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

Telefon: +49 202 439 5296
Fax: +49 202 439 5201
E-Mail: sek-amna{at}


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Electric Networks

From the fully automatic coffee machine to the central processing units, electronic circuits and computer chips enhance the quality of our daily life. Since these circuits consist of millions of network elements, like resistors, capacitors, inductors and transistors, chip design relies strongly on circuit simulation. The computed electric behavior is used by the designer to rate and validate new developements before production.

Miniaturization of single elements and ultra high integration is the ongoing trend to enhance the performance of all electronic devices. It leads to smaller devices driven by higher frequencies and smaller signals and overall it leads from micro- to nanotechnolgy.

In turn, modern circuit simulators have to face several challenges: higher packing densities result in larger systems with increased power density, and smaller signals result in larger noise/signal ratio and thus stronger influence of parasitic effects, which could have been neglected before.

This leads to our ongoing research in the field of circuit simulation:

Former and ongoing projects



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
Sebastian Schöps; Herbert De Gersem; Andreas Bartel
Higher-Order Cosimulation of Field/Circuit Coupled Problems
IEEE Trans. on Magnetics, :to appear
Markus Brunk; Ansgar Jüngel
Self-heating in a coupled thermo-electric circuit-device model
Journal of Computational Electronics, 10(1-2):163-178
Juni 2011
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.

Guiseppe Ali; Andreas Bartel; Markus Brunk; Sebastian Schöps
A convergent iteration scheme for semiconductor/circuit coupled problems
Scientific Computing in Electrical Engineering SCEE 2010
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
Guiseppe Ali; Andreas Bartel; Michael Günther
Existence and uniqueness for an elliptic PDAE model of integrated circuits
SIAM Journal on Applied Mathamatics, 70:1587 -- 1610
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

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

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
Markus Brunk; Ansgar Jüngel
Heating of semiconductor devices in electric circuits
Roos, Janne and Costa, L., Autoren, Scientific Computing in Electrical Engineering - SCEE 2008. Band 14 aus Mathematics in Industry , Seite 261--272.
Herausgeber: Springer, Berlin
Guiseppe Ali; Giovanni Mascali; Roland Pulch
Hyperbolic {PDAE}s for semiconductor devices coupled with circuits
Roos, Janne and Costa, L., Autoren, Scientific Computing in Electrical Engineering. Mathematics in Industry aus 14 , Seite 305--312.
Herausgeber: Springer, Berlin
Markus Brunk; Ansgar Jüngel
Numerical Coupling of Electric Circuit Equations and Energy-Transport Models for Semiconductors
SIAM Journal on Scientific Computing, 30:873 - 894
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