Mixed electroelastic waves and CFL stability conditions in computational piezoelectricity

Authors:
R. V. N. Melnik;K. N. Zotsenko
Affiliations:
University of Southern Denmark, MCI, Sonderborg, Grundtvigs Alle 150, DK-6400, Denmark;Electronic Data Systems Australia, 60 Currington Street, Sydney, NSW 2000, Australia
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

Modelling vibrational dynamics of piezoelectric materials and structures undergoing mechanical and/or electric loadings is a challenging interdisciplinary area at the interface of applied mathematics, materials science and engineering. When numerical methods are applied to such problems stability criteria play a fundamental role in the success of the entire modelling exercise. The main result of this paper is a complete and rigorous derivation of the generalisation of the classical Courant-Friedrichs-Lewy stability condition to the case of dynamic piezoelectricity for variational difference schemes.