A5100417045- Solidification and crystal growth phenomena
- Advanced Numerical Methods in Computational Mathematics
- Differential Equations and Numerical Methods
- Advanced Mathematical Modeling in Engineering
- Fluid Dynamics and Thin Films
- Computational Fluid Dynamics and Aerodynamics
- Aluminum Alloy Microstructure Properties
- Fluid Dynamics and Turbulent Flows
- nanoparticles nucleation surface interactions
- Numerical methods for differential equations
- Numerical methods in inverse problems
- Sparse and Compressive Sensing Techniques
- Gas Dynamics and Kinetic Theory
- Block Copolymer Self-Assembly
- Electromagnetic Simulation and Numerical Methods
- Stability and Controllability of Differential Equations
- Theoretical and Computational Physics
- Fractional Differential Equations Solutions
- Navier-Stokes equation solutions
- Matrix Theory and Algorithms
- Mathematical Biology Tumor Growth
- Combustion and Detonation Processes
- Aluminum Alloys Composites Properties
- Flame retardant materials and properties
- Neural Networks Stability and Synchronization
Beijing Institute of Technology
2018-2025
United Imaging Healthcare (China)
2025
University of Massachusetts Dartmouth
2015-2024
Wuhan Institute of Technology
2022-2024
Guiyang Medical University
2024
Shanghai Jiao Tong University
2002-2023
Jilin University
2019-2023
Peking University
2023
Qilu Hospital of Shandong University
2023
Shandong Academy of Agricultural Sciences
2023
We construct unconditionally stable, uniquely solvable, and second-order accurate (in time) schemes for gradient flows with energy of the form $\int_\Omega ( F(\nabla\phi({\bf x})) + \frac{\epsilon^2}{2}|\Delta\phi({\bf x})|^2 ) d{\bf x}$. The construction involves appropriate combination extension two classical ideas: (i) convex-concave decomposition functional (ii) secant method. As an application, we derive epitaxial growth models slope selection ($F({\bf y})= \frac14(|{\bf y}|^2-1)^2$)...
Despite great advances in vitrimer, it remains highly challenging to achieve a property portfolio of excellent mechanical properties, desired durability, and high fire safety. Thus, catalyst-free, closed-loop recyclable transesterification vitrimer (TPN
In this paper, we devise and analyse an unconditionally stable, second-order-in-time numerical scheme for the Cahn–Hilliard equation in two three space dimensions. We prove that our two-step is energy stable uniquely solvable. Furthermore, show discrete phase variable bounded |$L^\infty (0,T;L^\infty )$| chemical potential (0,T;L^2)$| , any time step sizes, dimensions, finite final |$T$| . subsequently these variables converge with optimal rates appropriate norms both include work a detailed...
In this paper we present and analyze finite difference numerical schemes for the Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both first second order accurate temporal algorithms are considered. scheme, treat nonlinear terms surface diffusion term implicitly, update linear expansive mobility explicitly. We provide theoretical justification that algorithm has unique solution, such positivity is always preserved arguments, i.e., phase variable between −1 1, at...
We present an error analysis for unconditionally energy stable, fully discrete finite difference scheme the Cahn-Hilliard-Hele-Shaw equation, a modified Cahn-Hilliard equation coupled with Darcy flow law. The scheme, proposed by S. M. Wise, is based on idea of convex splitting. In this paper, we rigorously prove first order convergence in time and second space. Instead (discrete) $L_s^\infty (0,T;L_h^2) \cap L_s^2 (0,T; H_h^2)$ estimate, which would represent typical approach, provide H_h^1)...
In this paper we propose and analyze a finite difference numerical scheme for the Poisson-Nernst-Planck equation (PNP) system. To understand energy structure of PNP model, make use Energetic Variational Approach (EnVarA), so that system could be reformulated as non-constant mobility <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript negative 1"> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow...
In this paper, we propose and analyze a fully discrete finite element projection method for the magnetohydrodynamic (MHD) equations. A modified Crank–Nicolson Galerkin are used to discretize model in time space, respectively, appropriate semi-implicit treatments applied fluid convection term two coupling terms. These approximations result linear system with variable coefficients which unique solvability can be proved theoretically. addition, use second-order decoupling of Van Kan type [Van...
In this paper we provide a detailed convergence analysis for fully discrete second order (in both time and space) numerical schemes nonlocal Allen-Cahn (nAC) Cahn-Hilliard (nCH) equations. The unconditional unique solvability energy stability ensures $\ell^4$ stability. the nAC equation follows standard procedure of consistency estimate error function. For nCH equation, due to complicated form nonlinear term, careful expansion its gradient is undertaken an $H^{-1}$ inner product derived...
In this paper, we provide a detailed convergence analysis for first order stabilized linear semi-implicit numerical scheme the nonlocal Cahn–Hilliard equation, which follows from consistency and stability estimates error function. Due to complicated form of nonlinear term, adopt discrete <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript negative 1"> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow...