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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Partial differential-algebraic equations for refined network modelling and simulation
by
Michael Guenther
Centre for Scientific Computing and Mathematical Modelling, Technical University Karlsruhe, Germany

In electrical circuits design, a refined generalized network approach is used to describe secondary and parasitic effects of interconnected networks. This modelling ansatz yields initial-boundary value problems of mixed partial-differential and differential-algebraic equations (PDAEs). The analysis of this coupled system is based on both PDE- and DAE-techniques, a-priori energy estimates and perturbation index, and leads to an interpretation as an extended saddle-point problem of implicit type. If the network fulfils some topological conditions, this system is well-posed and has perturbation index 1 only: the solution of a slightly perturbed system does not depend on derivatives of the perturbations.

As method-of-lines applications are often used to embed PDAE models into time-domain network analysis packages, it is reasonable to demand that the analytical properties of the approximate DAE system obtained after semidiscretization are consistent with the original PDAE system. Especially, both should show the same sensitivity with respect to initial and boundary data.

http://www.mathematik.uni-karlsruhe.de/~iwrmm/Persons/Guenther/Welcome.html

Date received: December 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-09.