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
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,
|
| 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.
- 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)