A fractional phase-field model using an infinitesimal generator of \(\alpha\) stable Lévy process

DOI10.1016/j.jcp.2019.01.042zbMath1451.76127OpenAlexW2916171465MaRDI QIDQ2214652

Siwei Duo, Hong Wang

Publication date: 10 December 2020

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2019.01.042

zbMATH Keywords

rotational invariancefractional LaplacianRiemann-Liouville fractional derivativefractional Allen-Cahn model

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11) Liquid-liquid two component flows (76T06)

Related Items

Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm, A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape, Compatible Energy Dissipation of the Variable-Step \({\boldsymbol{L1}}\) Scheme for the Space-Time Fractional Cahn-Hilliard Equation, Variable-order fractional Laplacian and its accurate and efficient computations with meshfree methods, On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for the fractional Allen-Cahn equation, Fractional SUPG finite element formulation for multi-dimensional fractional advection diffusion equations, A fast Galerkin finite element method for a space-time fractional Allen-Cahn equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A space-time fractional phase-field model with tunable sharpness and decay behavior and its efficient numerical simulation
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Heat kernel estimates for the Dirichlet fractional Laplacian
• Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
• On a nonlocal phase separation model
• A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
• A nonlocal diffuse interface model for microstructure evolution of tin--lead solder
• Modeling and numerical simulations of dendritic crystal growth
• A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals.
• Modeling melt convection in phase-field simulations of solidification
• The Cauchy process and the Steklov problem
• A phase field concept for multiphase systems
• A tunable finite difference method for fractional differential equations with non-smooth solutions
• Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
• A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations
• On a nonlocal phase-field system
• Multi phase field model for solid state transformation with elastic strain
• An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
• A phase–field paradigm for grain growth and recrystallization
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• A Fast Finite Element Method for Space-Fractional Dispersion Equations on Bounded Domains in $\mathbb{R}^2$
• Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations