Algorithms for Scientific Computing
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.
Module version of WS 2017/8 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions
IN2001 is a semester module in English language at Bachelor’s level and Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
Content, Learning Outcome and Preconditions
- FFT: derivation and implementation
- Fast discrete cosine/sine transforms: derivation and implementation via FFT
- Applications: multi-dimensional data (images, video, audio) and FFT-based solvers for linear systems of equations
- Peano- and Hilbert curves: representation by algebraic and grammatical means
- Applications: organisation of multi-dimensional data; parallel, adaptive, and cache oblivious algorithms
Hierarchical numerical methods
- Hierarchical bases for one- and multi-dimensional problems
- Computational cost versus accuracy; Sparse Grids
- Adaptive representation of continuous data
- Applications: numerical quadrature, differential equations
- Outlook: multigrid methods, wavelets
Participants can analyse and judge the efficiency of such methods by deriving statements about the required computational cost and - where applicable - the achieved accuracy and by comparing them with corresponding results for other methods.
The students are able to transfer the methodology to new methods for related problems.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|Algorithms for Scientific Computing (IN2001)
|Bader, M. Wille, M.
Mon, 14:00–16:00, MI HS2
Wed, 08:00–10:00, MI HS2
Fri, 10:00–12:00, MI HS2
Learning and Teaching Methods
Students will be encouraged to study literature and to get involved with the topics in depth. In the tutorials, concrete problems will be solved - partially in teamwork - and selected examples will be discussed.
- Charles van Loan, Computational Frameworks for the Fast Fourier Transform, SIAM, 1992
- M. Bader, Space-Filling Curves - An Introduction with Applications to Scientific Computing, Springer-Verlag, 2013
- H. Sagan, Space-Filling Curves, Springer-Verlag, 1994
- H.-J. Bungartz, Skript Rekursive Verfahren und hierarchische Datenstrukturen in der numerischen Analysis, http://www5.in.tum.de/lehre/vorlesungen/algowiss/Bungartz_HierVerf.ps.gz
- H.-J. Bungartz, M. Griebel: Sparse Grids, Acta Numerica, Volume 13, p. 147-269. Cambridge University Press, May 2004
Description of exams and course work
The examination consists of a written exam of 120 minutes in which students show that they are able to find solutions for algorithmic problems arising in the field of scientific computing in a limited time. Questions and small tasks concerning code are used to test the student´s knowledge on known and related hierarchical methods as well as their ability to implement them. Example algorithms and questions are used to examine the capability of analyzing the efficiency of algorithms and the accuracy of a given method.
The exam may be repeated at the end of the semester.