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Parametric Model Reduction via Interpolating Orthonormal Bases

  • Ralf ZimmermannEmail author
  • Kristian Debrabant
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

In projection-based model reduction (MOR), orthogonal coordinate systems of comparably low dimension are used to produce ansatz subspaces for the efficient emulation of large-scale numerical simulation models. Constructing such coordinate systems is costly as it requires sample solutions at specific operating conditions of the full system that is to be emulated. Moreover, when the operating conditions change, the subspace construction has to be redone from scratch.

Parametric model reduction (pMOR) is concerned with developing methods that allow for parametric adaptations without additional full system evaluations. In this work, we approach the pMOR problem via the quasi-linear interpolation of orthogonal coordinate systems. This corresponds to the geodesic interpolation of data on the Stiefel manifold. As an extension, it enables to interpolate the matrix factors of the (possibly truncated) singular value decomposition. Sample applications to a problem in mathematical finance are presented.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of Southern DenmarkOdenseDenmark

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