Scientific Computing I - Winter 15

Term

Winter 15

Lecturer

Dr. rer. nat. Tobias Neckel

Time and Place

Wednesday, 10:15-11:45; HS 2 (starts Oct 21)

Audience

Computational Science and Engineering, 1st semester

Tutorials

Denis Jarema, time and place: I group: Wednesday, 14:00-15:45, MI 02.13.008, II group: Monday, 14:15-16:00, MI 03.13.010 (starts Oct 26)

Exam

written exam: Feb 18, 2016, 10:30-12:00, room: 00.02.001, MI HS 1, Friedrich L. Bauer Hörsaal (5602.EG.001)
exam review: Feb 29, 2016, 12:30-13:15, room 02.07.023
2nd exam: Apr 07, 2016, 11:00-12:30, room MW2050 (moved!)
2nd exam review: Apr 27, 2016, 16:00-17:30, room 02.05.058

Semesterwochenstunden / ECTS Credits

4 SWS (2V+2Ü) / 5 Credits

TUMonline

tba

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Announcements

• the room for the 2nd exam has been moved: It is now MW2050
• The Q&A session takes place on 01.02.2016 (Mon) at 14:00-18:00, room 03.13.010. Send any questions you have to scicomp1_QA@mailsccs.in.tum.de until 28.01.2015 (Thu).
• The tutorial on 23.12.2015 (Wed) is moved to 21.12.2015 (Mon) 16:00-18:00, room 03.13.010.
• Starting from 02.11.2015 the tutorial slot on Monday at 16:00-18:00 is moved to Wednesday 14:00-16:00, room 02.13.008.

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 21	Introduction - CSE/Scientific Computing as a discipline	slides: discipline.pdf, fibo.pdf printing versions: discipline-2x4.pdf, fibo-2x4.pdf
Oct 26	Worksheet 1	Worksheet 1, Solution 1
Nov 2/4	Worksheet 2	Worksheet 2, Solution 2
Nov 4	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 printing version: population-2x4.pdf
Nov 9/11	Worksheet 3	Worksheet 3, Solution 3
Nov 11	Population Models - Continuous Modelling (parts III to IV)	slides: population2.pdf printing version: population2-2x4.pdf
Nov 16/18	Worksheet 4	Worksheet 4, Solution 4, ws4_ex1.py ipython notebook version: W4-Direction_Fields_for_ODE.ipynb
Nov 18	Numerical Methods for ODEs (part I)	slides: ode_numerics.pdf python worksheets: Numerics ODE maple worksheets: numerics_ode.mws, maple_numerics_ode.pdf printing version: ode_numerics-2x4.pdf
Nov 23/25	Worksheet 5	Worksheet 5, Solution 5, ws5_ex1.py
Nov 25	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
Nov 30, Dec 2	Worksheet 6	Worksheet 6, Solution 6, ws6_ex3.py
Dec 2	Heat Transfer - Discrete and Continuous Models	slides: heatmodel.pdf python worksheets: Heat Transfer maple worksheets: poisson2D.mws, poisson2D.pdf printing version: heatmodel-2x4.pdf
Dec 7/9	Worksheet 7	Worksheet 7, Solution 7, ws7_ex1.py visualization of ODE solvers
Dec 9	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 printing version: heateq-2x4.pdf
Dec 14/16	Worksheet 8	Worksheet 8, Solution 8, ws8_ex2.py
Dec 16 Jan 13	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 printing version: pde_fem-2x4.pdf
Dec 21	Worksheet 9	Worksheet 9, Solution 9, ws9_ex2.py
Jan 11/13	Worksheet 10	Worksheet 10, Solution 10
Jan 20	Case Study: Computational Fluid Dynamics	slides: study_cfd.pdf printing version: study_cfd-2x4.pdf
Jan 18/20	Worksheet 11	Worksheet 11, Solution 11, ws11_ex1.py
Jan 25/27	Worksheet 12	Worksheet 12, Solution 12, ws12_ex1.py, ws12_ex2.py

Exams

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

• 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)