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Chair of Applied Mathematics / Numerical Analysis
Bergische Universität Wuppertal
Faculty of Mathematics and Natural Sciences
Gaußstraße 20
D42119 Wuppertal
Germany
Phone: +49 202 439 5296
Fax: (Fax currently unavailable)
EMail: sekamna{at}math.uniwuppertal.de
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Multirate
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. cosimulation). 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, Cosimulation or especially dedicated multirate methods are designed to use the inherent step size to resolve the timedomain behaviour of each subystem with the required accuracy. This requires a timestepping for each.
Group members working in that field
Cooperations
 Herbert de Gersem, K.U. Leuven, Belgium
 Jan ter Maten, TU Eindhoven and NXP, the Netherlands
Publications
24. 
Multiscale Modeling and Multirate TimeIntegration of Field/Circuit Coupled Problems
of Elektrotechnik
Publisher: VDI Verlag, Düsseldorf
2011
ISBN: 9783183398218
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. 
23. 
A cosimulation framework for multirate timeintegration of field/circuit coupled problems
IEEE Transactions on Magnetics,
46:3233  3236
2010

22. 
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 
21. 
Polynomial chaos for multirate partial differential algebraic equations with random parameters
Applied Numerical Mathematics,
59(10):2610  2624
2009

20. 
Waveletbased adaptive grids for multirate partial differentialalgebraic equations
Applied Numerical Mathematics,
59(34):495  506
2009

19. 
Variational methods for solving warped multirate partial differential algebraic equations
SIAM Journal on Scientific Computing,
31(2):1016  1034
2008
DOI: 10.1137/050638886

18. 
Transformation qualities of warped multirate partial differential algebraic equations
In Breitner, M.; Denk, G.; Rentrop, P., editor,
page 27  42.
Publisher: Springer, Berlin
2008

17. 
Waveletcollocation of multirate PDAEs for the simulation of radio frequency circuits
In Jäger, W., editor,
page 19  28.
Publisher: Springer, Berlin
2008

16. 
Multirate partial differential algebraic equations for simulating radio frequency signals
European Journal of Applied Mathematics,
18:709  743
2007

15. 
WaveletBased Simulation of Multirate Partial DifferentialAlgebraic Systems in Radio Frequency Applications
of FortschrittBerichte VDI Reihe 20
Publisher: VDIVerlag, Düsseldorf
2007

14. 
Index analysis of multirate partial differentialalgebraic systems in RFcircuits
In Anile, A. M. and Ali, Guiseppe and Mascali, Giovanni, editor,
Scientific Computing in Electrical Engineering. Mathematics in Industry
, page 93  100.
Publisher: Springer, Berlin
2006

13. 
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
Volume 9
of Mathematics in {I}ndustry
, page 129136.
The {E}uropean {C}onsortium for {M}athematics in {I}ndustry
Publisher: SpringerVerlag, Berlin,
2006
