In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.

Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization / Beretta, E.; Francini, E.; Vessella, S.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 1095-7154. - STAMPA. - 49:(2017), pp. 756-776. [10.1137/16M1082160]

Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization

FRANCINI, ELISA;VESSELLA, SERGIO
2017

Abstract

In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.
2017
49
756
776
Beretta, E.; Francini, E.; Vessella, S.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1045293
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