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 9

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 exam, time/day see below

Semesterwochenstunden / ECTS Credits

2V + 2Ü / 5 Credits

TUMonline

Scientific Computing II

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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 9, 16)
• Multigrid Methods
  • 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
  • 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)
  • Molecular Dynamics (Modelling)
  • Molecular Dynamics (Time-Stepping)
  • Molecular Dynamics (Force Computation: Linked Cell, Barnes-Hut, Fast Multipole)
    • 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)
• 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. Cambridge University Press, 1995.
• R. Beatson, L. Greegard. A short course on fast multipole methods (lecture script)