[an error occurred while processing this directive]
Introduction to Scientific Computing |
|
(winter 2003/2004) |
Max Emans
Audience:
Time and Place:
Wednesday 11:30-13:00,
lecture room 02.07.023,
first lesson Oct 22
Final Exam:
Tuesday, Feb 17 2004, 12:00-14:00,
lecture room 02.07.023.
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.
Starting from mathematical models (derivation, analysis, and classification;
various examples), their numerical treatment is discussed (discretization of
differential systems, grid generation).
The next chapter deals with the efficient implementation of numerical algorithms,
both on monoprocessors and parallel computers (architectural features, parallel
programming, load distribution, parallel numerical algorithms).
Finally, some remarks on the interpretation of numerical results (visualization)
are made.
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:
Introduction/Mathematical Modelling
Ordinary Differential Equations
Partial Differential Equations
- Wed, Dec 3, slides07.pdf
(see also the Maple worksheet
poisson1D.mws)
- Wed, Dec 10, slides08.pdf
(see also the Maple worksheets
heat1D.mws,
and heat1D_disc.mws)
- Wed, Dec 17, slides08.pdf
(see also the Maple worksheets
heat1D_disc.mws,
and heat1D_impl.mws)
addendum:
- sumparts.pdf
(Summation by parts), and
- heatenergy.pdf
(detailed analysis of the discrete energy for the explicit
time stepping scheme).
- Wed, Jan 14, slides09.pdf
(see also the Maple worksheet
poisson2D.mws)
Solvers for Systems of Linear Equations
For further material (online script and last year's exercises),
please refer to CSE's
Virtual Teaching Centre.
Tutorial:
Monday 11-13, lecture room 02.07.023,
first tutorial Oct 27
Exercises:
- for Mon, Nov 03, exercise01.pdf
- for Mon, Nov 10, exercise02.pdf
- for Mon, Nov 17, exercise03.pdf
- for Mon, Nov 24, exercise04.pdf
- for Mon, Dez 01, exercise05.pdf
- for Mon, Dez 08, exercise06.pdf
(corrects a typing error in the printed worksheets!)
- for Mon, Dez 15, exercise07.pdf
- for Mon, Jan 12, exercise08.pdf
- for Mon, Jan 19, exercise09.pdf
- for Mon, Jan 26, exercise10.pdf
- for Mon, Feb 02, exercise11.pdf
(optional/additional)
- for Mon, Feb 09, exercise12.pdf
(optional/additional)
Maple-Worksheets
| topic |
worksheet |
completed worksheet |
| Introduction to Maple |
tutorial.mws |
- |
| Handling of differential equations by Maple |
introduction.mws |
introduction_sol.mws |
| Modelling population growth |
growtheq.mws |
growtheq_sol.mws |
| Numerical Treatment of Ordinary Differetial Equations |
numerical_ode.mws |
numerical_ode_sol.mws |
| PDE: Poisson's equation in 1D |
poisson1D.mws |
- |
| PDE: Heat equation in 1D |
heat1D.mws |
- |
| - explicit schemes |
heat1D_disc.mws |
- |
| - implicit schemes |
heat1D_impl.mws |
- |
| - leap-frog scheme |
heat1D_leap.mws |
- |
| PDE: Poisson's equation in 2D |
poisson2D.mws |
- |
| Gauss-Seidel and Jacobi relaxation |
relaxation.mws |
- |
| Multigrid |
multigrid.mws |
- |
Literature
- 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:
Iterative Solution of Large Sparse Systems of Equations,
Springer, 1993
- Hackbusch:
Elliptic Differential Equations - Theory and Numerical Treatment,
Springer, 1992
Michael Bader