@TechReport{ it:2000-019,
author = {Torsten S{\"o}derstr{\"o}m and Bharath Bhikkaji},
title = {Reduced order models for diffusion systems},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2000},
number = {2000-019},
month = aug,
abstract = {Mathematical models for diffusion processes like heat
propagation, dispersion of pollutants etc., are normally
partial differential equations which involve certain
unknown parameters. To use these mathematical models as the
substitutes of the true system, one has to determine these
parameters.
Partial differential equations (PDE) of the form \bea
\frac{\partial u(x,t)}{\partial t} = \mathcal{L} u(x,t)
\label{eq1.1} \eea where $ \mathcal{L}$ is a linear
differential (spatial) operator, describe infinite
dimensional dynamical systems. To compute a numerical
solution for such partial differential equations, one has
to approximate the underlying system by a finite order one.
By using this finite order approximation, one then computes
an approximate numerical solution for the PDE.
We consider a simple case of heat propagation in a
homogeneous wall. The resulting partial differential
equation, which is of the form (\ref{eq1.1}), is
approximated by finite order models by using certain
existing numerical techniques like Galerkin and Collocation
etc. These reduced order models are used to estimate the
unknown parameters involved in the PDE, by using the well
developed tools of system identification.
In this paper we concentrate more on the model reduction
aspects of the problem. In particular, we examine the model
order reduction capabilities of the Chebyshev polynomial
methods used for solving partial differential equation. }
}