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