Introduction to Scientific Computing II  Summer 09
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 Term
 Summer 09
 Lecturer
 Dr. Miriam Mehl
 Time and Place
 Tuesday 8:1510:00, lecture room MI 02.07.023, first lecture April 21
 Audience
 Computational Science and Engineering, 2nd semester (Module IN2141)
 Tutorials
 Monday 9:1510:00, 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, 18.0020:00, room: HS1
material: one handwritten 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 ObjectOrientation. Elsevier, 1999.
 D. Rapaport. The art of molecular dynamics simulation. Camebridge University Press, 1995.