TY - JOUR
T1 - Anisotropy in wavelet-based phase field models
AU - Korzec, Maciek
AU - Münch, Andreas
AU - Süli, Endre
AU - Wagner, Barbara
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/623515
UR - http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12429
UR - http://www.scopus.com/inward/record.url?scp=84962747542&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2016.21.1167
DO - 10.3934/dcdsb.2016.21.1167
M3 - Article
SN - 1531-3492
VL - 21
SP - 1167
EP - 1187
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 4
ER -