Oberwolfach Preprints (OWP)

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Browsing Oberwolfach Preprints (OWP) by Author "Altmann, Robert"

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    Simulation of multibody systems with servo constraints through optimal control
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2015) Altmann, Robert; Heiland, Jan
    We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path. Modelling the system using Newton's second law { \The force acting on an object is equal to the mass of that object times its acceleration.\ { and enforcing the servo constraints directly leads to dierential-algebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5 which already poses high regularity conditions. Also, common approaches for the numerical time-integration will likely fail. If one relaxes the servo constraints and considers the system from an optimal control point of view, the strong regularity conditions vanish and the solution can be obtained by standard techniques. By means of a spring-mass system, we illustrate the theoretical and expected numerical diculties. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization.
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    Time Discretization Schemes for Hyperbolic Systems on Networks by ε-Expansion
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2019) Altmann, Robert; Zimmer, Christoph
    We consider partial differential equations on networks with a small parameter ϵ, which are hyperbolic for ϵ>0 and parabolic for ϵ=0. With a combination of an ϵ-expansion and Runge-Kutta schemes for constrained systems of parabolic type, we derive a new class of time discretization schemes for hyperbolic systems on networks, which are constrained due to interconnection conditions. For the analysis we consider the coupled system equations as partial differential-algebraic equations based on the variational formulation of the problem. We discuss well-posedness of the resulting systems and estimate the error caused by the ϵ-expansion.