Multigrid
Exponential time differencing for stiff systems
Journal of Computational Physics
Geometrical image segmentation by the Allen-Cahn equation
Applied Numerical Mathematics
Adaptive Mesh Refinement for Multiscale Nonequilibrium Physics
Computing in Science and Engineering
Journal of Scientific Computing
Journal of Computational Physics
Spectral implementation of an adaptive moving mesh method for phase-field equations
Journal of Computational Physics
An efficient algorithm for solving the phase field crystal model
Journal of Computational Physics
A Wavelet-Laplace Variational Technique for Image Deconvolution and Inpainting
IEEE Transactions on Image Processing
Multiphase image segmentation using a phase-field model
Computers & Mathematics with Applications
Surface embedding narrow volume reconstruction from unorganized points
Computer Vision and Image Understanding
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We present an unconditionally stable second-order hybrid numerical method for solving the Allen-Cahn equation representing a model for antiphase domain coarsening in a binary mixture. The proposed method is based on operator splitting techniques. The Allen-Cahn equation was divided into a linear and a nonlinear equation. First, the linear equation was discretized using a Crank-Nicolson scheme and the resulting discrete system of equations was solved by a fast solver such as a multigrid method. The nonlinear equation was then solved analytically due to the availability of a closed-form solution. Various numerical experiments are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, we show that the scheme is unconditionally stable and second-order accurate in both time and space.