Scientific Computing II - Summer 14

Term

Summer 2014

Lecturer

Prof. Dr. Michael Bader

Time and Place

t.b.a.

Audience

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

Tutorials

Kaveh Rahnema (time and place t.b.a.)

Exam

written exam

Semesterwochenstunden / ECTS Credits

2V + 2Ü / 5 Credits

TUMonline

see last year's lecture: Scientific Computing II

---

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

will be made available throughout the lecture ...

|- | Apr 23 || Multigrid Methods, Animations || Apr 29 || Sheet2, Solution, smoothers.m || |- | Apr 30 || Multigrid Methods (Part II) || May 06 || Sheet3, Solution, code_exercise3.tar |- | May 07 || Multigrid Methods (Part III) || May 13 || Sheet4, smooth.m, Solution, code_exercise4.tar |- | Mai 14 || (student assembly - no lecture) || May 20 || (holiday - no lecture) || |- | Mai 21|| (holiday - no lecture) || May 27 || Steepest Descent and Conjugate Gradient Methods
(Maple worksheet quadratic_forms.mws, also as PDF) || |- | May 28 || CG and Preconditioning
(Maple worksheet conjugate_gradient.mws, also as PDF) || June 3|| Sheet5, Solution |- | June 4 || CG and Preconditioning (cont.) || June 10 || Sheet6, Solution, Code_Ex5, Code_Ex6, Solution_Ex5, Solution_Ex6 |- || June 11 || Molecular Dynamics (Intro)
(Maple worksheet twobody.mws, also as PDF || June 17 || Sheet7, Solution, code_exercise7.tar |- || June 18 || Molecular Dynamics, Pt. 1 || June 24 || Sheet8, Solution, code_exercise8.tar |- | June 25 || Time Integration
Maple worksheet circles_ode.mws, also as PDF) || July 1 || Sheet9, Solution, code_exercise9.tar |- | July 1 || short-range potentials and (parallel) implementation || July 8 || Sheet10, Solution |- | July 9 || long-range potentials, tree algorithms || July 15 || Sheet11, Solution |- | July 16 || "all questions answered" (on exercises & tutorials) || - || |- |}

-->

Literature

• William L. Briggs, Van Emden Henson, Steve F. McCormick. A Multigrid Tutorial. Second Edition. SIAM. 2000.
• Ulrich Trottenberg, Cornelis Oosterlee, Anton Schüller. Multigrid. Elsevier, 2001.
• 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.

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/