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Title: A problem in control of elastodynamics with piezoelectric effects
Abstract We consider an optimal control problem where the state equations are a coupled hyperbolic–elliptic system. This system arises in elastodynamics with piezoelectric effects—the elastic stress tensor is a function of elastic displacement and electric potential. The electric flux acts as the control variable and bound constraints on the control are considered. We develop a complete analysis for the state equations and the control problem. The requisite regularity on the control, to show the well-posedness of the state equations, is enforced using the cost functional. We rigorously derive the first-order necessary and sufficient conditions using adjoint equations and further study their well-posedness. For spatially discrete (time-continuous) problems, we show the convergence of our numerical scheme. Three-dimensional numerical experiments are provided showing convergence properties of a fully discrete method and the practical applicability of our approach.  more » « less
Award ID(s):
1818772
PAR ID:
10128244
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
IMA Journal of Numerical Analysis
ISSN:
0272-4979
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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