Geometric integration and discrete-time port-Hamiltonian systems

Abstract: The interest of this talk is to show possibilities to preserve “structure” when continuous-time port-Hamiltonian (PH) models are translated via numerical integration to the discrete-time domain. On the example of a simple (mechanical) Hamiltonian system with one degree of freedom, we first illustrate symplecticity, i.e., area preservation in the phase plane, of the flow as an underlying structural property, from which energy conservation is derived. Consequently, we give examples for numerical integration schemes that are symplectic or energy-conserving.

Both families of integrators can be used for the definition of discrete-time PH systems, where the definitions of discrete-time port variables play a fundamental role to describe energy transfer over the system boundary. We highlight similarities and differences using the two paths, in particular based on the discrete-time energy balance equations.

Finally, we give two examples from our recent research, where discrete-time models of geometrically nonlinear systems – elastic continua and beams – are obtained with structure-preserving methods.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

( slides | video )

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Port-Hamiltonian Seminar

Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY

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