Mixed Electroelastic Waves and CFL Stability Conditions in Computational Piezoelectricity

Melnik, R.V.N. and  Zotsenko, K.N.

Applied Numerical Mathematics,  48, 41--62, 2004

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.