Computer Science and Engineering
Model Reduction and Approximation: Theory and Algorithms

Chapter 9: Comparison of Methods for Parametric Model Order Reduction of Time-Dependent Problems

Abstract

9.1 ▪ Introduction
In this work, we consider parametrized dynamical systems of order n,
with a parameter (vector) p ∊ ℝd; x(t; p) ∊ ℝn, y(t; p) ∊ ℝq, and u(t) ∊ ℝm; and parameter-dependent system matrices E(p), A(p) ∊ ℝn×n, B(p) ∊ ℝn×m, and C(p) ∊ ℝq×n.

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Information

Published In

cover image Computational Science & Engineering
Model Reduction and Approximation: Theory and Algorithms
Pages: 377 - 407
Editors: Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, Mario Ohlberger, Universität Münster, Münster, Germany, Albert Cohen, Université Pierre et Marie Curie, Paris, France, and Karen Willcox, Massachusetts Institute of Technology, Cambridge, Massachusetts
ISBN (Print): 978-1-611974-81-2
ISBN (Online): 978-1-611974-82-9

History

Published online: 14 July 2017

Keywords

  1. Model reduction
  2. Rational Interpolation and Approximation
  3. Proper orthogonal decomposition
  4. Reduced basis method
  5. Tensor methods

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Notes

33
This work was supported partially by the German Research Foundation (DFG) grant BE 2174/AN693, Multivariate Interpolation Methods for Parametric Model Reduction (MIM4PMOR), by the DFG EXC 1003 Cells in Motion—Cluster of Excellence, and by the Center for Developing Mathematics in Interaction, DEMAIN, Münster, Germany. The authors also want to acknowledge the Baden-Württemberg Stiftung gGmbH for funding as well as the DFG for financial support within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart.

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