Scientific Computing I - Winter 14

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Term
Winter 14
Lecturer
Dr. rer. nat. Tobias Neckel
Time and Place
Wednesday, 10:15-11:45; Interims Hörsaal 2 (5620.01.102), (starts Oct 15)
Audience
Computational Science and Engineering, 1st semester
Tutorials
Denis Jarema, time and place: I group: Monday, 16-18, MI 03.13.010, II group: Monday, 14-16, MI 03.13.010 (starts Oct 20)
Exam
written exam
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
tumonline lecture, tumonline tutorial



Announcements

  • The lecture does not take place on the 22nd of October due to the plenary meeting of the student's union.


Contents

The lecture will cover the following topics in scientific computing:

  • typical tasks in the simulation pipeline in scientific computing;
  • classification of mathematical models (discrete/continuous, deterministic/stochastic, etc.);
  • modelling with (systems) of ordinary differential equations (example: population models);
  • modelling with partial differential equations (example: heat equations);
  • numerical treatment of models (discretisation of ordinary and partial differential equations: introduction to Finite Volume and Finite Element Methods, grid generation, assembly of the respective large systems of linear equations);
  • analysis of the resulting numerical schemes (w.r.t. convergence, consistency, stability, efficiency);

An outlook will be given on the following topics:

  • efficient implementation of numerical algorithms, both on monoprocessors and parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
  • interpretation of numerical results (visualization)

Lecture Notes and Material

Slides of the lectures, as well as worksheets and solutions for the tutorials, will be published here as they become available.

Day Topic Material
Oct 15 Introduction - CSE/Scientific Computing as a discipline slides: discipline.pdf, fibo.pdf;
printing versions: discipline-2x4.pdf, fibo-2x4.pdf
Oct 20 Worksheet 1 (for the lecture on Oct 15) Worksheet 1, Solution 1
Oct 27 Worksheet 2 (for the lecture on Oct 15) Worksheet 2, Solution 2
Oct 29 Population Models - Continuous Modelling (Parts I to IV) slides: population.pdf;
python worksheets: Lotka Volterra, Population Models;
maple worksheets: lotkavolt.mws, popmodel.mw
maple_lotkavolt.pdf, maple_popmodel.pdf
printing version: population-2x4.pdf
Nov 3 Worksheet 3 (for the lecture on Oct 29) Worksheet 3, Solution 3
Nov 5 Population Models - Continuous Modelling (Parts I to IV) slides: population2.pdf;
printing version: population2-2x4.pdf

Exams

Catalogue of Exam Questions

The following catalogue contain questions collected by students of the lectures in winter 05/06 and 06/07. The catalogue is intended for preparation for the exam, only, and serves as some orientation. It's by no means meant to be a complete collection.

Last Years' Exams

Please, be aware that there are always slight changes in topics between the different years' lectures. Hence, the previous exams are not fully representative for this year's exam.

Literature

Books and Papers

  • A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press (in particular Chapter 3,5,6)
  • G. Strang: Computational Science and Engineering, Wellesley-Cambridge Press, 2007
  • G. Golub and J. M. Ortega: Scientific Computing and Differential Equations, Academic Press (in particular Chapter 1-4,8)
  • Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998 (in particular Chapter 1-4,7,10)
  • A. Tveito, H.P. Langtangen, B. Frederik Nielsen und X. Cai: Elements of Scientific Computing, Texts in Computational Science and Engineering 7, Springer, 2010 (available as ebook)
  • B. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (excellent online material)
  • D. Braess: Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics, Cambridge University Press (in particular I.1, I.3, I.4, II.2)


Online Material

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