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Arbeitsgruppe Angewandte Mathematik / Numerische Analysis
Bergische Universität Wuppertal
Fakultät 04
Gaußstraße 20
D-42119 Wuppertal

Telefon: +49 202 439 5296
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E-Mail: sek-amna{at}


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Computational Magnetics

Many electro-technical devices such as e.g. printed circuit boards, electrical drives and antenna systems can be simulated on the basis of electrical circuits. However, the increasing frequencies and the decreasing size force designers to account for wave propagation effects, eddy-current effects, ferromagnetic saturation and hysteresis. For wave propagation effects and eddy-current effects, the results of stand-alone field simulation can be represented by an order-reduced equivalent model, which is then inserted in the overall circuit model. The representation of field-dependent nonlinearities and hysteresis effects, however, is not straightforward.

2D Simulation of a Transformer
2D Simulation of a Transformer

The coupled field and circuit simulation becomes troublesome when a large number of time steps is required. This occurs when e.g. simulating an electrical drive where the machine requires 10 periods of 50 Hz to reach nominal speed whereas the switching of the Insulated Gate Bipolar Transistors in the frequency converter switches at 20 kHz, necessitating a time steps in the order of a microsecond to be used in the simulation. Since the field model consists typically of a few million degrees of freedom, all those unknowns have to be solved in every time step. Fortunately, the relevant time constants in electrical-energy converter are in the range 50 Hz. Hence the field model does not have to be time-stepped at the same rate as the circuit model, in which fast switches are present. The use of adaptive multirate time-integration schemes can reduce the numerical complexity of the problem substantially.

Research Questions


Former and ongoing projects


Christof Kaufmann; G
Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles
Fontes et al, Autoren, ECMI2012 proceedings
Herausgeber: Springer, Berlin
Timo Hülsmann; Andreas Bartel; Sebastian Schöps; Herbert De Gersem
Extended Brauer Model for Ferromagnetic mmaterial: Analysis & Computation
SCEE 2012 Proceedings, :accepted
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
Sebastian Schöps; Herbert De Gersem; Andreas Bartel
Higher-Order Cosimulation of Field/Circuit Coupled Problems
IEEE Trans. on Magnetics, :to appear
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
Sebastian Schöps
Multiscale Modeling and Multirate Time-Integration of Field/Circuit Coupled Problems
aus Elektrotechnik
Herausgeber: VDI Verlag, Düsseldorf
ISBN: 978-3-18-339821-8

Zusammenfassung: 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.

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
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
Roos, Janne and Costa, L., Autoren, Scientific Computing in Electrical Engineering. Mathematics in Industry aus 14 , Seite 341-- 348.
Herausgeber: Springer, Berlin
Michael Günther; Uwe Feldmann; E. Jan W. ter Maten
Modeling and discretization of circuit problems
Schilders, W. H. A. and ter Maten, E. Jan W., Autoren,
Seite 523 -- 659.
Herausgeber: Elsevier North Holland, Amsterdam
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