Computational Physics and Materials Science
Sommersemester 2007
Contents
Following the course requires basic knowledge in a programming language (Fortran, C/C++, Python, ...).
The lecture will cover the following subjects:
- Basic Numerical Methods
- Interpolation
- Differentiation
- Integration
- Ordinary Differential Equations
- Euler method
- Predictor-corrector methods
- Runge-Kutta method
- Stepsize control
- Molecular Dynamics
- Molecular dynamics at constant energy -- Verlet algorithm
- Constant pressure -- Andersen scheme
- Constant temperature -- Nose scheme
- Constant bond length -- SHAKE algorithm
- Monte Carlo Simulations
- Random number generators
- Monte Carlo integration
- Importance sampling through Markov chains
- Simulation of classical liquids (Metropolis algorithm)
- Simulation of the Ising model
- Critical slowing down and block algorithms
- Quantum Monte Carlo methods
- Partial Differential Equations
- Initial value problems
(time dependent Schrödinger equation, diffusion equation, stability analysis, Crank-Nicholson algorithm)
- Boundary value problems
(Jacobi and damped Jacobi method, Fast Fourier transform)
- Finite element method
(Galerkin, Ritz, weak form of PDE, triangulation)
Literature
- Tao Pang, An Introduction to Computational Physics (Cambridge University Press)
- J. M. Thijssen, Computational Physics
(Cambridge University Press)
- Koonin, Meredith, Computational Physics (Addison-Weseley)
- W. H. Press et al, Numerical Recipes (Cambridge University Press)
(online version)
Exercise sheets
- 1, discussion 25.04., 1.pdf ,
ex1a.C,
ex1b.C,
ex1c.C,
ex1d.C,
ex2a.C,
ex2b.C
- 2, discussion 03.05., 2.pdf,
ex3.cpp,
ex4.cpp
- 3, discussion 10.05., 3.pdf,
ex5a.cpp,
ex5c.cpp,
ex6.cpp
- 4, discussion 14.05./24.05., 4.pdf
ex7.xm
ex8.xm
- 5, discussion 24.05., 5.pdf,
ex9a.xm,
ex9b.xm,
cu.txt
- 6, discussion 31.05., 6.pdf,
ex10.xm
- 7, discussion Wednesday, 06.06. , 7.pdf
ex12.cpp,
ex13a.cpp,
ex13b.cpp
- 8, discussion 14.06. and 21.06., 8.pdf
ex14a.cpp,
ex14b.cpp,
ex14c.cpp
- 9, discussion Wednesday, 04.07. , 9.pdf,
ex16.cpp,
ex17.cpp
- 10, discussion 12.07., 10.pdf,
ex19.flt
Links to software related to the course
peter.schwab@physik.uni-augsburg.de, April 2007
