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

Elena Beretta; Elisa Francini; Sergio Vessella

doi:10.1137/16M1082160

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

Elena Beretta, Elisa Francini, Sergio Vessella

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	756-776
Number of pages	21
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	2
DOIs	https://doi.org/10.1137/16M1082160
State	Published - 2017

Keywords

Conductivity equation
Dirichlet to Neumann map
Polygonal inclusion
Shape derivative

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/16M1082160

Cite this

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

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.",

keywords = "Conductivity equation, Dirichlet to Neumann map, Polygonal inclusion, Shape derivative",

author = "Elena Beretta and Elisa Francini and Sergio Vessella",

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AU - Beretta, Elena

AU - Francini, Elisa

AU - Vessella, Sergio

PY - 2017

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N2 - 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.

AB - 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.

KW - Conductivity equation

KW - Dirichlet to Neumann map

KW - Polygonal inclusion

KW - Shape derivative

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

Abstract

Keywords

ASJC Scopus subject areas

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