  Model reduction using the proper orthogonal decomposition (POD) method is
applied to the dynamics of ferroelastic patches to study the first order square
to rectangular phase transformations. Governing equations for the system
dynamics are constructed by using the Landau-Ginzburg theory and are solved
numerically. By using the POD method, a set of empirical orthogonal basis
functions is first constructed, then the system is projected onto the subspace
spanned by a small set of basis functions determined by the associated singular
values. The performance of the low dimensional model is verified by simulating
nonlinear thermo-mechanical waves and square to rectangular transformations in
a ferroelastic patch. Comparison between numerical results obtained from the
original PDE model and the low dimensional one is carried out.
