Wang, L. and Melnik R.V.N.
Computational Science - ICCS 2005, Part 1, Lecture Notes in Computer Science, LNCS 3514, Springer, 884--891, 2005
In this paper we analyse the performance of a low dimensional model for the nonlinear thermo-mechanicalwaves. The model has been obtained by using proper orthogonal decomposition methods combined with a Galerkin projection. First, we analyse the original PDE model in order to obtain the system states at many time instances. Then, by using an empirical orthogonal basis extracted from our numerical results, we construct an empirical low dimensionalmodel. Finally, we compare the results obtained with the original PDE model and those obtained with our low-dimensionalmodel. These comparisons are carried out for mechanically induced phase transformations in a shape-memory alloy rod.
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