**Model reduction applied to square to rectangular martensitic transformations using proper orthogonal decomposition**

**Wang, L. and Melnik, R.V.N.**

*Applied Numerical Mathematics*, *57 (5-7*), * 510-520, 2007*

### Abstract:

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 thermomechanical 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.