Speaker
Description
Simulations of complex dynamical systems using the Finite Element Method (FEM) can become computationally very expensive since large systems of equations have to be solved for multiple instances in time or frequency. Projection-based model order reduction (MOR) methods are state-of-the-art methods to compute an accurate approximate solution of the high-dimensional model with significantly less computational effort. For multi-query applications, the reduced model should also maintain parametric dependencies of the original model, which can be achieved by parametric Model Order Reduction (pMOR) methods. Many of those methods require an affine representation of the parametric dependency, which is difficult to realize for, e.g., geometric parameters [1].
PMOR based on matrix interpolation does not require such an affine parametric dependency [3]. In this method, local reduced models are computed for a set of samples in the parameter space. Afterwards, the reduced operators are transformed to a common basis and interpolated so that reduced models can be predicted for queried parameter points. To judge the accuracy of the predicted reduced model without having to evaluating the high-dimensional model, error estimators can be used. Recently, a survey on a-posteriori error estimators for parametric reduced models has been published [2]. All of these error estimators require the full operators, the reduced operators and the reduced basis at the queried parameter point. In pMOR by matrix interpolation, however, only the predicted reduced operators are available after the interpolation. In this work, different ways how the error estimators can be applied in the context of pMOR by matrix interpolation are investigated and compared.
References
[1] P. Benner, S. Gugercin, and K. Willcox. A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review, 57(4):483_531, Jan 2015.
[2] L. Feng, S. Chellappa, and P. Benner. A posteriori error estimation for model order reduction of parametric systems. Advanced Modeling and Simulation in Engineering Sciences, 11(1):5, Mar 2024.
[3] H. Peuscher, J. Mohring, R. Eid, and B. Lohmann. Parametric model order reduction by matrix interpolation. Automatisierungstechnik, 58:475_484, Aug 2010.
