Scientific Computing II - Summer 15

Term

Summer 2015

Lecturer

Prof. Dr. Michael Bader

Time and Place

Monday 14.30-16.00, lecture room MI HS 2

Audience

Computational Science and Engineering, 2nd semester
others: see module description

Tutorials

Arash Bakhtiari
Tuesdays 10-12, lecture room MI 02.07.023 (from Apr 21),
First Tutorial: Apr 17 (Fri, 12-14)

Exam

repeat exam (written): Fri, Oct 2, 08.30-10.15 (Interim 2)

Semesterwochenstunden / ECTS Credits

2V + 2Ü / 5 Credits

TUMonline

Scientific Computing II

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Announcements

• lecture on Friday, Apr 24, 12.15-13.45: in lecture hall MI HS 3 (replaces the lecture on Mon, Apr 27)
• change of tutorial: the tutorial slot will move from Wed to Tue 10-12 in seminar room MI 02.07.023
• change of lecture: the lecture slot will move from Tue 10-12 to Mon 14.30-16.00 and into lecture hall MI HS 2

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 students in computer science, mathematics, or some field of science or engineering who already have a certain background in the numerical treatment of (partial) differential equations.

Lecture Notes and Material

All further announcements, worksheets and information can be found on the Moodle-page of this course.

Lecture Slides

• Introduction, Relaxation Methods (Apr 14, 20)
• Multigrid Methods (Part I: Apr 20, 24; Part II: Apr 24, May 4; Part III: May 11, 18)
  • On the history of the Multigrid method creation (website article by R.P. Fedorenko)
  • some multigrid animations
• Steepest Descent and Conjugate Gradient Methods (Part I: May 18, Part II: Jun 1, Part II: Jun 8)
  • additional material: Maple worksheet quadratic_forms.mws, also as PDF
  • additional material: Maple worksheet conjugate_gradient.mws, also as PDF
• Guest lecture by George Biros on n-body methods
• Molecular Dynamics:
  • Molecular Dynamics (Intro) (Jun 22)
  • Molecular Dynamics (Modelling) (Jun 22)
  • Molecular Dynamics (Time-Stepping) (Jun 29)
  • Molecular Dynamics (Force Computation: Linked Cell, Barnes-Hut, Fast Multipole) (Jul 6, 13)
    • additional material: article by Anderson: An implementation of the fast multipole method without multipoles (PDF can be accessed via LRZ proxy or after logging in to TUM's e-library)

Repeat Exam

• written exam
• Date: Fri, Oct 2
• Time: 8.30-10.15 - Please make sure to be in the lecture hall by 8:15, as the exam will start precisely at 8.30.
• Place: Interim 2 (black building in front of math/informatics)
• Duration: 90 min.
• material: no helping material of any kind is allowed during the exam
• Topics: everything that was covered in the lectures and tutorials

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

Old exams are available on the websites of the last years (note that the curriculum of the lecture has slightly changed since then!): [1] [2] [3]

Literature

• William L. Briggs, Van Emden Henson, Steve F. McCormick. A Multigrid Tutorial. Second Edition, SIAM, 2000 (available as eBook in the TUM library)
• Ulrich Trottenberg, Cornelis Oosterlee, Anton Schüller. Multigrid. Elsevier, 2001 (available as eBook in the TUM library)
• J.R. Shewchuk. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (download as PDF). 1994.
• V. Eijkhout: Introduction to High-Performance Scientific Computing (textbook, available as PDF on the website)
• M. Griebel, S. Knapek, G. Zumbusch, and A. Caglar. Numerical simulation in molecular dynamics. Springer, 2007 (available as eBook in the TUM library)
• 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 Applications. 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.

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/