# Computational Physics

## Lecture details

**The summer semester is held as a digital semester. In principle, as agreed by the universities in North Rhine-Westphalia, all courses that can be offered remotely will take place online for the entire summer semester.**

The lecture will be given by Prof. Mazzarello and Prof. 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 | N/A | 09.04.2020 - 16.07.2020 |

Thurs. 12.30pm - 2pm | N/A | 09.04.2020 - 16.07.2020 |

Fri. 12.30pm - 2pm | N/A | 17.04.2020 - 17.07.2020 |