Scientific Computing I - Winter 15

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Winter 15
Dr. rer. nat. Tobias Neckel
Time and Place
Wednesday, 10:15-11:45; HS 2 (starts Oct 21)
Computational Science and Engineering, 1st semester
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)
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits


  • The tutorial on 23.12.2015 (Wed) is moved to 21.12.2015 (Mon) 16:00-18:00, room 03.13.010.
  • 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.


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,
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,
ipython notebook version: W4-Direction_Fields_for_ODE.ipynb
Nov 18 Numerical Methods for ODEs
(part I)
slides: ode_numerics.pdf
python worksheets: Numerics ODE
maple worksheets: numerics_ode.mws,
printing version: ode_numerics-2x4.pdf
Nov 23/25 Worksheet 5 Worksheet 5, Solution 5,
Nov 25 Numerical Methods for ODEs
(part II)
slides: ode_numerics.pdf
python scripts for visualisation of stability: unstable explLLM2 example,
visualisation of stability regions,
explicit midpoint rule examples (Martini glass effec),
Martini glass effect in scaled plot
Nov 30, Dec 2 Worksheet 6 Worksheet 6, Solution 6,
Dec 2 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 7/9 Worksheet 7 Worksheet 7, Solution 7,
visualization of ODE solvers
Dec 9 1D Heat Equation - Analytical and Numerical Solutions slides: heateq.pdf, heatenergy.pdf

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

Dec 14/16 Worksheet 8 Worksheet 8, Solution 8,
Dec 16 Introduction to Finite Element Methods - Part I
Introduction to Finite Element Methods - Part II
slides: pde_fem.pdf
maple worksheets:, maple_fem.pdf
python worksheets: FEM
printing version: pde_fem-2x4.pdf
Dec 15 Worksheet 9 Worksheet 9


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.


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