Difference between revisions of "Scientific Computing I - Winter 15"

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| Numerical Methods for ODEs
 
| Numerical Methods for ODEs
| slides: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws15/ode_numerics.pdf ode_numerics.pdf] <!--<br>python worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/py/SciComp_Numerics_ODE.py Numerics ODE] <br>maple worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/maple/numerics_ode.mws numerics_ode.mws], <br>[http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/maple/maple_numerics_ode.pdf maple_numerics_ode.pdf] <br> printing version: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/ode_numerics-2x4.pdf ode_numerics-2x4.pdf]-->
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| slides: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws15/ode_numerics.pdf ode_numerics.pdf] <br>python worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws15/py/SciComp_Numerics_ODE_2.py Numerics ODE] <br>maple worksheets: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws15/maple/numerics_ode.mws numerics_ode.mws], <br>[http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws15/maple/maple_numerics_ode.pdf maple_numerics_ode.pdf] <br> printing version: [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws15/ode_numerics-2x4.pdf ode_numerics-2x4.pdf]
 
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| Nov 23/25
 
| Nov 23/25

Revision as of 09:38, 23 November 2015

Term
Winter 15
Lecturer
Dr. rer. nat. Tobias Neckel
Time and Place
Wednesday, 10:15-11:45; HS 2 (starts Oct 21)
Audience
Computational Science and Engineering, 1st semester
Tutorials
Denis Jarema, time and place: I group: Wednesday, 14:00-15:45, MI 02.13.008, II group: Monday, 14:15-16:00, MI 03.13.010 (starts Oct 26)
Exam
tba
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
tba



Announcements

  • Starting from 02.11.2015 the tutorial slot on Monday at 16:00-18:00 is moved to Wednesday 14:00-16:00, room 02.13.008.

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 21 Introduction - CSE/Scientific Computing as a discipline slides: discipline.pdf, fibo.pdf
printing versions: discipline-2x4.pdf, fibo-2x4.pdf
Oct 26 Worksheet 1 Worksheet 1, Solution 1
Nov 2/4 Worksheet 2 Worksheet 2, Solution 2
Nov 4 Population Models - Continuous Modelling (Parts I to II) 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 9/11 Worksheet 3 Worksheet 3, Solution 3
Nov 11 Population Models - Continuous Modelling (Parts III to IV) slides: population2.pdf
printing version: population2-2x4.pdf
Nov 16/18 Worksheet 4 Worksheet 4, Solution 4, ws4_ex1.py
ipython notebook version: W4-Direction_Fields_for_ODE.ipynb
Nov 18 Numerical Methods for ODEs slides: ode_numerics.pdf
python worksheets: Numerics ODE
maple worksheets: numerics_ode.mws,
maple_numerics_ode.pdf
printing version: ode_numerics-2x4.pdf
Nov 23/25 Worksheet 5 (for the lecture on Nov 12) Worksheet 5

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