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 journalArticle

    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 journalArticle

    @article{49a348c1a74442a3b1a617ebd60e217d,
    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",
    year = "2017",
    month = "1",
    day = "1",
    doi = "10.1137/16M1082160",
    language = "English (US)",
    volume = "49",
    pages = "756--776",
    journal = "SIAM Journal on Mathematical Analysis",
    issn = "0036-1410",
    publisher = "Society for Industrial and Applied Mathematics Publications",
    number = "2",

    }

    TY - JOUR

    T1 - Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization

    AU - Beretta, Elena

    AU - Francini, Elisa

    AU - Vessella, Sergio

    PY - 2017/1/1

    Y1 - 2017/1/1

    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

    UR - http://www.scopus.com/inward/record.url?scp=85018790436&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85018790436&partnerID=8YFLogxK

    U2 - 10.1137/16M1082160

    DO - 10.1137/16M1082160

    M3 - Article

    VL - 49

    SP - 756

    EP - 776

    JO - SIAM Journal on Mathematical Analysis

    JF - SIAM Journal on Mathematical Analysis

    SN - 0036-1410

    IS - 2

    ER -