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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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Highly integrated electric cicuits show a phenomenon called latency. That is, a processed signal causes activity only in a small subset of the whole circuit (imagine a central processing unit), whereas the other part of the system behaves almost constant over some time - is latent. Such an electric system can be described as coupled system, where the waveforms show different time scales, also refered to as multirate.

More generally, any coupled problem formulation due to coupled physical effects, may cause a multirate problem: image the simulation of car driving on the road, there you need a model for the wheel, the chassis, the dampers, the road,... (cf. co-simulation). Again each system is covered by their own time constant, which might vary over several orders of magnitude comparing different subsystems.

Classical methods cannot exploit this multirate potential, but resolve everything on the finest scale. This causes an over sampling of the latent components. In constrast, Co-simulation or especially dedicated multirate methods are designed to use the inherent step size to resolve the time-domain behaviour of each subystem with the required accuracy. This requires a time-stepping for each.

Group members working in that field

Former and ongoing Projects



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
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

Roland Pulch
Polynomial chaos for multirate partial differential algebraic equations with random parameters
Applied Numerical Mathematics, 59(10):2610 -- 2624
Andreas Bartel; Stephanie Knorr; Roland Pulch
Wavelet-based adaptive grids for multirate partial differential-algebraic equations
Applied Numerical Mathematics, 59(3--4):495 -- 506
Roland Pulch
Variational methods for solving warped multirate partial differential algebraic equations
SIAM Journal on Scientific Computing, 31(2):1016 -- 1034
Roland Pulch
Transformation qualities of warped multirate partial differential algebraic equations
In Breitner, M.; Denk, G.; Rentrop, P., Editor,
Seite 27 -- 42.
Herausgeber: Springer, Berlin
Stephanie Knorr; Roland Pulch; Michael Günther
Wavelet-collocation of multirate PDAEs for the simulation of radio frequency circuits
In Jäger, W., Editor,
Seite 19 -- 28.
Herausgeber: Springer, Berlin
Roland Pulch; Michael Günther; Stephanie Knorr
Multirate partial differential algebraic equations for simulating radio frequency signals
European Journal of Applied Mathematics, 18:709 -- 743
Stephanie Knorr
Wavelet-Based Simulation of Multirate Partial Differential-Algebraic Systems in Radio Frequency Applications
aus Fortschritt-Berichte VDI Reihe 20
Herausgeber: VDI-Verlag, Düsseldorf
Stephanie Knorr; Michael Günther
Index analysis of multirate partial differential-algebraic systems in RF-circuits
In Anile, A. M. and Ali, Guiseppe and Mascali, Giovanni, Editor, Scientific Computing in Electrical Engineering. Mathematics in Industry , Seite 93 -- 100.
Herausgeber: Springer, Berlin
Michael Striebel; Michael Günther
Multirate {M}ethods in {C}hip {D}esign: {I}nterface {T}reatment and {M}ulti {D}omain {E}xtensions
In Anile, A. M. and Ali, Guiseppe and Mascali, Giovanni, Editor, Scientific {C}omputing in {E}lectrical {E}ngineering {SCEE} 2004 Band 9 aus Mathematics in {I}ndustry , Seite 129--136.
The {E}uropean {C}onsortium for {M}athematics in {I}ndustry
Herausgeber: Springer-Verlag, Berlin,
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