Abstract

We discuss the computation of balanced truncation model reduction for a class of descriptor systems which include the semidiscrete Oseen equations with time-independent advection and the linearized Navier–Stokes equations, linearized around a steady state. The purpose of this paper is twofold. First, we show how to apply standard balanced truncation model reduction techniques, which apply to dynamical systems given by ordinary differential equations, to this class of descriptor systems. This is accomplished by eliminating the algebraic equation using a projection. The second objective of this paper is to demonstrate how the important class of ADI/Smith-type methods for the approximate computation of reduced order models using balanced truncation can be applied without explicitly computing the aforementioned projection. Instead, we utilize the solution of saddle point problems. We demonstrate the effectiveness of the technique in the computation of reduced order models for semidiscrete Oseen equations.

MSC codes

  1. 15A24
  2. 37M99
  3. 37N10
  4. 93A15

Keywords

  1. model reduction
  2. control
  3. descriptor systems
  4. differential algebraic equations
  5. Oseen equations
  6. linearized Navier–Stokes equations

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: 1038 - 1063
ISSN (online): 1095-7197

History

Submitted: 5 February 2007
Accepted: 19 October 2007
Published online: 5 March 2008

MSC codes

  1. 15A24
  2. 37M99
  3. 37N10
  4. 93A15

Keywords

  1. model reduction
  2. control
  3. descriptor systems
  4. differential algebraic equations
  5. Oseen equations
  6. linearized Navier–Stokes equations

Authors

Affiliations

Matthias Heinkenschloss

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