Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation
type: Item
instance of: scholarly article
title: Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation
zbMATH Open document ID: 1504.65172
author: Dingwen Deng
author: Zilin Zhao
publication date: 2022-12-01T00:00:00Z
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 7625621
zbMATH Keywords: nonlinear Allen-Cahn equation
zbMATH Keywords: energy-dissipation-preserving ADI methods
zbMATH Keywords: discrete energy-dissipation laws
zbMATH Keywords: error estimations
zbMATH Keywords: high performance
MaRDI profile type: Publication
full work available at URL: j.camwa.2022.10.023
OpenAlex ID: W4308749536
cites work: Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
cites work: Geometrical image segmentation by the Allen-Cahn equation
cites work: Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights
cites work: Phase-Field Models for Multi-Component Fluid Flows
cites work: Maximum norm error analysis of an unconditionally stable semi‐implicit scheme for multi‐dimensional Allen–Cahn equations
cites work: Q4039920
cites work: Infinite-dimensional dynamical systems in mechanics and physics
cites work: A bifurcation problem for a nonlinear partial differential equation of parabolic type†
cites work: Generation, propagation, and annihilation of metastable patterns
cites work: Metastable patterns in solutions of ut = ϵ2uxx − f(u)
cites work: The Global Dynamics of Discrete Semilinear Parabolic Equations
cites work: The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
cites work: Travelling wave solutions of the Cahn-Allen equation by using first integral method
cites work: Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
cites work: An unconditional stable compact fourth-order finite difference scheme for three dimensional Allen-Cahn equation
cites work: A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation
cites work: Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
cites work: Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen–Cahn equation
cites work: Numerical analysis of a stabilized Crank-Nicolson/Adams-Bashforth finite difference scheme for Allen-Cahn equations
cites work: A new second-order maximum-principle preserving finite difference scheme for Allen-Cahn equations with periodic boundary conditions
cites work: A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen-Cahn equations
cites work: The discrete maximum principle and energy stability of a new second-order difference scheme for Allen-Cahn equations
cites work: Linear energy stable and maximum principle preserving semi-implicit scheme for Allen-Cahn equation with double well potential
cites work: Q3385079
cites work: A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
cites work: An efficient high-order algorithm for solving systems of reaction-diffusion equations
cites work: An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations
cites work: Numerical simulation of the three dimensional Allen-Cahn equation by the high-order compact ADI method
cites work: A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations
cites work: The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients
cites work: An economical difference scheme for heat transport equation at the microscale
cites work: The multistep finite difference fractional steps method for a class of viscous wave equations
cites work: A new fourth-order numerical algorithm for a class of nonlinear wave equations
cites work: The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations
cites work: The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations
cites work: Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
cites work: Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
cites work: Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
cites work: A novel linear second order unconditionally energy stable scheme for a hydrodynamic \(\mathbf{Q} \)-tensor model of liquid crystals
cites work: Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential
cites work: Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard model
cites work: Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation
cites work: Analysis of some finite difference schemes for two-dimensional Ginzburg-Landau equation
cites work: Optimal point-wise error estimate of a compact difference scheme for the coupled Gross-Pitaevskii equations in one dimension
cites work: Numerical analysis of a conservative linear compact difference scheme for the coupled Schrödinger–Boussinesq equations
DOI: 10.1016/J.CAMWA.2022.10.023
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 7625621