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Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows

Journal Article · · SIAM Journal on Numerical Analysis
DOI:https://doi.org/10.1137/21m1446496· OSTI ID:1980777

Not provided.

Research Organization:
Univ. of South Carolina, Columbia, SC (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0020270
OSTI ID:
1980777
Journal Information:
SIAM Journal on Numerical Analysis, Vol. 60, Issue 4; ISSN 0036-1429
Publisher:
Society for Industrial and Applied Mathematics (SIAM)
Country of Publication:
United States
Language:
English

References (50)

Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations journal January 2019
A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening journal June 1979
Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy journal June 2020
A Third Order Exponential Time Differencing Numerical Scheme for No-Slope-Selection Epitaxial Thin Film Model with Energy Stability journal July 2019
A new Lagrange multiplier approach for gradient flows journal August 2020
Generalized SAV approaches for gradient systems journal October 2021
Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation journal June 2021
The Cahn-Hilliard Equation with Logarithmic Potentials journal August 2011
Exponential Time Differencing for Stiff Systems journal March 2002
Mass- and energy-preserving exponential Runge–Kutta methods for the nonlinear Schrödinger equation journal February 2021
A positivity-preserving, energy stable and convergent numerical scheme for the Cahn–Hilliard equation with a Flory–Huggins–Degennes energy journal January 2019
Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes journal January 2021
Numerical Analysis of a Continuum Model of Phase Transition journal October 1991
Time-Fractional Allen–Cahn Equations: Analysis and Numerical Methods journal November 2020
Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models journal February 2013
A stable and conservative finite difference scheme for the Cahn-Hilliard equation journal February 2001
Energy-stable Runge–Kutta schemes for gradient flow models using the energy quadratization approach journal August 2019
Strong Stability-Preserving High-Order Time Discretization Methods journal January 2001
A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation journal January 2014
Traveling wave solutions of Allen–Cahn equation with a fractional Laplacian journal August 2015
Functions of Matrices book January 2008
Exponential integrators journal May 2010
A variant of scalar auxiliary variable approaches for gradient flows journal October 2019
Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations journal February 2017
A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows journal January 2020
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation journal October 2020
Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations journal August 2021
Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection journal September 2017
Fast Explicit Integration Factor Methods for Semilinear Parabolic Equations journal May 2014
Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen–Cahn Equation with Nonlocal Constraint journal May 2021
Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle journal January 2021
On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation journal January 2020
The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing journal January 2020
Geometric integration using discrete gradients
  • McLachlan, Robert I.; Quispel, G. R. W.; Robidoux, Nicolas
  • Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 357, Issue 1754 https://doi.org/10.1098/rsta.1999.0363
journal April 1999
Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection journal July 2014
An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models journal January 2011
On the maximum principle preserving schemes for the generalized Allen–Cahn equation journal January 2016
Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy journal January 2012
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows journal January 2018
The scalar auxiliary variable (SAV) approach for gradient flows journal January 2018
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows journal January 2019
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations journal June 2010
Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle journal June 2016
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation journal January 2009
Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models journal January 2006
Efficient and linear schemes for anisotropic Cahn–Hilliard model using the Stabilized-Invariant Energy Quadratization (S-IEQ) approach journal May 2019
Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations journal January 2022
Convergence Analysis for the Invariant Energy Quadratization (IEQ) Schemes for Solving the Cahn–Hilliard and Allen–Cahn Equations with General Nonlinear Potential journal February 2020
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation journal March 2021
Fast High-Order Compact Exponential Time Differencing Runge–Kutta Methods for Second-Order Semilinear Parabolic Equations journal October 2015