A second-order, global-in-time energy stable implicit-explicit Runge-Kutta scheme for the phase field crystal equation
DOI10.1137/24m1637623MaRDI QIDQ6652419
Haifeng Wang, Hong Zhang, Xueqing Teng
Publication date: 12 December 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
optimal rate convergence analysisimplicit-explicit Runge-Kutta methodphase field crystal equationlinear stabilizationglobal-in-time energy stability
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Statistical mechanics of crystals (82D25) 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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) 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) Crystals in solids (74N05) Integro-partial differential equations (35R09) PDEs in connection with statistical mechanics (35Q82)
Cites Work
- Unnamed Item
- Unnamed Item
- An unconditionally energy-stable method for the phase field crystal equation
- Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation
- Unconditionally stable schemes for higher order inpainting
- Unconditionally stable methods for gradient flow using convex splitting Runge-Kutta scheme
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
- Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
- Semi-implicit level set methods for curvature and surface diffusion motion
- First and second order numerical methods based on a new convex splitting for phase-field crystal equation
- Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
- On the stabilization size of semi-implicit Fourier-spectral methods for 3D Cahn-Hilliard equations
- Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
- A linear energy stable scheme for a thin film model without slope selection
- A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation
- Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations
- Energy-decreasing exponential time differencing Runge-Kutta methods for phase-field models
- Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
- Long-time simulation of the phase-field crystal equation using high-order energy-stable CSRK methods
- Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation
- A third order exponential time differencing numerical scheme for no-slope-selection epitaxial thin film model with energy stability
- Improving the accuracy of convexity splitting methods for gradient flow equations
- A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method
- A linearly second-order energy stable scheme for the phase field crystal model
- Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations
- Long Time Stability of a Classical Efficient Scheme for Two-dimensional Navier–Stokes Equations
- Spectral Methods
- An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
- Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation
- An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
- Convergence of Spectral Methods for Burgers’ Equation
- Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection
- Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
- An adaptive BDF2 implicit time-stepping method for the phase field crystal model
- An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation
- Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
- A Second-Order, Linear, \(\boldsymbol{L^\infty}\)-Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation
- Large time-stepping, delay-free, and invariant-set-preserving integrators for the viscous Cahn-Hilliard-Oono equation
- Energy diminishing implicit-explicit Runge-Kutta methods for gradient flows
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