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Arbeitsgruppe Angewandte Mathematik / Numerische Analysis
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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. 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

Cooperations

Publications

Referenzen
42.
A. Bartel; M. Günther
Inter/extrapolation-based multirate schemes -- a dynamic-iteration perspective
2020

Schlüsselwörter: math.NA, cs.NA, 65L05, 65L80

41.
Chr. Hachtel; A. Bartel; M. Günther; A. Sandu
Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
Journal of Computational and Applied Mathematics, :112499
2019
40.
C. Hachtel; J. Kerler-Back; A. Bartel; M. Günther; T. Stykel
Multirate DAE/ODE-Simulation and Model Order Reduction for Coupled Field-Circuit Systems
Scientific Computing in Electrical Engineering
Seite 91--100.
Herausgeber: Springer International Publishing,
2018
39.
C. Hachtel; M. Günther; A. Bartel
Model Order Reduction for Multirate ODE-Solvers in a Multiphysics Application
Russo, G. and Capasso, V. and Nicosia, G. and Romano, V., Autoren, Progress in Industrial Mathematics at ECMI 2014 Band 22 aus Mathematics in Industry
2017
38.
E. J. W. ter Maten; P. A. Putek; M. Günther; R. Pulch; C. Tischendorf; C. Strohm; W. Schoenmaker; P. Meuris; B. De Smedt; P. Benner; L. Feng; N. Banagaaya; Y. Yue; R. Janssen; J. J. Dohmen; B. Tasić; F. Deleu; R. Gillon; A. Wieers; H.-G. Brachtendorf; K. Bittner; T. Kratochvíl; J. Petřzela; R. Sotner; T. Götthans; J. Dřínovský; S. Schöps; D. J. D. Guerra; T. Casper; H. De Gersem; U. Römer; P. Reynier; P. Barroul; D. Masliah; B. Rousseau
Nanoelectronic COupled problems solutions - nanoCOPS: modelling, multirate, model order reduction, uncertainty quantification, fast fault simulation
Journal of Mathematics in Industry, 7(1)
2016
37.
E. J. W. ter Maten; P. A. Putek; M. Günther; R. Pulch; C. Tischendorf; C. Strohm; W. Schoenmaker; P. Meuris; B. De Smedt; P. Benner; L. Feng; N. Banagaaya; Y. Yue; R. Janssen; J. J. Dohmen; B. Tasić; F. Deleu; R. Gillon; A. Wieers; H.-G. Brachtendorf; K. Bittner; T. Kratochvíl; J. Petřzela; R. Sotner; T. Götthans; J. Dřínovský; S. Schöps; D. J. D. Guerra; T. Casper; H. De Gersem; U. Römer; P. Reynier; P. Barroul; D. Masliah; B. Rousseau
Nanoelectronic COupled problems solutions - nanoCOPS: modelling, multirate, model order reduction, uncertainty quantification, fast fault simulation
Journal of Mathematics in Industry, 7
2016
36.
M. Günther; Chr. Hachtel; A. Sandu
Multirate GARK Schemes for Multiphysics Problems
Scientific Computing in Electrical Engineering
Seite 115--121.
Herausgeber: Springer International Publishing,
2016
35.
C. Hachtel; M. Günther; A. Bartel
Interface Reduction for Multirate ODE-Solvers
Bartel, A. and Clemens, M. and Günther, M. and ter Maten, J., Autoren, Scientific Computing in Electrical Engineering Band 23 aus Mathematics in Industry , Seite 185--193.
Herausgeber: Springer,
2016
34.
Chr. Hachtel; A. Bartel; M. Günther
Interface Reduction for Multirate ODE-Solver
Bartel, A. and Clemens, M. and Günther, M. and ter Maten, E. J. W., Autoren, Scientific Computing in Electrical Engineering at SCEE 2014, Wuppertal, Germany, July 2014
Herausgeber: Springer, Berlin,
2016
33.
M. Günther; A. Sandu
Multirate generalized additive Runge Kutta methods
Numerische Mathematik, 133(3):497--524
2015
32.
D. Shcherbakov; M. Ehrhardt; M. Günther; M. Peardon
Force-gradient nested multirate methods for Hamiltonian systems
Computer Physics Communications, 187:91--97
2015
31.
G. Ali; A. Bartel; M. Günther; V. Romano; S. Schöps
Simulation of Coupled PDAEs: Dynamic Iteration and Multirate Simulation
Mathematics in Industry
Seite 103--156.
Herausgeber: Springer Berlin Heidelberg,
2015
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