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
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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 -

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.