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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
7.
K. Mohaghegh; R. Pulch; M. Striebel; J. ter Maten
Model order reduction for semi-explicit systems of differential algebraic systems
Troch, I. and Breitenecker, F., Autoren, Proceedings MATHMOD 09 Vienna - Full Papers CD Volume , Seite 1256-1265.
2009
6.
T. Bechtold; M. Striebel; K. Mohaghegh; E. J. W. ter Maten
Nonlinear Model Order Reduction in Nanoelectronics: Combination of POD and TPWL
PAMM, 8(1):10057--10060
2008
5.
Th. Voss; A. Verhoeven; T. Bechtold; J. ter Maten
Model Order Reduction for Nonlinear Differential Algebraic Equations in Circuit Simulation
Bonilla, L. L. and Moscoso, M. and Platero, G. and Vega, J. M., Autoren, Progress in Industrial Mathematics at ECMI 2006 Band 12 aus Mathematics in Industry
Seite 518--523.
Herausgeber: Springer Berlin Heidelberg,
2008
4.
A. Verhoeven; T. Voss; P. Astrid; E. J. W. ter Maten; T. Bechtold
Model order reduction for nonlinear problems in circuit simulation
PAMM, 7(1):1021603--1021604
2007
3.
A. J. Vollebregt; T. Bechtold; A. Verhoeven; E. J. W. ter Maten
Model Order Reduction of Large Scale ODE Systems: MOR for ANSYS versus ROM Workbench
Ciuprina, G. and Ioan, D., Autoren, Scientific Computing in Electrical Engineering at SCEE 2006 Band 11 aus Mathematics in Industry
Seite 175--182.
Herausgeber: Springer Berlin Heidelberg,
2007
2.
T. Bechtold; A. Verhoeven; E. J. W. ter Maten; T. Voss
Model order reduction: and advanced, efficient and automated computational tool for microsystems
Cutello, V. and Fotia, G. and Puccio, L., Autoren, Applied and Industrial Mathematics in Italy II, Selected contributions from the 8th SIMAI conference Band 75 aus Series on Advances in Mathematics for Applied Sciences , Seite 113-124.
Herausgeber: World Scientific Publishing Co. Pte. Ltd., Singapore,
2007
1.
J. ter Maten; A. Verhoeven; T. Voss; T. Bechtold; W. Schilders
Model order reduction for linear and nonlinear circuit simulation
Workshop Gesellschaft für Mess- und Automatisierungstechnik (GMA), Fachausschuss 1.30 Modellbildung, Identifikation und Simulation in der Automatisierungstechnik , Seite 53-77.
VDI/VDE-TU München-Univ. des Saarlandes
2006
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