Scientific Computing I - Winter 08: Difference between revisions
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| term = Winter 08 | | term = Winter 08 | ||
| lecturer = [[Michael Bader|Dr. Michael Bader]] | | lecturer = [[Michael Bader|Dr. Michael Bader]] | ||
| timeplace = Wednesday, | | timeplace = Wednesday, 12:30-14:00., lecture room MI 02.07.023, start: Oct 22 | ||
| credits = 2 SWS (2V) / 3 Credits | | credits = 2 SWS (2V) / 3 Credits | ||
| audience = Computational Science and Engineering, 1st semester | | audience = Computational Science and Engineering, 1st semester | ||
Revision as of 08:33, 21 October 2008
- Term
- Winter 08
- Lecturer
- Dr. Michael Bader
- Time and Place
- Wednesday, 12:30-14:00., lecture room MI 02.07.023, start: Oct 22
- Audience
- Computational Science and Engineering, 1st semester
- Tutorials
- -
- Exam
- written exam (time and day t.b.a.)
- Semesterwochenstunden / ECTS Credits
- 2 SWS (2V) / 3 Credits
- TUMonline
- {{{tumonline}}}
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 is conceived as an introduction to the thriving field of numerical simulation for computer scientists, mathematicians, engineers, or natural scientists without an already strong background in numerical methods.
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
- slides, handout
- Fibonacci's Rabbits, Classification of Models
- Oct
- slides, handout
- Continous Population Models I - Single Species Models
- Nov
- slides
- Maple worksheet: popmodel.mws
- Continous Population Models II & III - Systems of ODE, Analysis of ODE Models
- slides, handout population models
- Maple worksheets: lotkavolt.mws, dirfields.mws
- Numerical Methods for ODE
- Nov
- slides, handout
- Maple worksheet: numerics_ode.mws
- Discrete Models for the Heat Equation
- Dec
- slides, handout
- Maple worksheet: poisson2D.mws
- Heat Equation - Analytical and Numerical Solution
- Dec
- 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)
- Grid Generation
- Dec
- slides, handout
- Discretisation of PDEs, Finite Element Method
- Jan
- slides, handout
- Maple worksheets: poisson2D.mws, fe.mws
- Case Study - Computational Fluid Dynamics
- Feb
- slides, handout
- Conclusion and Outlook
- Feb
- slides, handout
Exam
A written exam will be offered at the end of the lecture period.
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.