Scientific Computing I - Winter 10

Term

Winter 10

Lecturer

Dr. rer. nat. Tobias Weinzierl

Time and Place

Thursday, 8:00-12:00; please see timetable

Audience

Computational Science and Engineering, 1st semester (Module IN2005)

Tutorials

-

Exam

written exam, February 25

Semesterwochenstunden / ECTS Credits

2 SWS (2V) / 3 Credits

TUMonline

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Announcements

Please see the changed exam date

Contents

This course provides an overview of scientific computing, i. e. of the different tasks to be tackled on the way towards powerful numerical simulations. The entire "pipeline" of simulation is discussed:

• mathematical models: derivation, analysis, and classification
• numerical treatment of these models: discretization of (partial) differential systems, grid generation
• efficient implementation of numerical algorithms: implementation on monoprocessors vs. parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
• interpretation of numerical results & visualization
• validation

The course Scientific Computing 1 is intended for students in the Master's Program Computational Science and Engineering and of the English-language programs of the Department of Computer Science. Students in all other study programs, please consider our lecture Modellbildung und Simulation (see the lecture from summer term 2008, for example), instead.

Timetable, Lecture Notes, and Material

Due to the high number of interested students, we changed the location of the lecture to room 5123.EG.019 (Am Coulombwall 1, LMU Physics department), and we typically start at 8:30. However, as the room is not available on November 4, both, starting time and lecture duration differ on this very day.

• October 28: First lecture (start 8:15; lecture room MI 02.07.023)
  • Organisation
  • The Discipline
  • A Simple Population Model
  • Classification of Models
• November 4: Shorter lecture (start 8:00; lecture room 5123.EG.019; only till 10:00)
  • ODE Basics
  • ODEs Continued
  • Systems of ODEs
• November 11: Lecture (start 8:30; lecture room 5123.EG.019)
  • Numerics of ODEs
  • Implicit Methods
  • Sophisticated ODE Schemes
• November 25: Lecture (start 8:30; lecture room 5123.EG.019)
  • Basics of PDEs
  • Types of PDEs
  • Finite Differences
• December 9: Lecture (start 8:30; lecture room 5123.EG.019)
  • Finite Volumes
  • Finite Elements
  • Assembly Strategies & Grid Types
• January 13: Lecture (start 8:30; lecture room 5123.EG.019)
  • Parabolic PDEs
  • CFL Condition & Neumann Stability
  • Implicit Schemes for Parabolic PDEs
• January 20: No lecture

Exam

• Date of final exam: February 25, 2011 (see TUMOnline)
• Registration: Please register via TUMOnline (see TUMOnline)
• Room: MW 1050
• Helping material: One hand-written A4 sheet of paper, dictionary (if necessary)
• Exam topics are all topics covered during the lectures. See the catalogue of exam questions and previous years' exams below.
• Exam review: March 17, 2011. 2pm-4pm, Room 02.05.041.

Catalogue of Exam Questions

The following catalogue contain questions collected by students of the lectures in winter 05/06 and 06/07. The catalogue is intended for preparation for the exam, only, and serves as some orientation. It's by no means meant to be a complete collection.

• Modelling, ODEs
• Modelling, PDEs
• PDE numerics

Last Years' Exams

Please, be aware that there are always slight changes in topics between the different years' lectures. Hence, the previous exams are not fully representative for this year's exam.

• exam winter 05/06
• exam winter 06/07
• exam winter 07/08

Repetition

• If you wanna take part in the repetition exam, you have register at TUMOnline at the begin of the summer term.
• After the deadline of the registration, you'll be informed whether the repetition is oral or written.
• The repetition exam will take place at the end of the summer term, i.e. at the same period when the regular summer term exams take place.

Literature

Books and Papers

• B. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (excellent online material)
• A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press (in particular Chapter 3,5,6)
• G. Golub and J. M. Ortega: Scientific Computing and Differential Equations, Academic Press (in particular Chapter 1-4,8)
• D. Braess: Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics, Cambridge University Press (in particular I.1, I.3, I.4, II.2)
• Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998 (in particular Chapter 1-4,7,10)

Online Material

• Website for pre-2005 courses in Scientific Computing (more extensive - several of the topics have moved to other lectures, or are reduced in extent, now); website is accessible from the "Rechnerhalle" or with login/password (contact lecturer)
• Website for the book of A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science
  • Maple Computational Toolbox Files: contains an introduction worksheet to Maple plus several worksheets related to CSE, which are covered in this textbook.
• ODE Software for Matlab (website by J.C. Polking, Rice University)