Scientific Computing I - Winter 14

Term

Winter 14

Lecturer

Dr. rer. nat. Tobias Neckel

Time and Place

Wednesday, 10:15-11:45; Interims Hörsaal 2 (5620.01.102), (starts Oct 15)

Audience

Computational Science and Engineering, 1st semester

Tutorials

Denis Jarema, time and place: I group: Monday, 16-18, MI 03.13.010, II group: Monday, 14-16, MI 03.13.010 (starts Oct 20)

Exam

written exam Jan 30, 2015, 16:30-18:00, room: Interimshörsaal 1

Semesterwochenstunden / ECTS Credits

4 SWS (2V+2Ü) / 5 Credits

TUMonline

tumonline lecture, tumonline tutorial

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Announcements

• The repetition exam review will take place on Thursday, April 16, 16:15-17:30, in room 02.07.023.
• The repetition exam will take place on Wednesday, April 8, 14:30-16:00, in MI Hörsaal 3 (00.06.011, 5606.EG.011), 1 handwritten DinA4 page (both sides) is the only allowed aid.
• The exam review will take place on Friday, February 13, 10:00-11:00, in room 02.07.023.
• The exam will take place on Friday, January 30, 16:30-18:00, in Interims Hörsaal 1 (5620.01.101), 1 handwritten DinA4 page (both sides) is the only allowed aid.
• The tutorial does not take place on the 22nd of December.
• The lecture does not take place on the 22nd of October due to the plenary meeting of the student's union.

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 15	Introduction - CSE/Scientific Computing as a discipline	slides: discipline.pdf, fibo.pdf printing versions: discipline-2x4.pdf, fibo-2x4.pdf
Oct 20	Worksheet 1 (for the lecture on Oct 15)	Worksheet 1, Solution 1
Oct 27	Worksheet 2 (for the lecture on Oct 15)	Worksheet 2, Solution 2
Oct 29	Population Models - Continuous Modelling (Parts I to IV)	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 3	Worksheet 3 (for the lecture on Oct 29)	Worksheet 3, Solution 3
Nov 5	Population Models - Continuous Modelling (Parts I to IV)	slides: population2.pdf printing version: population2-2x4.pdf
Nov 10	Worksheet 4 (for the lecture on Nov 5)	Worksheet 4, Solution 4, ws4_ex1.py
Nov 12 Nov 18	Numerical Methods for ODEs	slides: ode_numerics.pdf python worksheets: Numerics ODE maple worksheets: numerics_ode.mws, maple_numerics_ode.pdf printing version: ode_numerics-2x4.pdf
Nov 17	Worksheet 5 (for the lecture on Nov 12)	Worksheet 5, Solution 5, ws5_ex1.py
Nov 24	Worksheet 6 (for the lecture on Nov 18)	Worksheet 6, Solution 6, ws6_ex3.py
Nov 26	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 1	Worksheet 7 (for the lecture on Nov 18)	Worksheet 7, Solution 7, ws7_ex1.py
Dec 3	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 8	Worksheet 8 (for the lecture on Nov 26)	Worksheet 8, Solution 8, ws8_ex2.py
Dec 10 Jan 7	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 15	Worksheet 9 (for the lecture on Dec 3)	Worksheet 9, Solution 9, ws9_ex2.py
Jan 12	Worksheet 10 (for the lectures on Dec 10 and Jan 7)	Worksheet 10, Solution 10
Jan 14 Jan 21	Case Study: Computational Fluid Dynamics	slides: study_cfd.pdf printing version: study_cfd-2x4.pdf
Jan 19	Worksheet 11 (for the lecture on Dec 10 and Jan 7)	Worksheet 11, Solution 11, ws11_ex1.py
Jan 26	Worksheet 12 (for the lecture on Dec 10 and Jan 7)	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)