Scientific Computing I - Winter 14

Term

Winter 14

Lecturer

Dr. rer. nat. Tobias Neckel

Time and Place

Wednesday, 10:15-11:45; MI 00.13.009A, (starts Oct 10)

Audience

Computational Science and Engineering, 1st semester

Tutorials

Denis Jarema, time and place: I group: Monday, 16-18, MI 03.07.30, (starts Oct 20), II group: Thursday, 8-10, MI 02.07.023 (starts Oct 23)

Exam

written exam

Semesterwochenstunden / ECTS Credits

4 SWS (2V+2Ü) / 5 Credits

TUMonline

tumonline

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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 20, 23	Worksheet 1 (for the lecture on Oct 15)	Worksheet 1, Solution 1 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)