Research Group Numerical Mathematics (Partial Differential Equations)






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Research Group Numerical Mathematics
(Partial Differential Equations)

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Prof. Dr. Roland Herzog [ Contact ]

Optimal Control of Partial Differential Equations (4V, 2Ü)

Contents

Partial differential equations (PDEs) describe a countless number of phenomena in the natural sciences, such as heat conduction, the propagation of sound and electromagnetic waves the motion of fluids and the behavior of quantum physical particles. Besides the numerical simulation of such processes, one is often interested in their optimization, e.g., for economical reasons, or in order to improve material qualities. This leads to optimization and optimal control problems for PDEs.

Goals of this class

In this class you will
  • get to know some basic examples of optimal control problems with PDEs,
  • learn about necessary and sufficient optimality conditions (as a starting point for numerical solution schemes),
  • learn to use numerical methods for the solution of optimal control problems.
This class complements well the following other classes: This class can serve as a preparatory step towards a thesis in the work group Numerical Mathematics (Partial Differential Equations).

You may also consider the list of all classes for additional information.

This class can serve as a research module in numerical mathematics (large) or as a research module in optimization (large).

News

28.07.2010 Die Liste typischer Prüfungsfragen wurde aktualisiert und enthält nun auch Fragen zum §15: A-priori-Fehlerabschätzungen.
13.07.2010 Hinweis auf Lehrveranstaltungen des WS2010/11: Ausgewählte Kapitel der FEM (Vertretungsprofessor Dr. Egger), Optimale Steuerung partieller Differentialgleichungen II
08.07.2010 Dr. Roman Unger bietet vom 04.-08.10.2010 einen Matlab-Kurs an. Interessenten melden sich bitte direkt bei ihm.
16.06.2010 Es werden ab sofort Prüfungstermine vergeben.

Dates

Class Wednesday 11:30 - 13:00 (3. LE) 2/B202 Roland Herzog Office hours: Monday, 12:30 - 13:45 and by appointment
Class Thursday 7:30 - 9:00 (1. LE) 2/B202 Roland Herzog
Tutorial Monday 7:30 - 9:00 (1. LE) 2/B202 Gerd Wachsmuth Office hours: by appointment

Additional lecture material

Tutorials

Additional tutorial material

Exam

There will be oral examinations for participants who would like to acquire a "Fachprüfung" (subject examination) or a "Schein mit Note" (certificate with mark). (A list of typical questions may help you to prepare for the exam.) For participants who would like a "Schein ohne Note" (certificate without mark) it is sufficient to hand in at least 10 successfully processed homework problems (out of a total of 14 problem sheets). Prüfungstermine sind an folgenden Tagen erhältlich:
  • Donnerstag, 29.07.2010
  • Mittwoch, 25.08.2010
  • Donerstag, 30.09.2010
Termine werden ab sofort über das Sekretariat (Anne-Kristin Glanzberg, Reichenhainer Str. 41, Zimmer 615) vergeben.

Supplementary References

The lecture follows the book (in German) In addition, you may want to consider a book about functional analysis, e.g., For auxiliary results we will sometimes refer to the following books:

Matlab-Einführungen

Es wird empfohlen, dass Sie sich mit den Grundlagen von Matlab vertraut machen (nicht nur für diese Lehrveranstaltung).