博文
- Thermodynamics of coupling method
- coarse: GL fine: partical Lifshiz-Slyozov, Ohta-Kawasaki, Swift-Hohenberg barrier problem, intrinsically slow process, downhill but small Onsager coefficient, and vastly different time scales (stiff equations) Coupling between particle model and continuum description. Free energy from restraint ...
- GENERIC formalism
- General Equation for Non-Equilibrium Reversible-Irreversible Coupling. reversible and irreversible dynamics, Hamiltonian and Dissipative dynamics Coarse: Cahn-Hilliard phase field fine: Fokker-Planck phase space Grmela Öttinger, Dynamics and thermodynamics of complex fluids. ...
- Chitin as a composite material
- Materials science of chitin: Arthropods have adapted to every habitat on earth, adaptive material Building block: Organic matric, Inorganic nano-particles, Cuticle Homogenization, porous media, topological distribution X-ray wide angle diffraction, lobster Hierarchical modeling of stiffness st ...
- Class Website Moved
- Class website has been moved to http://202.121.182.14:8080/faculty/leizhang/teaching.html
- Homework 3
- homework3.pdf
- Week 3
- Runge-Kutta Method General one-step method, consistency, convergence, Taylor expansion method, Runge-Kutta method - idea from numerical quadrature, general formulation of Runge-Kutta method, parameters (R-K matrix, R-K nodes, R-K weights), constraints on the parameters, order condition, absolute sta ...
- Homework 2
- homework2.pdf
- Example code for implicit Euler method
- euler_backward.m newton4euler.m
- Week 2
- Multistep method Construction of multistep method by Lagrange polynomial, Adams-Bashforth method, order condition for general multistep method, characteristic polynomial, zero-stability, convergence. Readings: Iserles: 19-23. Suli: 21-22, 24-29.
- Week 1
- 1. Euler method Convergence proof of Euler method, truncation error 2. Trapezoid method Order of the numerical method, convergence proof 3. theta-method Truncation error Readings: Iserles: 3-10, 13-15 Suli: 4-6, 7-9
