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Topological derivative for nucleation of non-circular voids. The Neumann problem. (English) Zbl 1050.49028
Gulliver, Robert (ed.) et al., Differential geometric methods in the control of partial differential equations. Proceedings of the 1999 AMS-IMS-SIAM joint summer research conference, University of Colorado, Boulder, CO, USA, June 27–July 01, 1999. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-1927-5/pbk). Contemp. Math. 268, 341-361 (2000).
Summary: The hitherto existing literature concerning the topological derivative of shape functionals concerned perturbations of domains caused by introduction of circular or ball openings. In the present study the notion of the topological derivative is generalized to the case of openings of arbitrary shape. The paper is concerned with energy functionals related to the 2D Neumann problem.
For the entire collection see [Zbl 0956.00042].

49Q10 Optimization of shapes other than minimal surfaces
65K10 Numerical optimization and variational techniques
49K20 Optimality conditions for problems involving partial differential equations
74K25 Shells
93C20 Control/observation systems governed by partial differential equations
35J50 Variational methods for elliptic systems