Linear multi-step methods and their numerical stability for solving gradient flow equations

A new class of implicit–explicit BDFk SAV schemes for general dissipative systems and their error analysis

(2022) Fukeng Huang et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Energy-decreasing exponential time differencing Runge–Kutta methods for phase-field models

(2022) Zhaohui Fu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Phase‐field‐crystal study on the crack propagation behavior in a nanoscale two‐dimensional lattice in the presence of nonlinear disturbance strains

(2021) Shi Hu et al.   FATIGUE & FRACTURE OF ENGINEERING MATERIALS & STRUCTURES

Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations

(2021) Xavier Antoine et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical Investigation to the Effect of Initial Guess for Phase-Field Models

(2021) Sungha Yoon   East Asian Journal on Applied Mathematics

Fully-discrete energy-preserving scheme for the space-fractional Klein–Gordon equation via Lagrange multiplier type scalar auxiliary variable approach

(2021) Qiong-Ao Huang et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models

(2020) Yuezheng Gong et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation

(2020) Xiaoli Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A gPAV-based unconditionally energy-stable scheme for incompressible flows with outflow/open boundaries

(2020) Lianlei Lin et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations

(2020) Hong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Arbitrarily high-order linear energy stable schemes for gradient flow models

(2020) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

gPAV-based unconditionally energy-stable schemes for the Cahn–Hilliard equation: Stability and error analysis

(2020) Yanxia Qian et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Efficient and linear schemes for anisotropic Cahn–Hilliard model using the Stabilized-Invariant Energy Quadratization (S-IEQ) approach

(2019) Zhen Xu et al.   COMPUTER PHYSICS COMMUNICATIONS

Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation

(2019) Qi Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

A family of second-order energy-stable schemes for Cahn–Hilliard type equations

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An unconditionally energy stable scheme for simulating wrinkling phenomena of elastic thin films on a compliant substrate

(2019) Qiong-Ao Huang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy†

(2019) Qiong-Ao Huang   Communications in Computational Physics

Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models

(2019) Yuezheng Gong et al.   COMPUTER PHYSICS COMMUNICATIONS

A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Wrinkling pattern evolution on curved surfaces

(2019) Yan Zhao et al.   JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

Surface wrinkling of anisotropic films bonded on a compliant substrate

(2018) Si-Fan Yin et al.   INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation

(2018) Qiang Du et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach

(2018) Xiaofeng Yang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Analysis and Approximation of a Fractional Cahn--Hilliard Equation

(2017) Mark Ainsworth et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Nonlinear analysis of compressed elastic thin films on elastic substrates: From wrinkling to buckle-delamination

(2014) Kui Pan et al.   INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

(2013) A. Baskaran et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Phase field approach for simulating solid-state dewetting problems

(2012) Wei Jiang et al.   ACTA MATERIALIA

Solid-State Dewetting of Thin Films

(2012) Carl V. Thompson   Annual Review of Materials Research

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

(2010) Jie Shen et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations

(2010) C. Miehe et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Fracture analysis of a magnetoelectroelastic solid with a penny-shaped crack by considering the effects of the opening crack interior

(2008) Xian-Ci Zhong et al.   INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

The Variational Approach to Fracture

(2008) Blaise Bourdin et al.   JOURNAL OF ELASTICITY