Certified Coupled Model Order Reduction

Certified Model Order Reduction for Coupled Multi-Physics Systems

Project Description

The project is based on and extends a previous joint project of the groups from the Institute of Engineering and Computational Mechanics (ITM) and the Institute of Applied Analysis and Numerical Simulation (IANS). It aims at certified coupled model order reduction (CCMOR) of multi-physics systems. Coupled multi-physics systems are generally high dimensional nonlinear models and therefore, their repeated numerical simulation with varying parameters is prohibitively expensive. Henceforth, model order reduction (MOR) techniques can be applied to reduce the discretized mechanical system leading to faster numerical simulations. However, the resulting approximation introduces additional errors which have to be controlled. In order to improve both the approximation itself, as well as the error estimation, the project aims to extend existing MOR techniques for coupled mechanical systems to the case of coupled multi-physics systems by developing structure-preserving MOR techniques which consider the underlying physics and maintain them in the reduced model.

Single pH-system with flow and effort variables between storage, dissipation and an external port
Single pH-system with flow and effort variables between storage, dissipation and an external port
Various singular pH-systems are coupled into one large pH-system
Various singular pH-systems are coupled into one large pH-system

The project aims to use certain preservation principles, i.e. based on (generalized) port-Hamiltonian (PH) or contact Hamiltonian structure of the problems. 
The project further targets on developing efficient structure-preserving integrators as well as MOR and basis generation techniques that maintain the identified structure, i.e. certain relevant physical conditions, in the reduced models.

Ideally, these techniques should result in small bases for the reduced system that provide a higher accuracy and better stability than current basis generation techniques and overall faster numerical simulation than physics-agnoscent approaches. Leveraging the underlying structure, we will improve existing error estimation techniques for both the states and outputs of interest. In particular, high effectivity and small overestimation will be realized by extending auxiliary linear problem (ALP) based error estimates to our structure-preserving MOR framework. Both the quality of the approximation and the error estimates as well as the computational benefit of the MOR approach will be tested on thermo-mechanical systems and systems with fluid-structure interaction (FSI).

Discbreak as an example of a thermomechanical system [MatterEtAl19]
Discbreak as an example of a thermomechanical system [MatterEtAl19]
Guitar as an example for fluid-structure interaction [BrauchlerEtAl19]
Guitar as an example for fluid-structure interaction [BrauchlerEtAl19]

Software

The developed methods and algorithms will be efficiently implemented in the joint software package CCMOR.

RBmatlab software package
RBmatlab software package
Morembs software  package
Morembs software package

References

[FehrHaasdonk20] Fehr, J.; Haasdonk, B. (Eds.): IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22-25, 2018: MORCOS 2018. IUTAM Bookseries. Springer. 2020. (doi:10.1007/978-3-030-21013-7)

[MatterEtAl19] Matter, F.; Ziegler, P.; Iroz, I.; Eberhard, P.: Simulation of Thermoelastic Problems with the Finite Element Method. In Proceedings in Applied Mathematics and Mechanics, 2019. (doi: 10.1002/pamm.201900035)

[BrauchlerEtAl19] Brauchler, A.; Ziegler, P.; Benatti Camargo, S.; Eberhard, P.: Experimental and Simulative Examination of the String-Soundboard Coupling of an Acoustic Guitar. Proceedings of ISMA 2019, Detmold, 13. - 17. September 2019.

Funding Source

German Research Foundation (DFG)

Principal investigators
Research Staff

Contact

This image shows Jörg Fehr
apl. Prof. Dr.-Ing.

Jörg Fehr

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