Please use this identifier to cite or link to this item: http://dx.doi.org/10.18419/opus-10269
Authors: Buchfink, Patrick
Bhatt, Ashish
Haasdonk, Bernard
Title: Symplectic model order reduction with non-orthonormal bases
Issue Date: 2019
metadata.ubs.publikation.typ: Preprint
metadata.ubs.publikation.seiten: 19
URI: http://elib.uni-stuttgart.de/handle/11682/10286
http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-102864
http://dx.doi.org/10.18419/opus-10269
Abstract: Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g. structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such a ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction.
Appears in Collections:08 Fakultät Mathematik und Physik

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