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.


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).


  • 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