Scientific Computing I - Winter 13
- Winter 13
- Dr. rer. nat. Tobias Neckel
- Time and Place
- Wednesday, 10:15-11:45; MI 00.13.009A, (starts Oct 23)
- Computational Science and Engineering, 1st semester (Module IN2005)
- Denis Jarema, time and place: Monday, 16-18, MI 00.013.009a, (starts Oct 28)
- 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
- 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.
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.
|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
|Nov 11||Worksheet 3 (for the lecture on Nov 6)||Worksheet3, Solution,|
|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
|Nov 25||Worksheet 5 (for the lecture on Nov 20)|| Worksheet5, Solution, |
ws5b.mw, ws5c.mw, ws5d.mw,
|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 |
|Dec 16||Worksheet 8 (for the lecture on Dec 11)||Worksheet8, Solution,|
| Dec 18
| Introduction to Finite Element Methods - Part I
Introduction to Finite Element Methods - Part II
|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, |
|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 |
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.
- midterm exam winter 02/03, Solution
- final exam winter 02/03, Solution
- midterm exam winter 04/05, Solution
- final exam winter 04/05, Solution
- exam winter 05/06
- exam winter 06/07
- exam winter 07/08, solution
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)
- Website for the book of A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science
- Maple Computational Toolbox Files: contains an introduction worksheet to Maple plus several worksheets related to CSE, which are covered in this textbook.
- ODE Software for Matlab (website by J.C. Polking, Rice University)