Chair of Applied Mathematics / Numerical Analysis
Bergische Universität Wuppertal
Faculty of Mathematics and Natural Sciences
Phone: +49 202 439 5296
Fax: +49 (0) 202 439 5201
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.
Multirate ROW-Methods of Mixed Type for Circuit Simulation
van Rienen, U. and Günther, M. and Hecht, D., editor, Scientic Computing in Electrical Engineering, Lecture Notes in Computational Science and Engineering , page 241--249.
Multirate Methods in Electrical Circuit Simulation
Anile, A. M. and Capasso, V. and Greco, A., editor, Progress in Industrial Mathematics at ECMI 2000 of Mathematics in Industry 1 , page 258--265.
Generalised Multirate --- Two ROW-type Versions for Circuit simulation
Unclas- sified NatLab Report No. 2000/804
Publisher: Philips Electronics,
Partitioning and multirate strategies in latent electric circuits
Bank, R. E. and et al., editor, Mathematical modelling and simulation of electrical circuits and semiconductor devices
Publisher: Basel, Birkhäuser,
Multirate ROW methods and latency of electric circuitsAppl.~Numer.~Math., 13:83--102
Multirate Rosenbrock-Wanner Verfahren zur Integration von elektrischen Schaltkreisen
Technische Universität at München,