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K. Rouzbeh:
"Modellierung und Behandlung von Zustandsereignissen in der Systemsimulation - Alternative Methoden, Vergleich und Benchmarks";
Supervisor, Reviewer: F. Breitenecker, A. Körner, H. Ecker; Institut für Analysis und Scientific Computing, 2016; oral examination: 2016-06-22.

This thesis deals with analysis, comparison and some further developments of methods for state event determination in hybrid and variable-structure systems - from view of
mathematics, and from view of case studies in mechatronics.
The thesis first reviews `classical´ methods for state event location, where a zero search for the event superimposes the ODE solver.
In the following the author concentrates on generic methods for state event location, which integrate the zero search into the ODE solver algorithm. Here, the approximation of the state vector at an event is based on the step-size calculation until the event, using a reformulation of the ODE solver. A `direct´ approach reformulates an explicit ODE solver by integration of the zero search for the step-size until the event, resulting in an `extended´ zero
search, an implicit algorithm. The thesis therefore concentrates on an `implicit´ generic approach, which integrates the zero search onto an implicit ODE solver. This strategy modifies the zero search for the implicit solver algorithm appropriately by integration the zero search for the step-size until the event.
The theoretical part of the thesis continues with event location in DAE systems. For hybrid systems, described by semi-explicit DAEs, the author presents an extended strategy:
the zero search for the step-size until the event is implemented into the multidimensional zero search for the algebraic states and for the system states. This method can also be used for
fully-implicit systems, after index reduction of the system.
The last part of the theoretical part of the thesis analyses an alternative method for state event location, the Henon method. There, independent variable and one dependent
variable are `exchanged´, so that no zero search for the event location is necessary, but the system becomes (much) more complicated.
The practical part of the theses analyses the compared and developed strategies for event location with three case studies from mechatronics: bouncing ball (hybrid ODE system), filament pendulum (DAE system with variable structure), and rotor - stator dynamics (hybrid DAE system).