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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 Jan 30, 2015, 16:30-18:00, room: Interimshörsaal 1
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
tumonline lecture, tumonline tutorial



Contents

Announcements

  • The repetition exam review will take place on Thursday, April 16, 16:15-17:30, in room 02.07.023.
  • The repetition exam will take place on Wednesday, April 8, 14:30-16:00, in MI Hörsaal 3 (00.06.011, 5606.EG.011), 1 handwritten DinA4 page (both sides) is the only allowed aid.
  • The exam review will take place on Friday, February 13, 10:00-11:00, in room 02.07.023.
  • The exam will take place on Friday, January 30, 16:30-18:00, in Interims Hörsaal 1 (5620.01.101), 1 handwritten DinA4 page (both sides) is the only allowed aid.
  • The tutorial does not take place on the 22nd of December.
  • 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
Nov 10 Worksheet 4 (for the lecture on Nov 5) Worksheet 4, Solution 4, ws4_ex1.py
Nov 12
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 17 Worksheet 5 (for the lecture on Nov 12) Worksheet 5, Solution 5, ws5_ex1.py
Nov 24 Worksheet 6 (for the lecture on Nov 18) Worksheet 6, Solution 6, ws6_ex3.py
Nov 26 Heat Transfer - Discrete and Continuous Models slides: heatmodel.pdf
python worksheets: Heat Transfer
maple worksheets: poisson2D.mws, poisson2D.pdf
printing version: heatmodel-2x4.pdf
Dec 1 Worksheet 7 (for the lecture on Nov 18) Worksheet 7, Solution 7, ws7_ex1.py
Dec 3 1D Heat Equation - Analytical and Numerical Solutions slides: heateq.pdf, heatenergy.pdf

python worksheets: 1D Heat Equation,
1D Heat Equation - Implicit Schemes
maple worksheets: heat1D_disc.mw, maple_heat1D_disc.pdf,
heat1D_impl.mw, maple_heat1D_impl.pdf
printing version: heateq-2x4.pdf

Dec 8 Worksheet 8 (for the lecture on Nov 26) Worksheet 8, Solution 8, ws8_ex2.py
Dec 10
Jan 7
Introduction to Finite Element Methods - Part I
Introduction to Finite Element Methods - Part II
slides: pde_fem.pdf
maple worksheets: fem.mw, maple_fem.pdf
python worksheets: FEM
printing version: pde_fem-2x4.pdf
Dec 15 Worksheet 9 (for the lecture on Dec 3) Worksheet 9, Solution 9, ws9_ex2.py
Jan 12 Worksheet 10 (for the lectures on Dec 10 and Jan 7) Worksheet 10, Solution 10
Jan 14
Jan 21
Case Study: Computational Fluid Dynamics slides: study_cfd.pdf

printing version: study_cfd-2x4.pdf

Jan 19 Worksheet 11 (for the lecture on Dec 10 and Jan 7) Worksheet 11, Solution 11, ws11_ex1.py
Jan 26 Worksheet 12 (for the lecture on Dec 10 and Jan 7) Worksheet 12, Solution 12, ws12_ex1.py, ws12_ex2.py

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