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Scientific Computing I - Winter 13

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Term
Winter 13
Lecturer
Dr. rer. nat. Tobias Neckel
Time and Place
Wednesday, 10:15-11:45; MI 00.13.009A, (starts Oct 23)
Audience
Computational Science and Engineering, 1st semester (Module IN2005)
Tutorials
Denis Jarema, time and place: Monday, 16-18, MI 00.013.009a, (starts Oct 28)
Exam
written exam, Feb 10, 2014, 10:30-12:00, room: Interimshörsaal 1,
written repetition exam, Apr 9, 2014, 17:30-19:00,
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
tumonline



Contents

Announcements

  • The Repetition exam review will take place on Tuesday, April 15, 15:00-16:00, in room 02.07.023.
  • The Repetition exam will take place on Wednesday, April 9, 17:30-19:00.
  • The Exam review will take place on Friday, February 21, 13:00-14:00, in room 02.07.023.
  • The Q&A session will take place on February, 04, 14:00-16:00 in room 03.13.010.
  • On January, 15, instead of a lecture, there will be a tutorial.
  • The lecture does not take place on the 30th 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 23 Introduction - CSE/Scientific Computing as a discipline slides: 01_discipline.pdf, 02_fibo.pdf
Oct 28 Worksheet 1 (for the lecture on Oct 23) Worksheet1, Solution
Nov 4 Worksheet 2 (for the lecture on Oct 23) Worksheet2, Solution
Nov 6 Population Models - Continuous Modelling (Parts I to IV) slides: population.pdf,
maple worksheets: lotkavolt.mws, popmodel.mw
maple_lotkavolt.pdf, maple_popmodel.pdf
Nov 11 Worksheet 3 (for the lecture on Nov 6) Worksheet3, Solution,

ws3.mw, Maple worksheet as pdf,
Java-Applet Game of Life

Nov 13 Population Models - Continuous Modelling (Parts I to IV) slides: population2.pdf
Nov 18 Worksheet 4 (for the lecture on Nov 13) Worksheet4, Solution,
ws4_b.mw, ws4_b as pdf,
ws4_d.mw, ws4_d as pdf
Nov 20 Numerical Methods for ODEs slides: ode_numerics.pdf
Maple worksheet: numerics_ode.mws
maple_numerics_ode.pdf
Nov 25 Worksheet 5 (for the lecture on Nov 20) Worksheet5, Solution,
ws5b.mw, ws5c.mw, ws5d.mw,
ws5.py
Dec 2 Worksheet 6 (for the lecture on Nov 27) Worksheet6, Solution, ws6_14b.mw, ws6.py
Dec 4 Heat Transfer - Discrete and Continuous Models heatmodel.pdf
Maple worksheet: poisson2D.mws also as PDF
Dec 9 Worksheet 7 (for the lecture on Dec 4) Worksheet7, Solution, ws7_15c.mw, ws7_15.py
Dec 11 1D Heat Equation - Analytical and Numerical Solutions heateq.pdf

IPyNb: heat_1D_disc.ipynb, heat_1D_impl.ipynb

Dec 16 Worksheet 8 (for the lecture on Dec 11) Worksheet8, Solution,

ws8_18c.mw, ws8_18.py

Dec 18
Jan 08
Introduction to Finite Element Methods - Part I
Introduction to Finite Element Methods - Part II
pde_fem.pdf
IPyNb: fem.ipynb
Jan 13 Worksheet 9 (for the lecture on Dec 11) Worksheet9, Solution updated!, ws9_20.mw ws9_20.py
Jan 15 Worksheet 10 (for the lecture on Dec 18) Worksheet10, Solution
Jan 20 Worksheet 11 (for the lecture on Jan 08) Worksheet11, Solution, hierarchical.mw, ws11_25.py
Jan 27 Worksheet 12 Worksheet12, Solution,

massmatrix.mw, ws13_27c.mw,
ws12_27.py, ws12_28.py

Jan 29 Case Study: Computational Fluid Dynamics - Part I study_cfd_partI.pdf
Feb 6 Case Study: Computational Fluid Dynamics - Part II study_cfd_partII.pdf

printing version of lecture slides!

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