Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model

DOI10.1016/j.apnum.2021.01.004zbMath1458.65111OpenAlexW3119480591MaRDI QIDQ1995954

Zhengguang Liu, Shuangshuang Chen

Publication date: 2 March 2021

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.01.004

zbMATH Keywords

fast Fourier transforminvariant energy quadratizationmodified phase field crystal modelstep-by-step

Mathematics Subject Classification ID

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) Numerical methods for discrete and fast Fourier transforms (65T50) Crystals in solids (74N05) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (5)

Novel, linear, decoupled and unconditionally energy stable numerical methods for the coupled Cahn-Hilliard equations ⋮ A simple and practical finite difference method for the phase-field crystal model with a strong nonlinear vacancy potential on 3D surfaces ⋮ Linear and unconditionally energy stable schemes for the modified phase field crystal equation ⋮ An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations ⋮ Numerical approximation of the square phase-field crystal dynamics on the three-dimensional objects

Cites Work

• Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation
• Global smooth solutions of the three-dimensional modified phase field crystal equation
• Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
• Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
• The scalar auxiliary variable (SAV) approach for gradient flows
• Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation
• Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard model
• A new Lagrange multiplier approach for gradient flows
• Efficient numerical scheme for a dendritic solidification phase field model with melt convection
• Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation
• A second order unconditionally stable scheme for the modified phase field crystal model with elastic interaction and stochastic noise effect
• An efficient and stable compact fourth-order finite difference scheme for the phase field crystal equation
• First- and second-order energy stable methods for the modified phase field crystal equation
• Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation
• Energy stable and convergent finite element schemes for the modified phase field crystal equation
• Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
• An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
• Analysis of finite element approximations of a phase field model for two-phase fluids
• Efficient numerical methods for phase-field equations
• The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• Energy stability and convergence of SAV block-centered finite difference method for gradient flows

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