Scientific Computing I - Winter 08: Difference between revisions

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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.  
''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 [http://www5.in.tum.de/lehre/vorlesungen/mod_sim/SS08/ lecture from summer term 2008], for example), instead.''
 


= Lecture Notes and Material =
= Lecture Notes and Material =

Revision as of 08:39, 22 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 (Module IN2005)
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 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
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

  • Date of final exam: Wednesday, February 4, 2009, during the lecture, i.e. 12:00-14:00.
  • 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

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