Welcome to Numerical Physics

**Description:**

In this PhD course, we study various topics in physics that require numerical tools. We will discuss problems, solution strategies, programming and solve several practical problems. The topics selected range from quantum physics over nanooptics to electronic device simulations.

Quantum physics: All cases are related to the nonlinear response of atoms in electric fields. We will discuss the Stark effect and field-induced ionization. Moreover, the effect of electron-electron interactions will be studied using Hartree-Fock, exact diagonalization and density functional theory. Course material includes “Electric, Optical and magnetic Properties of Nanostructures” 2016 version (found on TGP’s homepage).

Nanooptics/photonics: In nanooptics and photonics the theoretical study of propagation and scattering of light by nanostructures and nanophotonics components requires the solution of Maxwells equations. Several methods for solving Maxwells equations exist, and the most appropriate method to use depends on the geometry and what information that should be extracted. In this part of the Ph. D course we will go in depth with two such methods (Modal method, and Finite-element method). We use as course material the relevant chapters in the book: A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, “Numerical Methods in Photonics”, CRC Press, 2015.

Electronic devices: The main focus will be on thermal aspects in high power electronics. This ranges from electro-thermal coupling, to various approaches for handling large scale temperature simulations, to estimation of material fatigue induced by temperature variations. In general a key aspect is to develop/utilize models applicable on engineering level and compare with detailed computational methods.

The contents are listed below.

- 29/2 One-dimensional “atoms”, Stark effect and complex scaling
- 1/3 One-dimensional helium, Hartree-Fock solution and polarizability
- 2/3 Density-functional theory for one-dimensional systems
- 3/3 Modal method
- 4/3 Modal method
- 7/3 The Finite-Element method
- 8/3 (only half day) The Finite-Element method
- 9/3 Electro-thermal coupling in high power electronics.
- 10/3 Thermal simulation - From 1D resistor networks to lumped finite difference model to finite element solutions.
- 11/3 High cycle thermal induced fatigue in power modules.

Prerequisites: Basic knowledge in optics, quantum physics and electromagnetism.**Organizer: **Professor Thomas G. Pedersen, e-mail: tgp@nano.aau.dk**Lecturers: **Professor Thomas G. Pedersen, Associate Professor Thomas Søndergaard, Post doc Kristian B. Pedersen**ECTS:** 4.0**Time: **Each day from 9.00-12.00 and 13.00 to 15.30. See dates above.

**Place: **Skjernvej 4 ** **

**Zip code: **9220**City: **Aalborg East

**Number of seats: **30**Deadline: **08.02.2016

**Important information concerning PhD courses:** We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.

- Teacher: Thomas Garm Pedersen