Physics – Condensed Matter – Materials Science
Scientific paper
2007-02-28
Physics
Condensed Matter
Materials Science
Keywords: Phase transformation, ferroelastic patch, model reduction, proper orthogonal decomposition, Galerkin projection
Scientific paper
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.
Melnik Roderick V. N.
Wang Linxiang X.
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