Scientific Computing II - Summer 18

Term

Summer 2018

Lecturer

Prof. Dr. Michael Bader

Time and Place

Tuesday 10-12 (MI HS 2); first lecture: Tue, Apr 10

Audience

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

Tutorials

Carsten Uphoff, M.Sc., Nikola Tchipev, M.Sc.,
Friday 14-16, lecture room MI HS 2 (starts April 13)

Exam

written exams (Aug 2 and Oct 10)

Semesterwochenstunden / ECTS Credits

2V + 2Ü / 5 Credits

TUMonline

Scientific Computing II

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Announcements

• on Fri, Jul 27 (14-16, MI 02.07.023), there will be a questions&answers session about the exam topics (lecture only)

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
  • preconditioning
• molecular dynamics simulations
  • particle-based modelling (n-body simulation)
  • algorithms for efficient force calculation
  • parallelisation

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 Slides

Lecture slides will be published here. For future lectures, the respective slides from summer 2017 will be linked.

• Introduction, Relaxation Methods (Apr 10, 17)
• Multigrid Methods (Part I: Apr 17; Part II: Apr 20,24; Part III: May 15, 25)
  • some multigrid animations (more peas!)
  • if you're interested: On the history of the Multigrid method creation (website article by R.P. Fedorenko)
• Steepest Descent and Conjugate Gradient Methods (Part I&II: May 25, 29, Part III: May 29, Jun 5)
  • additional material: Maple worksheet quadratic_forms.mws, also as PDF
  • additional material: Maple worksheet conjugate_gradient.mws, also as PDF
• Molecular Dynamics:
  • Molecular Dynamics (Intro) (Jun 12)
  • Molecular Dynamics (Modelling) (Jun 12)
  • Molecular Dynamics (Time-Stepping) (Jun 19)
  • Molecular Dynamics (Force Computation: Linked Cell, Barnes-Hut, Fast Multipole) (Jun 26; Jul 3, 10)
    • 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)

Exercises

See the Moodle course.

Exams

• written exam (regular and repeat), working time: 105 minutes
• 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]

First Exam: Thursday, Aug 2

• Exam Review: Monday, Aug 27, 14.00-16.00; room: SCCS chair, printer room (glass box, directly after second door in 5th hallway on the second floor)
• Time: 11.00-12.45 - Please make sure to be in the lecture hall by 10.45, as the exam will start precisely at 11.00.
• Place: PH 2501 (Rudolf-Mößbauer-Hörsaal)

Second Exam: Wednesday, Oct 10

• Exam Review: Thursday, Oct 25, 13.00-15.00; room: SCCS chair, printer room (glass box, directly after second door in 5th hallway on the second floor)
• Time: 16.00-17.45 - Please make sure to be in the lecture hall by 15.45, as the exam will start precisely at 16.00.
• Place: Interim 2

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. Cambridge University Press, 1995.
• R. Beatson, L. Greegard. A short course on fast multipole methods (lecture script)