Introduction to Scientific Computing II - Summer 12

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Term
Summer 12
Lecturer
Prof. Dr. Michael Bader
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



Announcements

The review of the exam takes place on Wed., August 8 10-11am, 02.05.055

Repeat Exam

  • written exam
  • Date: Wed, 10 Oct 2012
  • Time: 8:30 - 10:00
    Please make sure to be in the exam room by 8.15, as the exam will start at 8.30.
  • Place: MW 1450 (in the engineering department!)
  • Duration: 90 min.
  • auxiliary material allowed:
    • one hand-written sheet of paper (Din A4), written on both sides
    • You are not allowed to use any other tools / devices (e.g. electronic dictionaries)
  • Topics: everything that was covered in the lectures and tutorials (except the last lecture, on long-range forces, July 17)

Please make sure that you are registered for the exam via TUMOnline!

Old exams are available on the websites of the last years:

http://www5.in.tum.de/lehre/vorlesungen/sci_compII/ss11/exam.pdf

http://www5.in.tum.de/lehre/vorlesungen/sci_compII/ss10/exam.pdf

http://www5.in.tum.de/lehre/vorlesungen/sci_compII/ss08/exam.pdf

Contents

This course provides a deeper knowledge in two important fields of scientific computing:

  • iterative solution of large sparse systems of linear equations:
    • 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 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

interpolate_4h.m
restrict_4h.m
restrict_fw.m

Homework-Solution
AnisotropicMG

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 MD Discretisation
solution
July 10 Time Integration
Implementation and Parallelisation		 July 16
July 17 Outlook on long-range potentials (not part of the exam)

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.
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