Spectral implementation of an adaptive moving mesh method for phase-field equations

Feng, Wenqiang; Yu, Peng; Hu, Sanmei; Liu, Zhe; Du, Qiang; Chen, Lei

doi:10.1016/j.jcp.2006.07.013

Cited by 82 publications

(41 citation statements)

References 30 publications

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“…Then a compact ETD multistep solution method for solving the variable mobility Cahn-Hilliad Eq. (1) is identical to (18) …”

Section: The Variable Mobility Problem With Periodic Boundary Conditionmentioning

confidence: 99%

“…Fast high order and efficient spatial discretizations have been widely used ranging from spectral discretizations [16], multigrid algorithms [17] and moving mesh implementations [18][19][20]. High order methods in both space and time are shown to be computationally more competitive for phase field simulations even in the sharp interface limit [21].…”

Section: Introductionmentioning

confidence: 99%

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Fast and accurate algorithms for simulating coarsening dynamics of Cahn–Hilliard equations

Zhang

2015

Computational Materials Science

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a b s t r a c tNumerical simulation of microstructure coarsening is a subject of great interest in computational materials science. The coarsening dynamics in a binary mixture can be modeled by the celebrated Cahn-Hilliard equations. To perform efficient and accurate long-time integrations, we develop a fast and stable high order numerical method for solving Cahn-Hilliard equations. The spatial discretization is carried out by the compact central difference scheme with FFT-based fast implementation while the time integration is done through the accurate exponential time differencing multistep approach. We demonstrate the effectiveness of the proposed method by numerical experiments and study computationally the coarsening kinetics corresponding to different choices of the diffusion mobility.

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“…Then a compact ETD multistep solution method for solving the variable mobility Cahn-Hilliad Eq. (1) is identical to (18) …”

Section: The Variable Mobility Problem With Periodic Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast and accurate algorithms for simulating coarsening dynamics of Cahn–Hilliard equations

Zhang

2015

Computational Materials Science

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“…In contrast to the traditional diffusive phase-field models, the (2.7) contains a nonlinear TV-diffusion operator rather than a linear Laplacian diffusion. This induces some difficulties for numerical solutions, but since the TV-term has the capability to preserve discontinuities and edges, the TVmodel might avoid mesh refinement as usually required for phase-field models [24,49]. This model can also be used for multi-phase segmentation [36,37].…”

Section: Image Segmentation Using Pclsmmentioning

confidence: 99%

“…Due to this nonlinear nature of the model, it will add some difficulties to solve the corresponding equations. However, this new model will avoid the difficulties with mesh refinement around the singular layers [24,49]. Moreover, both models can approximate the TV-norm of the function.…”

Section: Introductionmentioning

confidence: 99%

Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models

Rong

Wang

2011

Adv Comput Math

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An adaptive wavelet-based method is proposed for solving TV(total variation)-Allen-Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multiphase image segmentation. This method is also applied to image restoration and similar advantages are observed.

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“…Two strategies seem promising at present. One is an adaptive meshing technique that dynamically adjusts an Eulerian grid [54], and the other is a moving mesh scheme that incorporates Lagrangian movement of the grid points [17]. Three-dimensional codes using both methods are under development.…”

Section: Remarkmentioning

confidence: 99%

The nucleation and growth of gas bubbles in a Newtonian fluid: an energetic variational phase field approach

Naber¹,

Li²,

Feng³

2008

Contemporary Mathematics

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Abstract.In this paper, we study the nucleation and growth of gas bubbles in a Newtonian fluid. We employ a general energetic variational formulation with a phase-field method, and compare the analytical and numerical predictions of this new formulation with those of classical models. The new approach allows the study of bubble nucleation, growth and coalescence in a unified framework, and has the capability of modeling complex situations in polymer foaming, with multiple-bubble interaction, interaction with an external flow field, complex non-Newtonian rheology and non-Fickian diffusion.

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Spectral implementation of an adaptive moving mesh method for phase-field equations

Cited by 82 publications

References 30 publications

Fast and accurate algorithms for simulating coarsening dynamics of Cahn–Hilliard equations

Fast and accurate algorithms for simulating coarsening dynamics of Cahn–Hilliard equations

Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models

The nucleation and growth of gas bubbles in a Newtonian fluid: an energetic variational phase field approach

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