# Computational Physics

## Lecture details

The lecture will be given by Professor Mazzarello and by Professor Michielsen.

Description:

Computational physics encompasses a huge variety of topics. Therefore, the lecture can only cover a limited fraction of computational physics problems.
Topics include:

• What is computational physics and what is it used for? Traditional versus non-traditional computational physics
• Random numbers and their applications (random number generators, random walk, cellular automata, lattice Boltzman method, event-by-event simulations)
• Monte Carlo method (integration, statistical error, radioactive decay, percolation, importance sampling, Ising model, Markov chains, Metropolis Monte Carlo method)
• Molecular dynamics method (Runge Kutta, predictor-corrector, Euler, Euler-Cromer, Verlet, leap-frog, velocity Verlet, Hamiltonian splitting, accuracy and stability ,force calculations: truncation and shift of potentials, linked list method)
• Diffusion equation (random walk, Brownian motion, Crank-Nicolson, product formula approach, Chebychev algorithm, matrix exponential, stability and accuracy)
• Computational electrodynamics (Maxwell equation, FDTD: Yee algorithm and product formula approach, ADI, multipole methods, finite element method, dissipative materials, UPML)
• Time-(in)dependent Schrödinger equation (Leap-frog, Crank-Nicolson, product formula, Lanczos, Davidson, linear algebra: Gauss, LU decomposition)
• Exact diagonalization
• Quantum Monte Carlo method

Learning goals:

• Lectures: The students will obtain an overview of various numerical methods to solve by computer a variety of problems in science.
• Exercises: The students will write their own computer programs for problems drawn from various areas of physics, selected such that they can be worked out in a reasonable time frame, with reasonable computational resources (PC is sufficient).

Literature:

• T. Pang, An introduction to computational physics, Cambridge Univ. Press.
• J. M. Thijssen, Computational physics, Cambridge Univ. Press
• D. P. Landau, K. Binder, A Guide to Monte-Carlo Simulations in Statistical
Physics, Cambridge Univ. Press.
• W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannery,
Numerical Recipes: the Art of Scientific Computing, Cambridge Univ. Press.
Time Room Start/Finish

Thurs. 10.30am - 12pm

4263 (26C 401)

04.04.2019 - 11.07.2019 (12 dates)

Thurs. 12.30pm - 2pm 4281 (28A 203) 04.04.2019 - 11.07.2019 (12 dates)

Fri. 12.30pm - 2pm

4263 (26C 401) 05.04.2019 - 05.07.2019 (13 dates)