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

Elena Beretta, Elisa Francini, Sergio Vessella

    Research output: Contribution to journal › Article

    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 languageEnglish (US)
    Pages (from-to)756-776
    Number of pages21
    JournalSIAM Journal on Mathematical Analysis
    Volume49
    Issue number2
    DOIs
    StatePublished - Jan 1 2017

    Fingerprint

    Dirichlet-to-Neumann Map
    Shape Optimization
    Shape optimization
    Differentiability
    Conductivity
    Inclusion
    Shape Derivative
    Derivatives
    Triangular
    Optimization Problem
    Derivative
    Movement

    Keywords

    • Conductivity equation
    • Dirichlet to Neumann map
    • Polygonal inclusion
    • Shape derivative

    ASJC Scopus subject areas

    • Analysis
    • Computational Mathematics
    • Applied Mathematics

    Cite this

    Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization. / Beretta, Elena; Francini, Elisa; Vessella, Sergio.

    In: SIAM Journal on Mathematical Analysis, Vol. 49, No. 2, 01.01.2017, p. 756-776.

    Research output: Contribution to journal › Article

    Beretta, E, Francini, E & Vessella, S 2017, 'Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization', SIAM Journal on Mathematical Analysis, vol. 49, no. 2, pp. 756-776. https://doi.org/10.1137/16M1082160
    Beretta E, Francini E, Vessella S. Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization. SIAM Journal on Mathematical Analysis. 2017 Jan 1;49(2):756-776. https://doi.org/10.1137/16M1082160
    Beretta, Elena ; Francini, Elisa ; Vessella, Sergio. / Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization. In: SIAM Journal on Mathematical Analysis. 2017 ; Vol. 49, No. 2. pp. 756-776.
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