Balanced Truncation Model Reduction
for a Class of Descriptor Systems
with Application to the Oseen Equations

Matthias Heinkenschloss
Danny C. Sorensen
Kai Sun
Department of Computational and Applied Mathematics
Rice University

SIAM Journal on Scientific Computing, Vol 30 (2008), No. 2, pages 1038-1063.


We discuss the computation of balanced truncation model reduction for a class of descriptor systems which includes the semidiscrete Oseen equations with time independent advection. 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 afore mentioned 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.

Keywords. Model reduction, control, descriptor systems, differential algebraic equations, Oseen equations, linearized Navier Stokes equations.