Introduction to Scientific Computing II - Summer 09

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

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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		-

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.