Scientific Computing I - Winter 14: Difference between revisions
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| [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/uebungen/blatt12.pdf Worksheet 12] | | [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/uebungen/blatt12.pdf Worksheet 12], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/uebungen/blatt12solution.pdf Solution 12], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/py/ws12_ex1.py ws12_ex1.py], [http://www5.in.tum.de/lehre/vorlesungen/sci_comp/ws14/py/ws12_ex2.py ws12_ex2.py] | ||
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Revision as of 19:35, 26 January 2015
- 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
- Semesterwochenstunden / ECTS Credits
- 4 SWS (2V+2Ü) / 5 Credits
- TUMonline
- tumonline lecture, tumonline tutorial
Announcements
- 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,
|
| 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.
- 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
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
- 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)