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Chair of Applied Mathematics / Numerical Analysis
Bergische Universität Wuppertal
Faculty of Mathematics and Natural Sciences
Gaußstraße 20
D-42119 Wuppertal
Germany

Phone: +49 202 439 5296
Fax: (Fax currently unavailable)
E-Mail: sek-amna{at}math.uni-wuppertal.de

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Coupled DAE Problems

A circuit (DAE model) coupled to a magnetostatic field device (PDE model)

Coupled Problems of differential-algebraic equations (DAEs) arise typically from either multiphysical modeling (e.g. in circuit simulation with heating) or from refined modeling, where crucial parts of the original problem are replaced by a better, but computational more expensive model (e.g. circuits refined by field models). Furthermore splitting methods may turn a monolithic DAE problem into coupled subproblems, e.g. because of different time scales (multirate). In any case the DAEs arise from network approaches or space-discretization of PDAEs (Partial Differential Algebraic Equations).

Often the coupled equations have quite different properties, i.e., symmetries, definiteness or time scales. Thus the coupled system must be analyzed (e.g. the index) and tailored methods have to be developed (e.g. dynamic iteration).

Publications

References
25.
Michael Günther
COMSON- coupled multiscale similation and optimisation in nanoelectronics .
Publisher: Springer,
2014
24.
Christof Kaufmann; G
Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles
In Fontes et al, editor, ECMI2012 proceedings
Publisher: Springer, Berlin
2014
23.
Andreas Bartel; Markus Brunk; Sebastian Schöps
On the convergence rate of dynamic iteration for coupled problems with multiple subsystems
JCAM, :accepted
2013
22.
Andreas Bartel; Markus Brunk; Michael Günther; Sebastian Schöps
Dynamic iteration for coupled problems of electric circuits and distributed devices
SIAM J. Sci. Comput., 35(2):B315-B335
2013
21.
Daniel Heubes; Andreas Bartel; Matthias Ehrhardt
An Introduction to the Lattice Boltzmann Method for Coupled Problems.
In Ehrhardt, Matthias, editor, Volume 3 of Ebook Series
page 3-20.
Publisher: Bentham Science Publishers,
2013
20.
Sebastian Schöps; Herbert De Gersem; Andreas Bartel
Higher-Order Cosimulation of Field/Circuit Coupled Problems
IEEE Trans. on Magnetics, :to appear
2012
19.
Michael Günther
COMSON - a Marie Curie Research Training Network in Coupled Multiscale Simulation and Optimization in Nanoelectronics.
In Günther, Michael, editor,
Publisher: Springer, Heidelberg
2012

Note: in preparation

18.
Matthias Ehrhardt
Coupled Fluid Flow in Energy, Biology and Environmental Research.
In Ehrhardt,Matthias, editor, Volume 2 of Progress in Computational Physics
Publisher: Bentham Science Publishers Ltd,
2012
17.
Matthias Ehrhardt
An Introduction to Fluid-Porous Interface Coupling
In Ehrhardt, Matthias, editor,
Publisher: Bentham Science Publishers Ltd,
2012
16.
Matthias Ehrhardt
An Introduction to Fluid-Porous Interface Coupling
In M.Ehrhardt, editor, Coupled Fluid Flow in Energy, Biology and Environmental Research, Progress in Computational Physics Volume 2
Publisher: Bentham Science Publishers Ltd,
2012
15.
Markus Brunk; Ansgar Jüngel
Self-heating in a coupled thermo-electric circuit-device model
Journal of Computational Electronics, 10(1-2):163-178
June 2011
14.
Sebastian Schöps
Multiscale Modeling and Multirate Time-Integration of Field/Circuit Coupled Problems
of Elektrotechnik
Publisher: VDI Verlag, Düsseldorf
2011
ISBN: 978-3-18-339821-8

Abstract: This treatise is intended for mathematicians and computational engineers that work on modeling, coupling and simulation of electromagnetic problems. This includes lumped electric networks, magnetoquasistatic field and semiconductor devices. Their coupling yields a multiscale system of partial differential algebraic equations containing device models of any dimension interconnected by the electric network. It is solved in time domain by multirate techniques that efficiently exploit the structure. The central idea is the usage of lumped surrogate models that describe latent model parts sufficiently accurate (e.g. the field model by an inductance) even if other model parts (e.g. the circuit) exhibit highly dynamic behavior. We propose dynamic iteration and a bypassing technique using surrogate Schur complements. A mathematical convergence analysis is given and numerical examples are discussed. They show a clear reduction in the computational costs compared to single rate approaches.

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