65 research outputs found
An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations
We discuss model reduction for a particular class of quadratic-bilinear (QB)
descriptor systems. The main goal of this article is to extend the recently
studied interpolation-based optimal model reduction framework for QBODEs
[Benner et al. '16] to a class of descriptor systems in an efficient and
reliable way. Recently, it has been shown in the case of linear or bilinear
systems that a direct extension of interpolation-based model reduction
techniques to descriptor systems, without any modifications, may lead to poor
reduced-order systems. Therefore, for the analysis, we aim at transforming the
considered QB descriptor system into an equivalent QBODE system by means of
projectors for which standard model reduction techniques for QBODEs can be
employed, including aforementioned interpolation scheme. Subsequently, we
discuss related computational issues, thus resulting in a modified algorithm
that allows us to construct \emph{near}--optimal reduced-order systems without
explicitly computing the projectors used in the analysis. The efficiency of the
proposed algorithm is illustrated by means of a numerical example, obtained via
semi-discretization of the Navier-Stokes equations
Structure Preserving Model Order Reduction by Parameter Optimization
Model order reduction (MOR) methods that are designed to preserve structural
features of a given full order model (FOM) often suffer from a lower accuracy
when compared to their non structure preserving counterparts. In this paper, we
present a framework for MOR based on direct parameter optimization. This means
that the elements of the system matrices are iteratively varied to minimize an
objective functional that measures the difference between the FOM and the
reduced order model (ROM). Structural constraints are encoded in the
parametrization of the ROM. The method only depends on frequency response data
and can thus be applied to a wide range of dynamical systems. We illustrate the
effectiveness of our method on a port-Hamiltonian and on a symmetric second
order system in a comparison with other structure preserving MOR algorithms.Comment: 26 pages, 7 figure
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