Shape transformation using the modified Allen-Cahn equation

DOI10.1016/J.AML.2020.106487zbMath1440.65089OpenAlexW3024094130MaRDI QIDQ2186775

Jian Wang, Sangkwon Kim, Junseok Kim, Chaeyoung Lee, Hyundong Kim, Sungha Yoon, Jintae Park

Publication date: 9 June 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106487

zbMATH Keywords

phase-fieldAllen-Cahn equationmetamorphosisshape transformation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stefan problems, phase changes, etc. (80A22) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical interpolation (65D05) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (6)

Three-dimensional volume reconstruction from multi-slice data using a shape transformation ⋮ An efficient maximum bound principle preserving p-adaptive operator-splitting method for three-dimensional phase field shape transformation model ⋮ A second-order maximum bound principle preserving operator splitting method for the Allen-Cahn equation with applications in multi-phase systems ⋮ A simple shape transformation method based on phase-field model ⋮ Shape transformation on curved surfaces using a phase-field model ⋮ Hybrid numerical method for the Allen-Cahn equation on nonuniform grids

Cites Work

• An explicit hybrid finite difference scheme for the Allen-Cahn equation
• An efficient reproducing kernel method for solving the Allen-Cahn equation
• Using partial differential equations to generate free-form surfaces
• Fast, unconditionally energy stable large time stepping method for a new Allen-Cahn type square phase-field crystal model
• An unconditionally stable hybrid method for image segmentation
• Poisson shape interpolation

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