Inhalt
[ MEMPAKVNUOP ] KV Numerical Analysis and Optimization
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| Es ist eine neuere Version 2022W dieser LV im Curriculum Master's programme Artificial Intelligence 2024W vorhanden. |
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| (*) Unfortunately this information is not available in english. |
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| Workload |
Education level |
Study areas |
Responsible person |
Hours per week |
Coordinating university |
| 5,75 ECTS |
M1 - Master's programme 1. year |
Mathematics |
Ulrich Langer |
4 hpw |
Johannes Kepler University Linz |
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| Detailed information |
| Original study plan |
Master's programme Mechatronics 2015W |
| Objectives |
Get knowledge of concepts and acquirement of techniques for the continuous numerical treatment of relevant mathematical problems, typically appearing with physical and technical problems and of numerical methods for solving systems of optimization problems.
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| Subject |
- Introduction: from the model to the computer simulation, examples, typical problems for Partial Differential Equations (PDEs) and their technical background
- Variation formulation of Boundary Value Problems (BVP) and their discretization by means of the Finite Element Method (FEM)
- Time-dependent problems (Initial Boundary Value Problems (IBVP))
-Methods for solving systems of linear and nonlinear algebraic equations
-Optimization techniques (also in connection with “PDE-constrained” optimization problems)
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| Criteria for evaluation |
The course contains an oral examination.
The final score consists of the mark of the individual exercises (50 %) and of the mark of the oral exam (50 %). You pass the course when you get at least the mark “4” in each part. Please take the 4 exercises with you when you take the oral examination.
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| Language |
German |
| Study material |
The textbook “Methode der Finiten Elemente fuer Ingenieure” is published by Teubner.
[1] J.J.I.M. van Kan, A. Segal: Numerik partieller Differentialgleichungen für Ingenieure. B.G. Teubner Stuttgart 1995.
[2] Douglas C.C., Haase G., Langer U.: A Tutorial on Elliptic PDE Solvers and Their Parallelization. SIAM, Philadelphia 2003. (Parallelisierung numerischer Verfahren)
[3] Kikuchi N.: Finite Element Methods in Mechanics. Cambridge University Press, Cambridge 1986. (zur FEM, mit FE Programmen)
[4] Quarteroni A., Saleri F.: Scientific Computing with MATLAP. Texte in Computational Sciences and Engineering, v. 2, Springer-Verlag, Heidelberg 2003. (Numerische Verfahren mit MATLAB)
[5] Schwetlick H., Kretzschmar H.: Numerische Verfahren für Naturwissenschaftler und Ingeniere. Fachbuchverlag, Leipzig 1991
[6] Törnig W., Gipser M., Kaspar B.: Numerische Lösung von partiellen Differentialgleichungen der Technik. B.G. Teubner, Stuttgart 1991.
[7] Dahmen W., Reusken A.: Numerik für Ingenieure und Naturwissenschaftler. Springer-Verlag, Berlin Heidelberg 2006.
[8] Deuflhard P., Bornemann F.: Numerische Mathematik 2: Gewöhnliche Differentialgleichungen, 3. Auflage de Gruyter Verlag, Berlin, New York 2008. (zur numerischen Lösung von Systemen gewöhnlicher Differentialgleichungen)
[9] Strang G.: Wissenschaftliches Rechnen. Springer-Verlag, Berlin-Heidelberg 2010.
[10] Schwarz H.R.: Numerische Mathematik. B.G. Teubner, Stuttgart 1988.
[11] Geiger C., Kanzow C.: Numerische Verfahren zur Lösung unrestringierter Optimierungsaufgaben. Springer-Verlag, Berlin-Heidelberg 1999.
[12] Geiger C., Kanzow C.: Theorie und Numerik Verfahren restringierter Optimierungsaufgaben. Springer-Verlag, Berlin-Heidelberg 2002.
[13] More, J.J. and Wright, St.: Optimization Software Guide. SIAM, 1993.
[14] Literaturüberblick zur Optimierung: http://plato.asu.edu/sub/tutorials.html
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| Changing subject? |
No |
| Further information |
none
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| Corresponding lecture |
(*)ME3PAVOMAT4: VO Mathematik IV - Numerik (3 ECTS) + ME3PAUEMAT4: UE Mathematik IV - Numerik (1,5 ECTS)
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| On-site course |
| Maximum number of participants |
35 |
| Assignment procedure |
Assignment according to sequence |
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