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# Monte Carlo Methods with Applications to Plasma Physics

## Module MA5330

This Module is offered by TUM Department of Mathematics.

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.

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.

#### 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

#### 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

### Module Exam

#### Description of exams and course work

Oral examination. Questions on main techniques and ideas introduced in the lecture.

#### Exam Repetition

The exam may be repeated at the end of the semester.

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