the model based on the wavelet analogue, existence, uniqueness and continuous dependence on initial data are proved for weak solutions. Numerical studies of the wavelet based phase-field model show dendritic growth similar to the results obtained for classical phase-field models.en
dc.description.sponsorshipThe first author acknowledges the support by the DFG Matheon research centre, within the project C10, SENBWF in the framework of the program Spitzenforschung und Innovation in den Neuen Landern, Grant Number 03IS2151 and KAUST, award No. KUK-C1-013-04, and the hospitality of the Mathematical Institute at the University of Oxford during his Visiting Postdoctoral Fellowship.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectPhase-field modelen
dc.subjectwaveletsen
dc.subjectsharp interface modelen
dc.subjectfree boundariesen
dc.titleAnisotropy in wavelet-based phase field modelsen
dc.typeArticleen
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series Ben
dc.contributor.institutionTechnische Universität Berlin, Institute of Mathematics, Straße des 17. Juni 136, 10623 Berlin, Germanyen
dc.contributor.institutionMathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdomen
dc.contributor.institutionWeierstrass Institute, Mohrenstraße 39, 10117 Berlin, Germanyen
kaust.grant.numberKUK-C1-013-04en
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