Scientific Computing II - Summer 14

Term

Summer 2014

Lecturer

Prof. Dr. Michael Bader

Time and Place

Tuesday 10-12, lecture room MI 02.07.023
First Lecture: Apr 8

Audience

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

Tutorials

Kaveh Rahnema
Monday 10-12, lecture room MI 02.07.023,
First Tutorial: April 14

Exam

written exam, Wed, Jul 16, 13.30-15.00 in lecture hall Interim 2 (black building in front of FMI)

Semesterwochenstunden / ECTS Credits

2V + 2Ü / 5 Credits

TUMonline

Scientific Computing II

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Announcements

• on June 16, we will restart with a lecture (which replaces the usual tutorial)

Exam

• written exam
• Date: Wed, Jul 16
• Time: 13.30-15.00 - Please make sure to be in the lecture hall by 13:15, as the exam will start precisely at 13.30.
• Place: Interim 2 (black building in front of computer science/math building)
• 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]

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

lecture	material	tutorial	exercise	matlab
Apr 8	Introduction, Relaxation Methods	Apr 14	sheet1 , solution1
Apr 15	Multigrid Methods (Part I), Animations	Apr 21	- (Easter holiday)
Apr 28 (Mon)	Multigrid Methods (Part II)	Apr 29 (Tue)	sheet2 , solution2	smoothers.m
May 05 (Mon)	Multigrid Methods (Part II cont., Part III)	May 12	sheet3 ,solution3	code_exercise3
May 13	Multigrid Methods (Part III)	May 19	sheet4, solution4	smooth.m, code_exercise4
May 20	Steepest Descent and Conjugate Gradient Methods (Maple worksheet quadratic_forms.mws, also as PDF)	May 26	sheet5, solution5
May 27	CG and Preconditioning (Maple worksheet conjugate_gradient.mws, also as PDF)	Jun 2	sheet6	Code_Ex5, Code_Ex6, Solution_Ex5, Solution_Ex6
Jun 3	CG and Preconditioning (cont)	Jun 9&10	lecture and tutorial cancelled (holidays)
Jun 16 (Mon)	Molecular Dynamics (Intro) (Maple worksheet twobody.mws, also as PDF	-	-	-
Jun 17	Molecular Dynamics (Modelling)	Jun 23	sheet7, solution7
June 24	Time Integration Maple worksheet circles_ode.mws, also as PDF)	June 30	sheet8, solution8
July 1	short-range potentials and (parallel) implementation	July 7	sheet9, solution9
July 8	Discussion of previous exam questions	-	-	-

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/