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

Authors:
L. X. Wang;Roderick V. N. Melnik
Affiliations:
MCI, Faculty of Science and Engineering, University of Southern Denmark, Sonderborg DK-6400, Denmark;Mathematical Modelling & Computational Sciences, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, Canada, N2L 3C5
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 3
Cited 3

Spectral methods in MatLab

Spectral methods in MatLab
A New Look at Proper Orthogonal Decomposition

SIAM Journal on Numerical Analysis
Simulation of nonlinear thermomechanical waves with an empirical low dimensional model

ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I

Coupling control and human factors in mathematical models of complex systems

Engineering Applications of Artificial Intelligence
Low dimensional nonlinear thermomechanical models describing phase transformations and their applications

MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Phase-field approach to studying shape memory effects and thermomechanical properties of low dimensional nanostructures

NANOTECHNOLOGY'10 Proceedings of the 2nd WSEAS international conference on Nanotechnology

Quantified Score

Hi-index	0.00

Visualization

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 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.