Scientific Computing II - Summer 17

Term

Summer 2017

Lecturer

Prof. Dr. Michael Bader

Time and Place

Monday 14-16 (MI HS 2); first lectures: Mon, Apr 24, and Tue, Apr 25 (in tutorial slot)

Audience

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

Tutorials

Carsten Uphoff, M.Sc., Nikola Tchipev, M.Sc.
Tuesdays 10-12, lecture room MI HS 2 (from May 2)

Exam

written exam, time/day see below

Semesterwochenstunden / ECTS Credits

2V + 2Ü / 5 Credits

TUMonline

Scientific Computing II

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Announcements

• on Tue, Apr 25 (10-12, MI HS 2), there will be a lecture replacing the one on May 1.

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 2016 will be linked.

• Introduction, Relaxation Methods (Apr 24, 25)
• Multigrid Methods (Part I: Apr 25; Part II: May 8,15 Part III: May 15, 22)
  • 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 29, Part III: Jun 12, 19)
  • 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 19)
  • Molecular Dynamics (Modelling) (Jun 26)
  • Molecular Dynamics (Time-Stepping) (Jun 26, Jul 3)
  • Molecular Dynamics (Force Computation: Linked Cell, Barnes-Hut, Fast Multipole) (Jul 10, 17)
    • 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.

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.