Motion by mean curvature of curves on surfaces using the Allen-Cahn Equation

DOI10.1016/j.ijengsci.2015.10.002zbMath1425.65038OpenAlexW1846478001MaRDI QIDQ1623233

Darae Jeong, Yongho Choi, Minhyun Yoo, Seunggyu Lee, Junseok Kim

Publication date: 23 November 2018

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ijengsci.2015.10.002

zbMATH Keywords

closest point methodmotion by mean curvaturenarrow band domainAllen-Cahn Equationhybrid explicit scheme

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (21)

Numerical simulation of the zebra pattern formation on a three-dimensional model ⋮ The local tangential lifting method for moving interface problems on surfaces with applications ⋮ An efficient numerical method for reaction-diffusion equation on the general curved surfaces ⋮ An adaptive time-stepping algorithm for the Allen-Cahn equation ⋮ A finite difference method for a conservative Allen-Cahn equation on non-flat surfaces ⋮ Numerical simulation of binary fluid-surfactant phase field model coupled with geometric curvature on the curved surface ⋮ A convergent iterated quasi-interpolation for periodic domain and its applications to surface PDEs ⋮ Unconditionally maximum principle preserving finite element schemes for the surface Allen–Cahn type equations ⋮ Fast and efficient numerical method for solving the Allen-Cahn equation on the cubic surface ⋮ A radial basis function approximation method for conservative Allen-Cahn equations on surfaces ⋮ A Kernel-Based Least-Squares Collocation Method for Surface Diffusion ⋮ Solving partial differential equations on (evolving) surfaces with radial basis functions ⋮ A high-order meshless Galerkin method for semilinear parabolic equations on spheres ⋮ A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space ⋮ Numerical simulation and error estimation of the time-dependent Allen-Cahn equation on surfaces with radial basis functions ⋮ A phase-field model and its efficient numerical method for two-phase flows on arbitrarily curved surfaces in 3D space ⋮ Non-iterative compact operator splitting scheme for Allen-Cahn equation ⋮ A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces ⋮ Modeling and numerical simulation of surfactant systems with incompressible fluid flows on surfaces ⋮ A practical finite difference scheme for the Navier-Stokes equation on curved surfaces in \(\mathbb{R}^3\) ⋮ The stabilized semi-implicit finite element method for the surface Allen-Cahn equation

Cites Work

• Solving eigenvalue problems on curved surfaces using the closest point method
• An Eulerian formulation for solving partial differential equations along a moving interface
• Diffusion generated motion of curves on surfaces
• A simple embedding method for solving partial differential equations on surfaces
• The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface
• Variational problems and partial differential equations on implicit surfaces

This page was built for publication: Motion by mean curvature of curves on surfaces using the Allen-Cahn Equation