Solving Phase-Field Models with Fourier Spectral Methods

2017 ◽  
pp. 99-168
Author(s):  
S. Bulent Biner
Keyword(s):  
Phase Field ◽  
Spectral Methods ◽  
Phase Field Models ◽  
Fourier Spectral Methods

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

scholarly journals Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Zhan Chen
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Lagrangian Formulation ◽  
Global Minimizer ◽  
Solvation Model ◽  
Phase Field Models ◽  
Eulerian Formulation ◽  
Solvation Models ◽  
Similarity And Difference ◽  
Nonpolar Solvation

AbstractIn this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.

Sign in / Sign up

Export Citation Format

Share Document