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Stabilized Exponential-SAV Schemes Preserving Energy Dissipation Law and Maximum Bound Principle for The Allen–Cahn Type Equations

Journal Article · · Journal of Scientific Computing

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:
1976691
Journal Information:
Journal of Scientific Computing, Vol. 92, Issue 2; ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English

References (38)

A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening journal June 1979
Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations journal January 2019
Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn–Hilliard Model journal July 2019
A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation journal January 2019
A new Lagrange multiplier approach for gradient flows journal August 2020
Generalized SAV approaches for gradient systems journal October 2021
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints journal January 2012
Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation journal January 2019
Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes journal January 2021
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 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
A variant of scalar auxiliary variable approaches for gradient flows journal October 2019
Numerical analysis of a stabilized Crank–Nicolson/Adams–Bashforth finite difference scheme for Allen–Cahn equations journal April 2020
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
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 and accurate algorithms for simulating coarsening dynamics of Cahn–Hilliard equations journal October 2015
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
Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation journal September 2020
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
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
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
A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation journal January 2018
Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends journal December 2016
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