Numerical Simulation of Models

Recommended Prerequisites

Not applicable.

Teaching Methods

The theory oriented classes use the usual teaching tools available such as a blackboard and the video projection of materials and computer animations;

Classes will be focused mainly on discussing the matters including case studies and the study of illustrative examples.

Classes are open to discussion with the students.

Classes will be oriented towards the development of projects that seek to solve illustrative problems that are frequent and models of typical situations, in various fields of physics, or other areas.

Seeks to develop critical thinking and the creativity of students by encouraging them to suggest ideas, themes, etc., whose solution can be given by the Monte Carlo methods or other numerical methods developed in the course unit.

Learning Outcomes

It is intended that students acquire the skills to analyze, interpret and solve numerically solving problems that arise in science and engineering. Each of the four chapters that constitute the program corresponds to a specific type of problem that students are asked to study by conducting small projects.

Work Placement(s)

No

Syllabus

Chapter 1. Geometric Integration
1. Some interesting problems
2. The method Stormer-Verlet
3. Geometric properties
4. Conservation first integrals
5. Regressive error analysis

Chapter 2 Fourier techniques in evolving problems
1. Preliminary
2. Fourier series (review)
3. Initial condition problems of Fourier Analysis
4. Discrete Fourier Analysis
5. Discrete Fourier Transforms versus Fourier series
6. Spectral Methods

Chapter 3 Multigrid Methods
1 Poisson equation
2 Basic Iterative methods
3 Multigrid
4 Theoretical analysis of multigrid

Chapter 4 Numerical methods for conservation laws
1 Methods conservative
2 Numerical methods for conservation laws
3 Finite Volume Methods: Godunov method

Assessment Methods

Evaluation
presentation and discussion of topics of the programme or in connection with it, chosen at the suggestion of students: 10.0%
Problem solving: 40.0%
Project: 50.0%

Bibliography

1. E. Hairer, C. Lubich, G. Wanner, Geometric numerical integration illustrated by the StormerVerlet method, Acta Numerica (2003), pp. 399450.
2. C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer, New York, 1988.
3. Leveque, R.J. Finite volumes for hyperbolic problems, Cambridge University Press, Cambridge, 2002.
4. McCormick, S. Multigrid methods Philadelphia SIAM, Philadelphia,1987