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

• Autores: L. X. Wang, Roderick Melnik
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 57, Nº. 5-7, 2007, págs. 510-520
• Idioma: inglés
• DOI: 10.1016/j.apnum.2006.07.004
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• Resumen

  • 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.