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Syllabus for

Academic year
FAS070 - Advanced numerical methods and applications
 
Owner: RAMAS
3,0 Credits (ECTS 4,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 75 - EARTH AND SPACE SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0102 Examination 3,0 c Grading: TH   3,0 c   Contact examiner

In programs

TTFYA ENGINEERING PHYSICS, Year 4 (elective)
RAMAS MSc PROGRAMME IN ADVANCED TECHNIQUES IN RADIO ASTRONOMY AND SPACE SCIENCE, Year 1 (compulsory)

Examiner:

Bitr professor  Cathy Horellou



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

The course is open to 4th/5th-year students (or students at an equivalent
level) and graduate students with background in physics and mathematics.

Aim

This course will give an introduction to numerical techniques which can be used for solving a wide range of mathematical and physical problems. Examples will include analysis of astronomical spectra and computationally challenging problems such as N-body simulations of galaxies. A special emphasis will be put on wavelets. Wavelets have recently been introduced as the product of a lasting collaboration between physicists, mathematicians and engineers. They are the state of the art of digital signal/image processing, and overcome two basic handicaps of Fourier techniques:
(1) they are localized in both time/space and frequency/wavevector domains,
(2) they adapt the resolution to the problem analysed.
The most celebrated applications concern data compression and denoising, where improvements are of unprecedented level compared with classical techniques. Other important applications include: solution of partial differential equations in physics; analysis of multi-scale structures, fractals and turbulence. Furthermore, wavelets promise to have important applications in dynamical modelling of disc galaxies.

Goal

At the end of the course, the students will be familiar with numerical techniques and will be able to solve systems of linear equations, perform data interpolation/extrapolation, apply Monte Carlo methods, perform sorting, and integrate of differential equations (topics covered during the first part of the course). In addition, the students will have gained valuable knowledge and practice on Fourier transforms and on the use of wavelets to compress and denoise data (topics covered during the second part of the course).

Content

Solution of linear algebraic equations. Interpolation and extrapolation.
Evaluation of functions. Random numbers. Statistical description of data.
Modelling of data. Scientific computing. Computer experiments using particle models.
Collisionless particle models. Fourier transform. Windowed Fourier transform.
Related transforms. Applications. What are wavelets? Continuous wavelet transform.
Fast wavelet transform. Wavelet properties. Wavelet packets.
Application 1: data compression.
Application 2: data denoising.
Other important applications. State-of-the-art calculations using super-computers.
Optimizing the faithfulness and performance of galaxy simulations

Organisation

EXAMINERS: Cathy Horellou & Alessandro Romeo

Literature

* Course notes

* Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., Numerical Recipes, The Art of Scientific Computing, Second Edition,
Cambridge University Press (1992: Fortran version; 1993: C version; 1996: Fortran 90 version)

Examination

The exam will be in the form of two practical applications that the
students carry out during the course: (1) numerical simulations and
high-performance computing - application to galaxies and cosmology; (2)
computer experiments for data compression and denoising using wavelets.


Page manager Published: Mon 28 Nov 2016.