Introduction to Scientific Computing II - Summer 09
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- Term
- Summer 09
- Lecturer
- Dr. Miriam Mehl
- Time and Place
- Tuesday 8:15-10:00, lecture room MI 02.07.023, first lecture April 21
- Audience
- Computational Science and Engineering, 2nd semester (Module IN2141)
- Tutorials
- Monday 9:15-10:00, lecture room MI 02.07.023, first tutorial April 27
- Exam
- written exam
- Semesterwochenstunden / ECTS Credits
- 2V + 1Ü / 4 Credits
- TUMonline
- {{{tumonline}}}
Announcements
- Exam: Tuesday, July 14, 18.00-20:00, room: HS1
material: one hand-written page of notes is allowed, other materials, in particular electronic devices such as calculators or cell phones are not allowed
Contents
This course provides a deeper knowledge in two important fields of scientific computing:
- solution of large sparse systems of linear equations:
- Gaussian elemination
- relaxation methods
- multigrid methods
- steepest descent
- conjugate gradient methods
- molecular dynamics simulations
- the physical model
- the mathematical model
- approximations and discretization
- implementational aspects
- parallelisation
- examples of nanofluidic simulations
The course is conceived for computer scientists, mathematicians, engineers, or natural scientists with already a background in the numerical treatment of (partial) differential equations.
Lecture Notes and Material
lecture | slides | tutorial | exercise | matlab |
April 21 | Organization From Gaussian Elimination to Relaxation Methods |
April 27 | Exercise 1 | matrix.m error2.m main.m |
April 28 | Relaxation Methods | May 4 | Exercise 2 | error3.m residual.m jacobi_iteration.m gauss_seidel_iteration.m main.m |
May 5 | Multigrid | May 11 | Exercise 3 | Lecture: multigrid.m main.m Exercise: matrix.m gaussian.m residual_vec.m residual.m interpolate.m restrict.m gauss_seidel_iteration.m two_grid_iteration.m main.m |
May 12 | Multigrid Two Grid Fourier Analysis |
May 18 | Exercise 4 Slides |
|
May 19 | Steepest Descent and Conjugate Gradients | May 25 | Exercise 5 | residual_vec.m residual.m main.m |
May 26 | Preconditioned Conjugate Gradient Method & Iterative Solvers Overview | June 8 | Exercise 6 | |
June 9 | Molecular Dynamics - Introduction | - | - | - |
June 16 | Molecular Dynamics - Model | June 22 | Exercise A | - |
June 23 | Molecular Dynamics - Discretisation | June 29 | Exercise B | - |
June 30 | Molecular Dynamics - Algorithms | July 6 | Exercise C | - |
July 7 | July 13 | - | ||
July 14 | July 20 | - | ||
July 21 | July 22 | - |
Exam
Literature
- William L. Briggs, Van Emden Henson, Steve F. McCormick. A Multigrid Tutorial. Second Edition. SIAM. 2000.
- J.R. Shewchuk. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain. Edition 1.25. 1994.
- M. Griebel, S. Knapek, G. Zumbusch, and A. Caglar. Numerische Simulation in der Molekulardynamik. Springer, 2004.
- M. P. Allen and D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, 2003.
- D. Frenkel and B. Smith. Understanding Molecular Simulation from Algorithms to ASpplications. Academic Press (2nd ed.), 2002.
- R. J. Sadus. Molecular Simulation of Fluids; Theory, Algorithms and Object-Orientation. Elsevier, 1999.
- D. Rapaport. The art of molecular dynamics simulation. Camebridge University Press, 1995.