Scientific Computing I - Winter 17

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: 00.02.001, MI HS 1, Friedrich L. Bauer Hörsaal (5602.EG.001) (see below for details)

Semesterwochenstunden / ECTS Credits

4 SWS (2V+2Ü) / 5 Credits

TUMonline

lecture, tutorial, Moodle

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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,

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.
• a repeat exam will be offered

Final Exam

• Date of final exam: Feb 26, 2018, 13:30-15.00, room: 00.02.001, MI HS 1, Friedrich L. Bauer Hörsaal (5602.EG.001)
• 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
• Exam topics are all topics covered during the lectures. See the catalogue of exam questions and previous years' exams below.

Repeat Exam

• repeat exam is currently scheduled on Mar 28, 2018.

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.

• midterm exam winter 02/03, Solution
• final exam winter 02/03, Solution
• midterm exam winter 04/05, Solution
• final exam winter 04/05, Solution
• exam winter 05/06
• exam winter 06/07
• exam winter 07/08, solution
• exam winter 11/12
• exam winter repeat 11/12
• exam winter 12/13
• exam winter 13/14
• exam winter repeat 13/14
• exam winter 14/15
• exam winter repeat 14/15

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

• 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)