Monte Carlo Methods with Applications to Plasma Physics
Module MA5330
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Basic Information
MA5330 is a semester module in English language at Master’s level which is offered irregular.
This module description is valid from SS 2014 to SS 2014.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 180 h | 60 h | 6 CP |
Content, Learning Outcome and Preconditions
Content
The lecture will be devoted to the development of numerical algorithms based on the Monte Carlo Method. The principle of Monte Carlo methods, i.e. computing approximate expected values with random samples, will be explained as well as the notion of approximation it provides. Variance reduction techniques and their impact on the efficiency of the simulation will be discussed.
After the general introduction of the Monte Carlo method, a large part of the lecture will be devoted to its application to simulation of the Vlasov-Fokker-Planck equation occurring in plasma physics. Deterministic as well as stochastic differential equations will be solved to provide an approximation of the evolution of a probability density function. This will be linked to the Particle-In-Cell method often used in plasma physics for simulation of collision less and collisional plasmas.
An exercise class is associated to the lecture where as well analytical exercises as coding exercises in Matlab will be proposed.
After the general introduction of the Monte Carlo method, a large part of the lecture will be devoted to its application to simulation of the Vlasov-Fokker-Planck equation occurring in plasma physics. Deterministic as well as stochastic differential equations will be solved to provide an approximation of the evolution of a probability density function. This will be linked to the Particle-In-Cell method often used in plasma physics for simulation of collision less and collisional plasmas.
An exercise class is associated to the lecture where as well analytical exercises as coding exercises in Matlab will be proposed.
Learning Outcome
After successful completion of the module, students will be able to assess the class of problems to which Monte Carlo Methods can be applied, write the corresponding algorithms and improve and evaluate their efficiency. They will also have a good understanding of the Particle In Cell method of plasma physics and be able to numerically solve stochastic differential equations.
Preconditions
Introduction to numerical methods - Introduction to probability.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Monte Carlo Methods with Application to Plasma Physics | Sonnendrücker, E. | ||
| UE | 2 | Monte Carlo Methods with Application to Plasma Physics (Exercise Session) | Sonnendrücker, E. |
documents |
Learning and Teaching Methods
Vorlesungen - Rechnen von Übungsaufgaben - Programmieraufgaben
Media
Tafelarbeit + Skript
Literature
- Thomas Müller-Gronbach, Erich Novak, Klaus Ritter: Monte Carlo Algorithmen, Springer 2012
- Birdsall and Langdon, Plasma Physics via Computer Simulation, Taylor & Francis 2005
- Birdsall and Langdon, Plasma Physics via Computer Simulation, Taylor & Francis 2005