Numerical solution of Allen–Cahn model on surfaces via an effective method based on generalized moving least squares (GMLS) approximation and the closest point approach

Zamani-Gharaghoshi, Hasan; Dehghan, Mehdi; Abbaszadeh, Mostafa

doi:10.1016/j.enganabound.2023.04.019

Engineering Analysis with Boundary Elements

2023

DOI: 10.1016/j.enganabound.2023.04.019

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Numerical solution of Allen–Cahn model on surfaces via an effective method based on generalized moving least squares (GMLS) approximation and the closest point approach

Hasan Zamani-Gharaghoshi

Mehdi Dehghan

Mostafa Abbaszadeh

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Cited by 5 publications

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A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation

Li,

Teng,

Zeng

et al. 2024

Math Methods in App Sciences

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This paper mainly focuses on the dimension reduction of unknown finite element (FE) solution coefficient vectors in two‐grid Crank–Nicolson FE (TGCNFE) method for the nonlinear Allen–Cahn equation. For this purpose, a new TGCNFE method for the nonlinear Allen–Cahn equation is first developed and the unconditional stability and errors of TGCNFE solutions are analyzed. Thereafter, the most important thing is to lower the dimension of the unknown FE solution coefficient vectors by a proper orthogonal decomposition, to establish a new reduced‐dimension extrapolated TGCNFE (RDETGCNFE) method, and to analyze the unconditional stability and errors of RDETGCNFE solutions. Moreover, the correctness of our theoretical results is validated by some numerical experiments.

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A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation

Li,

Teng,

Zeng

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach

Abbaszadeh,

Salec,

Aal-Ezirej

2023

Opt Quant Electron

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Analysis and application of MLPG7 for diffusion equations with nonlinear reaction terms

Taghipoor,

Shirzadi,

Hosseinzadeh

2024

Engineering Analysis with Boundary Elements

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Numerical solution of Allen–Cahn model on surfaces via an effective method based on generalized moving least squares (GMLS) approximation and the closest point approach

Cited by 5 publications

References 33 publications

A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation

A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation

Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach

Analysis and application of MLPG7 for diffusion equations with nonlinear reaction terms

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