Certified Coupled Model Order Reduction

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

[RettbergEtAl23b] Rettberg, J.; Wittwar, D.; Buchfink, P.; Herkert, R.; Fehr, J.; Haasdonk, B.: Improved a posteriori Error Bounds for Reduced port-Hamiltonian Systems. Advances in Computational Mathematics, 2023. Preprint ArXiv: https://doi.org/10.48550/arXiv.2303.17329

[RettbergEtAl23a] Rettberg, J.; Wittwar, D.; Buchfink, P.; Brauchler, A.; Ziegler, P.; Fehr, J.; Haasdonk, B.: Port-Hamiltonian Fluid-Structure Interaction Modeling and Structure-Preserving Model Order Reduction of a Classical Guitar.
Mathematical and Computer Modelling of Dynamical Systems, 2023.
DOI: https://doi.org/10.1080/13873954.2023.2173238
Preprint ArXiv: http://arxiv.org/abs/2203.10061

[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.