Computational physics III
PHYS-332 / 3 crédits
Enseignant:
Langue: Anglais
Withdrawal: It is not allowed to withdraw from this subject after the registration deadline.
Remark: Pas donné en 2023-24
Summary
This course teaches the students practical skills needed for solving modern physics problems by means of computation. A number of examples illustrate the utility of numerical computations in various domains of physics.
Content
Fourier series and transforms Introduction to the Fourier series and transforms and their application. Mathematical properties: convergence, convolution, correlation, Gibbs phenomenon and the Wiener-Khinchin theorem. Fourier transform on discrete sampled data: aliasing and sampling theorem. Discrete Fourier transform (DFT) and fast Fourier transform (FFT). Applications: spectral analysis, filters. Fourier transforms in higher dimensionality.
Linear systems Introduction and examples. Gauss-Jordan elimination, LU factorization. Iterative refinement: tridiagonal and band diagonal systems. Iterative methods and preconditioning: Jacobi, Richards and gradient methods. Conjugate gradient method. Iterative vs direct methods.
Matrix manipulation and eigenvalues problems Introduction and examples. Properties and decomposition. Poweriteration. QR decomposition and iterative procedure. Singular value decomposition (SVD).
Learning Prerequisites
Recommended courses
1st and 2nd years numerical physics courses
Learning Outcomes
By the end of the course, the student must be able to:
- Choose the most suitable algorithm for solving given problem
- Integrate algorithms in computer codes and evaluate their performance
- Solve actual physics problems using numerical tools
Teaching methods
Ex cathedra presentations, exercises and work under supervision
Assessment methods
3 reports during the semester
Resources
Bibliography
J. F. James, A Student's guide to Fourier transforms, CUP 2011
L. N. Trefethen and D. Bau III, Numerical linear algebra, SIAM 1997
Ressources en bibliothèque
Moodle Link
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Pendant le semestre (session d'été)
- Matière examinée: Computational physics III
- Cours: 1 Heure(s) hebdo x 14 semaines
- TP: 2 Heure(s) hebdo x 14 semaines
Semaine de référence
| Lu | Ma | Me | Je | Ve | |
| 8-9 | |||||
| 9-10 | |||||
| 10-11 | |||||
| 11-12 | |||||
| 12-13 | |||||
| 13-14 | |||||
| 14-15 | |||||
| 15-16 | |||||
| 16-17 | |||||
| 17-18 | |||||
| 18-19 | |||||
| 19-20 | |||||
| 20-21 | |||||
| 21-22 |
Légendes:
Cours
Exercice, TP
Projet, autre