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A. Schirrer, S. Jakubek:
"Optimization-based formulations of absorbing boundary conditions in discrete-time wave propagation problems";
Vortrag: 19. Steirisches Seminar über Regelungstechnik und Prozessautomatisierung, Retzhof (eingeladen); 07.09.2015 - 09.09.2015; in: "19. Steirisches Seminar über Regelungstechnik und Prozessautomatisierung", (2015).

This contribution discusses two optimization-based methods to generate practical
and effcient absorbing boundaries for discrete-time wave propagation problems.
Absorbing boundary formulations are desirable when problems given on
large or infinite domains should only be studied locally at confined regions of
interest, such as the near-field solution in acoustic problems or local interaction
effects near contact points in catenaries or cable dynamics. We consider timediscrete
approximations of the solution represented by explicit time-marching
schemes.
One proposed method generates absorbing boundary conditions by direct optimization
of the coeffcients of the boundary stencil in a finite-difference discretization,
such that the re
ection coefficient is optimized. Stability criteria
are considered to obtain optimal and stable boundary conditions. The second
proposed method shown is inspired by the \perfectly matched layer" (PML).
The PML's absorption properties are emulated by a suitable optimal boundary
control law. High absorption performance even on badly conditioned discretization
grids is achieved with high computational efficiency. Additionally, it
allows the controlled modification of impedance in the boundary region, which is
not realizable with other concepts such as traditional absorbing boundary conditions.
The proposed methods are widely applicable for linear system dynamics having
wave propagation and lead to simple and computationally efficient model
structures with the desired absorbing properties. These features are crucial in
problems with real-time requirements, e.g. when creating design models of online
model predictive control. One current industrial application for these models are
real-time control tasks related to railway pantograph/catenary interaction.