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Arbeitsgruppe Angewandte Mathematik / Numerische Analysis
Bergische Universität Wuppertal
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Model Order Reduction

Model Order Reduction (MOR) is the art of reducing a system's complexity while preserving its input-output behavior as much as possible.

Processes in all fields of todays technological world, like physics, chemistry and electronics, but also in finance, are very often described by dynamical systems. With the help of these dynamical systems, computer simulations, i.e. virtual experiments, are carried out. In this way, new products can be designed without having to build costly prototyps.

Due to the demand of more and more realistic simulations, the dynamical systems, i.e., the mathematical models, have to reflect more and more details of the real world problem. By this, the models' dimensions are increasing and simulations can often be carried out at high computational cost only.

In the design process, however, results are needed quickly. In circuit design, e.g., structures may need to be changed or parameters may need to be altered, in order to satisfy design rules or meet the prescribed performance. One cannot afford idle time, waiting for long simulation runs to be ready.

Model Order Reduction allows to speed up simulations in cases where one is not interested in all details of a system but merely in its input-output behavior. That means, considering a system, one may ask:

  • How do varying parameters influence certain performances ?
    Using the example of circuit design: How do widths and lengths of transistor channels, e.g., influence the voltage gain of a circuit.
  • Is a system stable?
    Using the example of circuit design: In which frequency range, e.g., of voltage sources, does the circuit perform as expected
  • How do coupled subproblems interact?
    Using the example of circuit design: How are signals applied at input-terminals translated to output-pins?

Classical situations in circuit design, where one does not need to know internals of blocks are optimization of design parameters (widths, lengths, ...) and post layout simulations and full system verifications. In the latter two cases, systems of coupled models are considered. In post layout simulations one has to deal with artificial, parasitic circuits, describing wiring effects.

Model Order Reduction automatically captures the essential features of a structure, omitting information which are not decisive for the answer to the above questions. Model Order reduction replaces in this way a dynamical system with another dynamical system producing (almost) the same output, given the same input with less internal states.

MOR replaces high dimensional (e.g. millions of degrees of freedom) with low dimensional (e.g. a hundred of degrees of freedom ) problems, that are then used instead in the numerical simulation.

The working group "Applied Mathematics/Numerical Analysis" has gathered expertise in MOR, especially in circuit design. Within the EU-Marie Curie Initial Training Network COMSON, attention was concentrated on MOR for Differential Algebraic Equations. Members that have been working on MOR in the EU-Marie Curie Transfer of Knowledge project O-MOORE-NICE! gathered knowledge especially in the still immature field of MOR for nonlinear problems.

Current research topics include:

  • MOR for nonlinear, parameterized problems
  • structure preserving MOR
  • MOR for Differential Algebraic Equations
  • MOR in financial applications, i.e., option prizing

Group members working on that field

Publications

Referenzen
31.
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
30.
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
29.
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
28.
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
27.
K. Mohaghegh; R. Pulch; J. ter Maten
Model order reduction using singularly perturbed systems
Appl. Numer. Math., 103:72--87
2016
26.
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
25.
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
24.
R. Pulch; E. J. W. ter Maten; F. Augustin
Sensitivity analysis and model order reduction for random linear dynamical systems
Math. Comput. Simul., 111:80--95
2015
23.
R. Pulch; E. J. W. ter Maten
Stochastic Galerkin methods and model order reduction for linear dynamical systems
International Journal for Uncertainty Quantification, 5(3):255--273
2015
22.
A. C. Antoulas; R. Ionutiu; N. Martins; E. J. W. ter Maten; K. Mohaghegh; R. Pulch; J. Rommes; M. Saadvandi; M. Striebel
Model Order Reduction: Methods, Concepts and Properties
Günther, M., Autoren, Coupled Multiscale Simulation and Optimization in Nanoelectronics Band 21 aus Mathematics in Industry
Kapitel 4, Seite 159--265.
Herausgeber: Springer Berlin Heidelberg,
2015
21.
M. Striebel; E. J. W. ter Maten; K. Mohaghegh; R. Pulch
Circuit simulation and model order reduction
Günther, M., Autoren, Coupled Multiscale Simulation and Optimization in Nanoelectronics Band 21 aus Mathematics in Industry
Kapitel 4.1, Seite 163--192 and 257--260.
Herausgeber: Springer,
2015
20.
G. Ciuprina; J. F. Villena; D. Ioan; Z. Ilievski; S. Kula; E. J. W. ter Maten; K. Mohaghegh; R. Pulch; W. H. A. Schilders; L. M. Silveira; A. Ştefănescu; M. Striebel
Parameterized Model Order Reduction
Günther, M., Autoren, Coupled Multiscale Simulation and Optimization in Nanoelectronics Band 21 aus Mathematics in Industry
Kapitel 5, Seite 267--359.
Herausgeber: Springer Berlin Heidelberg,
2015
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