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Scientific Computing I - Winter 12

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Term
Winter 12
Lecturer
Prof. Dr. Michael Bader
Time and Place
Wednesday, 10-12; MI 00.13.009A (starts Oct 17)
Audience
Computational Science and Engineering, 1st semester (Module IN2005)
Tutorials
Philipp Neumann, time and place: Monday, 16-18, MI 00.013.009a
Exam
written exam, Feb 11, 2013
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
https://campus.tum.de/tumonline/lv.detail?clvnr=950078599



Contents

Announcements

  • The exam review will take place on Friday, March 8, 13:00-14:30, in room 02.07.023 and on Thursday, March 14, 13:00-14:30, in room E.2.044 (Leibniz Supercomputing Centre, Boltzmannstr. 1).
  • The lecture will start with a general overview on the field of CSE and Scientific Computing on Wed, Oct 17.
  • The exercises will -- except for the exercise on Dec 3 -- take place in room 00.013.009a (same room as for the lectures)

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 17 Introduction - CSE/Scientific Computing as a discipline slides: 01_discipline.pdf
Oct 17 Worksheet 1 (for the exercise on Oct 22) Worksheet1 Solution
Oct 19 Worksheet 2 (for the exercise on Oct 24) Worksheet2 Solution
Oct 29 Population Models - Discrete Modelling, Continuous Modelling (Parts I and II) slides: 02_fibo.pdf, 03_population.pdf
Oct 29 Worksheet 3 (for the exercise on Nov 5) Worksheet3,

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

Nov 7, Nov 14 Population Models - Continuous Modelling (Parts I to IV) 03_population.pdf, 04_population2.pdf
Maple worksheets: popmodel.mw (also as PDF), lotkavolt.mw (also as PDF), dirfields.mw (also as PDF)
Nov 7 Worksheet 4 (for the exercise on Nov 12) Worksheet4,

Solution, ws4b.mw, ws4b as pdf, ws4d.mw, ws4d as pdf

Nov 14 Worksheet 5 (for the exercise on Nov 19) Worksheet5,Solution, ws5b.mw, ws5c.mw, ws5d.mw
Nov 21 Numerical Methods for ODEs 05_ode_numerics.pdf
Maple worksheet: numerics_ode.mw (also as PDF)
Nov 21 Worksheet 6 (for the exercise on Nov 26) Worksheet6, Solution, ws14b.mw
Nov 28 Numerical Methods for ODEs (cont.) 05_ode_numerics.pdf
Maple worksheet: numerics_ode.mw (also as PDF);
Intermission: Modelling - Classification and Summary 06_modelling.pdf
Nov 28 Worksheet 7 (for the exercise on Dec 3) Worksheet7, Solution, ws15c.mw
Dec 5 Heat Transfer - Discrete and Continuous Models 07_heatmodel.pdf
Maple worksheet: poisson2D.mw (also as PDF)
Dec 5 Worksheet 8 (for the exercise on Dec 10) Worksheet8, Solution, ws8_18c.mw
Dec 12 1D Heat Equation - Analytical and Numerical Solutions 08_heateq.pdf
Worksheet: heatenergy.pdf
additional Maple worksheet (from an older lecture): heat1D_four.mw (also as PDF)
Dec 12 Worksheet 9 (for the exercise on Dec 17) Worksheet9, Solution, , ws9_20.mw
Dec 19 Worksheet 10 (for the holidays, no review in exercise!) Worksheet10, Solution, ws10_santa.mw
Jan 9, Jan 16 Introduction to Finite Element Methods - Part I 09_pde_fem.pdf
Maple worksheet: fem.mw (also as PDF)
Jan 11 Worksheet 11 Worksheet11, Solution
Jan 16 Introduction to Finite Element Methods - Part II 09_pde_fem.pdf
Jan 16 Worksheet 12 Worksheet12, Solution, hierarchical.mw
Jan 23 Case Study: Computational Fluid Dynamics - Part I 10_cfd.pdf
Jan 25 Worksheet 13 Worksheet13, Solution, massmatrix.mw, ws13_27c.mw
Jan 30 Case Study: Computational Fluid Dynamics - Part II 10_cfd.pdf (Note: slides have been corrected&updated since Jan 23!)
Feb 6 Case Study: Computational Fluid Dynamics - Part III 10_cfd.pdf

Exams

Finals

  • Date of final exam: 11 Feb 2013, 10.00am.
    Please be on time - the working time will start at 10.15, at the latest, and there will be organizational remarks and announcements before
  • Registration: via TUM-Online
  • Room: MW 0350 (in the Department of Mechanical Engineering)
  • Helping material: A hand-written A4 sheet (written on both sides) will be allowed as helping material during the exam - all other items (incl. electronic devices of any kind) will be forbidden.
  • Exam review: March 8, 13.00 - 14.30 (room: MI 02.07.023) and March 14, 13.00-14.30 (room: E.2.044 in Leibniz Supercomputing Centre, Boltzmannstr. 1)

Repeat Exam

  • Date of final exam: 18 Apr 2013, 16.00am.
    Please be on time - the working time will start at 16.15, at the latest, and there will be organizational remarks and announcements before
  • Registration: via TUM-Online
  • Room: MI 02.07.023
  • Helping material: A hand-written A4 sheet (written on both sides) will be allowed as helping material during the exam - all other items (incl. electronic devices of any kind) will be forbidden.
  • Exam topics are the same as for the regular exam.

Preparation for Exam

Please note that the extent (in semester hours) and content of the lecture has changed from winter term 2012/13. Hence, previous years' exams might miss topics discussed in this year or contain material that is no longer covered in the lecture.

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