Scientific Computing I - Winter 14

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

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Announcements

• 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

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.

• Modelling, ODEs
• Modelling, PDEs
• PDE numerics

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)