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Discrete Transparent Boundary Conditions for Parabolic Systems

Please always quote using this URN:urn:nbn:de:0296-matheon-2329
  • In this work we construct and analyse transparent boundary conditions (TBCs) for general systems of parabolic equations. These TBCs are constructed for the fully discrete scheme (-method, finite differences), in order to maintain unconditional stability of the scheme and to avoid numerical re ections. The discrete transparent boundary conditions (DTBCs) are discrete convolutions in time and are constructed using the solution of the Z{transformed exterior problem. We will analyse the numerical error of these convolution coefficients caused by the inverse Z{transformation. Since the DTBCs are non{local in time and thus very costly to evaluate, we present approximate DTBCs of a sum{of{exponentials form that allow for a fast calculation of the boundary terms. Finally, we will use our approximate DTBCs for an example of a uid stochastic Petri net and present numerical results.

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Metadaten
Author:Andrea Zisowsky, Matthias Ehrhardt
URN:urn:nbn:de:0296-matheon-2329
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2005/09/03
Release Date:2005/09/03
Institute:Technische Universität Berlin
Preprint Number:225
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