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
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, |
| 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: |
| Dec 4/6 | Worksheet 5 | Worksheet 5,
Solution 5, ws5_ex1.py |
| 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, |
| 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,
|
| 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.
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)