Fast algorithm for nonlocal Allen-Cahn equation with scalar auxiliary variable approach

DOI10.1016/j.aml.2021.107805OpenAlexW3215213222MaRDI QIDQ2077053

Changhui Yao, Y. H. Shi, Fen-Ling Wang, Yan-Min Zhao, Huijun Fan

Publication date: 22 February 2022

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

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107805

zbMATH Keywords

fast algorithmenergy stablenonlocal Allen-Cahn equationSAV approach

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Related Items (6)

Energy quadratization Runge-Kutta scheme for the conservative Allen-Cahn equation with a nonlocal Lagrange multiplier ⋮ Totally decoupled implicit-explicit linear scheme with corrected energy dissipation law for the phase-field fluid vesicle model ⋮ High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation ⋮ Fully discrete, decoupled and energy-stable Fourier-spectral numerical scheme for the nonlocal Cahn-Hilliard equation coupled with Navier-Stokes/Darcy flow regime of two-phase incompressible flows ⋮ Fast TT-M fourth-order compact difference schemes for a two-dimensional space fractional Gray-Scott model ⋮ Nonlinear semigroups for nonlocal conservation laws

Cites Work

• The scalar auxiliary variable (SAV) approach for gradient flows
• An implicit difference scheme for the time-fractional Cahn-Hilliard equations
• An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equation
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• Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint
• Optimal \(H^1\) spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation
• Time-fractional Allen-Cahn equations: analysis and numerical methods
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• Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes
• Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations
• A New Approach for a Nonlocal, Nonlinear Conservation Law
• Nonlocal Modeling, Analysis, and Computation
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations
• Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations
• Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions

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