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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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Runge-Kutta-Chebychev Method for Electro-Magnetic-Simulations

Elektromagnetische Felder bestimmen zum Beispiel das Verhalten von Transformatoren. Aufgrund des nichtlinearen Materialverhaltens (z.B. in einem Eisenkern) werdensolche Geräte im Zeitbereich simuliert. Man verwendet üblicherweise implizite Zeitintegrationsverfahren, siehe Vorlesung zur Numerik von gewöhnlichen Differentialgleichungen. Die Probleme sind steif und unterliegen damit Stabilitätsbeschränkungen bei expliziter Verfahren (d.h. kleine Zeitschrittweiten). Runge-Kutta-Chebychev Methoden (RKC) sind spezielle explizite Einschrittverfahren, deren Stabilitätsgebiet dynamisch angepasst werden kann.

Kommende Computer-Architekturen werden durch zunehmende Anzahl von Prozessorkernen bei gleichzeitighohen Kommunikationkosten voraussichtlich einen Paradigmenwechsel in der Numerik einleiten: es ist zuerwarten, dass daher explizite Verfahren zunehmend attraktiver werden. Genau an dieser Schnittstelle könnten die RKC-Verfahren zu einem Durchbruch der expliziten Verfahren führen.

Verwandte Publikationen

References
12.
Timo Hülsmann; Andreas Bartel; Sebastian Schöps; Herbert De Gersem
Extended Brauer Model for Ferromagnetic mmaterial: Analysis & Computation
SCEE 2012 Proceedings, :accepted
2013
11.
Andreas Bartel; Herbert De Gersem; Timo Hülsmann; U. Römer; Sebastian Schöps; T. Weiland
Quantification of Uncertainty in the Field Quality of Magnets Originating from Material Measurements
IEEE Trans. on Magnetics, 49(5):2367-2370
2013
10.
Andreas Bartel; Markus Brunk; Sebastian Schöps
On the convergence rate of dynamic iteration for coupled problems with multiple subsystems
JCAM, :accepted
2013
9.
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
8.
Sebastian Schöps; Herbert De Gersem; Andreas Bartel
Higher-Order Cosimulation of Field/Circuit Coupled Problems
IEEE Trans. on Magnetics, :to appear
2012
7.
Sebastian Schöps; Andreas Bartel; Markus Clemens
Higher Order Half-Explicit Time Integration of Eddy Current Problems Using domain substructuring
IEEE Trans. on Magnetics, :to appear
2012
6.
Markus Clemens; Sebastian Schöps; Herbert De Gersem; Andreas Bartel
Decomposition and Regularization of Nonlinear Anisotropic Curl-Curl DAEs
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 30(6):1701 - 1714
2011
5.
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.

4.
Guiseppe Ali; Andreas Bartel; Markus Brunk; Sebastian Schöps
A convergent iteration scheme for semiconductor/circuit coupled problems
Scientific Computing in Electrical Engineering SCEE 2010
2011
3.
Sebastian Schöps; Herbert De Gersem; Andreas Bartel
A co-simulation framework for multirate time-integration of field/circuit coupled problems
IEEE Transactions on Magnetics, 46:3233 -- 3236
2010
2.
Sebastian Schöps; Andreas Bartel; Herbert De Gersem
Multirate Time Integration of Field/Circuit Coupled Problems by {S}chur Complements
Scientific Computing in Electrical Engineering SCEE 2010
2010

Keywords: Circuit, Coupling, DAE, FEM, Field, FIT, Multirate, Waveform Relaxation

1.
Sebastian Schöps; Andreas Bartel; Herbert De Gersem; Michael Günther
DAE-index and convergence analysis of lumped electric circuits refined by 3-D magnetoquasistatic conductor models
In Roos, Janne and Costa, L., editor, Scientific Computing in Electrical Engineering. Mathematics in Industry of 14 , page 341-- 348.
Publisher: Springer, Berlin
2010
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