# Scientific Computing I - Winter 08

**Term**- Winter 08
**Lecturer**- Dr. Michael Bader
**Time and Place**- Wednesday, 10:15-11:45., lecture hall MI HS 2
**Audience**- Computational Science and Engineering, 1st semester (Module IN2005)
**Tutorials**- -
**Exam**- written exam (Feb 4, 2009, 10:00-12:00, MI HS 2 and MI 01.06.011)
**Semesterwochenstunden / ECTS Credits**- 2 SWS (2V) / 3 Credits
**TUMonline**- {{{tumonline}}}

## Contents

# Announcement:

- From Nov 5: change of time and lecture hall to
**Wed, 10-12, in MI HS 2**

# Contents

This course provides an overview of scientific computing, i. e. of the different tasks to be tackled on the way towards powerful numerical simulations. The entire "pipeline" of simulation is discussed:

- mathematical models: derivation, analysis, and classification
- numerical treatment of these models: discretization of (partial) differential systems, grid generation
- efficient implementation of numerical algorithms: implementation on monoprocessors vs. parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
- interpretation of numerical results & visualization
- validation

*The course Scientific Computing 1 is intended for students in the Master's Program Computational Science and Engineering. Students in all other study programs, please consider our lecture Modellbildung und Simulation (see the lecture from summer term 2008, for example), instead.*

# Lecture Notes and Material

(Material for future lectures refer to the lectures from winter term 2007, and will be updated throughout the semester)

- Introduction - Scientific Computing as a Discipline
- Oct 22
- slides, handout
- Fibonacci's Rabbits, Classification of Models
- Oct 22
- slides, handout
- Continous Population Models I & II - Single Species Models, Analysis of ODE Models
- Oct 29, Nov 5
- slides
- Maple worksheet: popmodel.mws
- Continous Population Models III & IV - Systems of ODE, Analysis of ODE Systems
- Nov 5, Nov 12
- slides, handout population models
- Maple worksheets: lotkavolt.mws, dirfields.mws
- Numerical Methods for ODE
- Nov 19 & 26, Dec 3
- slides, handout
- Maple worksheet: numerics_ode.mws
- Discrete Models for the Heat Equation
- Dec 3, Dec 10
- slides, handout
- Maple worksheet: poisson2D.mws
- Heat Equation - Analytical and Numerical Solution
- Dec 10,17
- slides, handout
- Maple worksheets: Fourier's method: heat1D_four.mws, Discretisation: heat1D_disc.mws, heat1D_impl.mws
- Additional material: Neumann stability (worksheet with solution), discrete energy (handout)
- Discretisation of PDEs, Finite Element Method
- Jan 7, 14, 21
- slides, handout
- Maple worksheets: poisson2D.mws, fe.mws
- Grid Generation
- Jan 28
- slides, handout
- Case Study - Computational Fluid Dynamics (not included this year)
- slides, handout
- Conclusion and Outlook
- Feb 28
- slides, handout

# Exam

- Date of final exam: Wednesday,
**February 4, 2009**. - Time and place: 10:00 - 12:00 in rooms
**MI HS 2**(names/login A-P) and**MI 01.06.011**(Q-Z) - Helping material: you are allowed to use
**one sheet (size A4) of paper**with**hand-written(!) notes**during the exam. Any further helping material (books, calculators, etc.) is forbidden! - Exam topics are all topics covered during the lectures; see the catalogue of exam questions and previous years' exams below.
- Repeat exam: a repeat exam will offered (only for students who failed the regular exam) in April or May 2009. The exam will be written or oral, depending on the number of participants.

### 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.

# Literature

- A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press
- Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (5th edition)
- Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993
- Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998
- Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996
- Hackbusch: Elliptic Differential Equations - Theory and Numerical Treatment, Springer, 1992

### 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.