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Scientific Computing I - Winter 17

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Term
Winter 17
Lecturer
Prof. Dr. Michael Bader
Time and Place
Wednesday, 10-12; MI HS 2 (starts Oct 25)
Audience
Computational Science and Engineering, 1st semester
Tutorials
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
Monday, Feb 26, 2018, 13:15, room: CH 21010, Hans-Fischer-Hörsaal (5401.01.101K)
2nd exam: Wednesday, Mar 28, 2018, 11:00-12:30.
Semesterwochenstunden / ECTS Credits
4 SWS (2V+2Ü) / 5 Credits
TUMonline
lecture, tutorial, Moodle



Contents

Announcements

  • Repetition exam review: Apr 25, Wed, 08:00-10:00 AM, MI 02.05.057. Student ID required.

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 25 Introduction - CSE/Scientific Computing as a discipline
Population Models - Discrete Modeling
slides: discipline.pdf,
fibo.pdf
Nov 6/8 Worksheet 1 Worksheet 1, Solution 1
Nov 13/15
Nov 20/22
Worksheet 2/3 Worksheet 2/3, Solution 2/3
Nov 15 Population Models - Continuous Modelling (Parts I to II) slides: population.pdf
python worksheets: Population Models
maple worksheets: popmodel.mw,
maple_popmodel.pdf
Nov 22 Population Models - Continuous Modelling (parts III to IV) slides: population2.pdf
python worksheets: Lotka Volterra,
maple worksheets: lotkavolt.mws,
maple_lotkavolt.pdf
Nov 27/29 Worksheet 4 Worksheet 4, Solution 4,

ws4_ex3_misc.ipynb

Nov 29 Numerical Methods for ODEs
(part I)
slides: ode_numerics.pdf
python worksheets: Numerics ODE
maple worksheets: numerics_ode.mws,
maple_numerics_ode.pdf
ipython:

SciComp_Numerics_ODE.ipynb

Dec 4/6 Worksheet 5 Worksheet 5,

Solution 5, ws5_ex1.py
ipython notebook version: ws5ex1.ipynb

Dec 6 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 11/13 Worksheet 6 Worksheet 6, Solution 6, ws6_ex1.py,

ws6_ex3.py, ws6_ex1.ipynb, ws6_ex3.ipynb, ws6_ex5.ipynb

Dec 6/13 Heat Transfer - Discrete and Continuous Models,
Finite Difference and Finite Volume Methods
slides: heatmodel.pdf
python worksheets: Heat Transfer
maple worksheets: poisson2D.mws, poisson2D.pdf
Dec 18/20 Worksheet 7 Worksheet 7, Solution 7, ws7_ex3.py
Dec 13/20 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 08/10 Worksheet 8 Worksheet 8, Solution 8, ws8_ex1.py
Jan 10/17 Introduction to Finite Element Methods slides: pde_fem.pdf
maple worksheets: fem.mw, maple_fem.pdf
python worksheets: FEM
Jan 15/17 Worksheet 9 Worksheet 9, Solution 9, ws9_ex2.py
Jan 22/24 Worksheet 10 Worksheet 10 ,Solution 10, ws10_ex2.py
Jan 24, 31
Feb 7
Case Study: Computational Fluid Dynamics slides: study_cfd.pdf
Jan 29/31 Worksheet 11 Worksheet 11, Solution 11, ws11_ex2.py
Feb 5/Feb 7 Worksheet 12 Worksheet 12, Solution 12, ws12_ex1.py

Exams

  • 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. An overview is given on slide 33 of the CFD slide-set: study_cfd.pdf.

Final Exam

  • Date of final exam: Feb 26, 2018, 13:30-15.00, room: Hans-Fischer-Hörsaal (CH 21010, Chemistry Department)
  • Please be on time (13.15 in the lecture hall) - the working time will start at 13.30, at the latest, and there will be organizational remarks and announcements before
  • Registration: via TUM-Online

Repeat Exam

  • repeat exam is currently scheduled on Mar 28, 2018, 11:00-12:30.

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.

The following catalogue contains 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.

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