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Scientific Computing I - Winter 16

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Term
Winter 16
Lecturer
Prof. Dr. Michael Bader
Time and Place
Wednesday, 10-12; MI HS 2 (starts Oct 26)
Audience
Computational Science and Engineering, 1st semester
Tutorials
Denis Jarema, Steffen Seckler
time and place:
  I group: Wednesday, 14:15-15:45, MI 02.07.023,
 II group: Monday, 14:15-15:45, MI 03.13.010
Exam
written exam: Mar 3rd, 2017, 13:30, room: 00.02.001, MI HS 1, Friedrich L. Bauer Hörsaal (5602.EG.001)
exam review: Mar 13, 2017, 09:00-11:00, room 02.07.023
2nd exam: Apr 11, 2017, 11:00
2nd exam review: Mai 04, 2017, 16:15-17:45, room 02.07.023
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
lecture, tutorial



Contents

Announcements

  • A Q&A session concerning the exam (focusing on the lectures) will take place on Feb 22, 2017 (Wed), 14:15-15:45, lecture hall MI HS 3 (not the "usual" lecture hall MI HS 2!).
  • The lecture on Dec 7 will be cancelled (dies academicus)
  • Election of CSE representative: on Nov 30, from 11.30, the CSE students attending the lecture will elect their representative; the lecture will end at 11.30.
  • The lecture on Nov 2 will be cancelled due to the students assembly (Fachschaftsvollversammlung)
  • The lecture in the first week (on Oct 19) will be cancelled, as the CSE students have an alternate program on this day

Contents

The lecture will cover the following topics in scientific computing:

  • typical tasks in the simulation pipeline in scientific computing;
  • classification of mathematical models (discrete/continuous, deterministic/stochastic, etc.);
  • modelling with (systems) of ordinary differential equations (example: population models);
  • modelling with partial differential equations (example: heat equations);
  • numerical treatment of models (discretisation of ordinary and partial differential equations: introduction to Finite Volume and Finite Element Methods, grid generation, assembly of the respective large systems of linear equations);
  • analysis of the resulting numerical schemes (w.r.t. convergence, consistency, stability, efficiency);

An outlook will be given on the following topics:

  • efficient implementation of numerical algorithms, both on monoprocessors and parallel computers (architectural features, parallel programming, load distribution, parallel numerical algorithms)
  • interpretation of numerical results (visualization)

Lecture Notes and Material

Slides of the lectures, as well as worksheets and solutions for the tutorials, will be published here as they become available.

Day Topic Material
Oct 26 Introduction - CSE/Scientific Computing as a discipline slides: discipline.pdf, fibo.pdf
Oct 24/26 Worksheet 1 Worksheet 1, Solution 1
Oct 31/Nov 2
Nov 7/9
Worksheet 2/3 Worksheet 2/3, Solution 2/3
Nov 9 Population Models - Continuous Modelling (Parts I to II) slides: population.pdf
python worksheets: Lotka Volterra, Population Models
maple worksheets: lotkavolt.mws, popmodel.mw
maple_lotkavolt.pdf, maple_popmodel.pdf
Nov 9, 16 Population Models - Continuous Modelling (parts III to IV) slides: population2.pdf
Nov 14/16 Worksheet 4 Worksheet 4, Solution 4
Nov 21/23 Worksheet 5 Worksheet 5, Solution 5, ws5_ex1.py
ipython notebook version: W5x-Direction_Fields_for_ODE.ipynb
Nov 23 Numerical Methods for ODEs
(part I)
slides: ode_numerics.pdf
python worksheets: Numerics ODE
maple worksheets: numerics_ode.mws,
maple_numerics_ode.pdf
Nov 28/30 Worksheet 6 Worksheet 6, Solution 6, ws6_ex1.py
Nov 30 Numerical Methods for ODEs
(part II)
slides: ode_numerics.pdf
python scripts for visualisation of stability: unstable explLLM2 example,
visualisation of stability regions,
explicit midpoint rule examples (Martini glass effec),
Martini glass effect in scaled plot
Dec 12/14 Worksheet 7 Worksheet 7, Solution 7, ws7_ex3.py
Dec 14 Heat Transfer - Discrete and Continuous Models slides: heatmodel.pdf
python worksheets: Heat Transfer
maple worksheets: poisson2D.mws, poisson2D.pdf
Dec 19/21 Worksheet 8 Worksheet 8, Solution 8, ws8_ex1.py
Dec 21 1D Heat Equation - Analytical and Numerical Solutions slides: heateq.pdf, heatenergy.pdf

python worksheets: 1D Heat Equation,
1D Heat Equation - Implicit Schemes
maple worksheets: heat1D_disc.mw, maple_heat1D_disc.pdf,
heat1D_impl.mw, maple_heat1D_impl.pdf

Jan 9/11 Worksheet 9 Worksheet 9, Solution 9, ws9_ex2.py
Jan 11
Jan 18/25
Introduction to Finite Element Methods - Part I
Introduction to Finite Element Methods - Part II
slides: pde_fem.pdf
maple worksheets: fem.mw, maple_fem.pdf
python worksheets: FEM
Jan 16/18 Worksheet 10 Worksheet 10 ,Solution 10, ws10_ex2.py
Jan 23/25 Worksheet 11 Worksheet 11, Solution 11, ws11_ex2.py
Jan 25
Feb 1, 8
Case Study: Computational Fluid Dynamics slides: study_cfd.pdf
Jan 30/Feb 1 Worksheet 12 Worksheet 12, Solution 12, ws12_ex1.py
Feb 6/8 Worksheet 13 Worksheet 13, Solution 13, ws13_ex1.py, ws13_ex2.py

Exams

Final Exam

  • Date of final exam: Mar 3rd, 2017, 13:30, room: 00.02.001, MI HS 1, Friedrich L. Bauer Hörsaal (5602.EG.001)
  • Please be on time - the working time will start at 13.30, at the latest, and there will be organizational remarks and announcements before
  • Registration: via TUM-Online
  • Helping material: A hand-written A4 sheet (written on both sides) will be allowed as helping material during the exam - all other items (incl. electronic devices of any kind) will be forbidden.
  • Exam topics are all topics covered during the lectures. See the catalogue of exam questions and previous years' exams below.

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.

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.

Literature

Books and Papers

  • A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press (in particular Chapter 3,5,6)
  • G. Strang: Computational Science and Engineering, Wellesley-Cambridge Press, 2007
  • G. Golub and J. M. Ortega: Scientific Computing and Differential Equations, Academic Press (in particular Chapter 1-4,8)
  • Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998 (in particular Chapter 1-4,7,10; available as eBook in the TUM library)
  • A. Tveito, H.P. Langtangen, B. Frederik Nielsen und X. Cai: Elements of Scientific Computing, Texts in Computational Science and Engineering 7, Springer, 2010 (available as ebook in the TUM library)
  • B. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (excellent online material)
  • 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)

Online Material