Introduction to Scientific Computing II - Summer 10

Term

Summer 10

Lecturer

Dr. rer. nat. Tobias Weinzierl

Time and Place

Tuesday 8:15-10:00, lecture room MI 02.07.023

Audience

Computational Science and Engineering, 2nd semester (Module IN2141)

Tutorials

Monday 9:00-9:45, lecture room MI 02.07.023

Exam

written exam on July 21st. Please register via TUM-Online.

Semesterwochenstunden / ECTS Credits

2V + 1Ü / 4 Credits

TUMonline

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Announcements

• May, 24 and May 25: No lecture and no tutorial due to Whit Holidays (Pfingstferien)
• May, 11: corrected slides online
• April, 27: corrected slides are online now. Annotated slides are available from the TeleTeachingTool Lecture Archive
• April, 26: First tutorial
• April, 20: First lecture
• April, 19: No tutorial

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

Annotated slides are available from the TeleTeachingTool Lecture Archive

lecture	slides	tutorial	exercise	matlab
April 20	Introduction	April 26	Matrix Assembly Installing Matlab
April 27	Gauss Elimination	May 3	Exercise 1	matrix.m error2.m main.m
May 04	Relaxation Methods	May 10	Exercise 2 slides	error3.m residual.m jacobi_iteration.m gauss_seidel_iteration.m main.m Solution_Tutorial Solution Homework
May 11	Relaxation Methods II	May 17	Exercise 3 slides	main.m residual.m main.m Solution SOR
May 18	Multigrid Game	May 31	Exercise 4 slides	multigrid-solver.tar.gz multigrid-solver-solution.tar.gz twogrid-solver-tutorial.tar.gz
June 1	Multigrid	June 7	Exercise 5	interpolate_4h.m restrict_4h.m restrict_fw.m restrict_fw.m Anisotropic Multigrid Solution Multigrid Solution
June 8	Krylov Methods	June 14	Exercise 6 slides	residual_vec.m residual.m Steepest Descent Solution
June 15	MD Introduction	June 21	Exercise A

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.