Introduction to Scientific Computing II - Summer 12

Term
Summer 12
Lecturer
Time and Place
Tuesday 8:30-10:00, lecture room MI 02.07.023
First Lecture: April 17
Audience
Computational Science and Engineering, 2nd semester (Module IN2141)
Tutorials
Wolfgang Eckhardt
lecture room MI 02.07.023, time:
Monday 9:00-9:45,
First Tutorial: April 23
Exam
written exam
Semesterwochenstunden / ECTS Credits
2V + 1Ü / 4 Credits
TUMonline
Scientific Computing II

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
• 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 material tutorial exercise matlab Apr 17 Introduction, Relaxation Methods Apr 23 Slides Matlab Code Apr 24 Multigrid Methods, Animations Apr 30 Iterative Solvers Homework Sheet Matlab Code Mai 1 (holiday - no lecture) May 7 Solution Homework Exercise Code Tutorial May 8 Multigrid Methods (cont.) May 14 slides Multigrid-Solver 2Grid-Solver May 15 Multigrid Methods (cont.),Animations May 21 Multigrid Multigrid-Solver May 22 Slides Two-grid analysis May 28 - (holiday) - May 29 - (holiday) June 4 - - June 5 Steepest Descent and Conjugate Gradient Methods(Maple worksheet quadratic.mws, also as PDF) June 11 Steepest-Descent/CG Slides SD/CG Solution-SD June 12,19 Preconditioned Conjugate Gradient Methods(Maple worksheet conjugate_gradient.mws, also as PDF) June 18 PCG PCG-Frame Solution June 19 Molecular Dynamics (Intro and Modelling) June 25 MD Introduction Slides June 26 Molecular Dynamics (Intro and Modelling)(Maple worksheet twobody.mws, also as PDF;Maple worksheet circles_ode.mws, also as PDF) July 2 MD Modelling Slides July 3 Molecular Dynamics (Modelling)Time Integration July 9

Further Material

Annotated slides for the lecture in summer 2010 /(given by Dr. Tobias Weinzierl) are available from the TeleTeachingTool Lecture Archive

Matlab (together with installation instructions) is available from https://matlab.rbg.tum.de/

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 (download as PDF). 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.