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