Introduction to Scientific Computing II - Summer 09
- Summer 09
- Dr. Miriam Mehl
- Time and Place
- Tuesday 8:15-10:00, lecture room MI 02.07.023, first lecture April 21
- Computational Science and Engineering, 2nd semester (Module IN2141)
- Monday 9:15-10:00, lecture room MI 02.07.023, first tutorial April 27
- written exam
- Semesterwochenstunden / ECTS Credits
- 2V + 1Ü / 4 Credits
- 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
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
- 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
From Gaussian Elimination to Relaxation Methods
|April 27||Exercise 1||matrix.m|
|April 28||Relaxation Methods||May 4||Exercise 2||error3.m|
|May 5||Multigrid||May 11||Exercise 3||Lecture:|
Two Grid Fourier Analysis
|May 18||Exercise 4
|May 19||Steepest Descent and Conjugate Gradients||May 25||Exercise 5||residual_vec.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||-|
- 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.