A Space-Time Finite Element Method for Neural Field Equations with Transmission Delays

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    Abstract

    We present and analyze a new space-time nite element method for the solution
    of neural eld equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on the spatial domain and the functionsinvolved, such as connectivity and delay functions. The use of a space-time discretization, with basis functions that are discontinuous in time and continuous in space (dGcG-FEM), is a natural way to deal with space-dependent delays, which is important for many neural eld applications. In
    this paper we provide a detailed description of a space-time dGcG-FEM algorithm for neural delay equations, including an a priori error analysis. We demonstrate the application of the dGcG-FEM algorithm on several neural eld models, including problems with an inhomogeneous kernel.
    Original languageEnglish
    Pages (from-to)B797–B818
    JournalSIAM journal on scientific computing
    Volume39
    Issue number5
    DOIs
    Publication statusPublished - 21 Dec 2017

    Fingerprint

    Space-time Finite Elements
    Space-time
    Finite element method
    Delay Equations
    Delay-dependent
    Error Analysis
    Error analysis
    Basis Functions
    Connectivity
    Discretization
    kernel
    Restriction
    Demonstrate
    Model

    Keywords

    • Neural fields
    • Transmission delays
    • Discontinuous Galerkin finite element methods
    • Space-time methods

    Cite this

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    title = "A Space-Time Finite Element Method for Neural Field Equations with Transmission Delays",
    abstract = "We present and analyze a new space-time nite element method for the solutionof neural eld equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on the spatial domain and the functionsinvolved, such as connectivity and delay functions. The use of a space-time discretization, with basis functions that are discontinuous in time and continuous in space (dGcG-FEM), is a natural way to deal with space-dependent delays, which is important for many neural eld applications. Inthis paper we provide a detailed description of a space-time dGcG-FEM algorithm for neural delay equations, including an a priori error analysis. We demonstrate the application of the dGcG-FEM algorithm on several neural eld models, including problems with an inhomogeneous kernel.",
    keywords = "Neural fields, Transmission delays, Discontinuous Galerkin finite element methods, Space-time methods",
    author = "Monika Polner and {van der Vegt}, J.J.W. and {van Gils}, S.A.",
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    day = "21",
    doi = "10.1137/16M1085024",
    language = "English",
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    publisher = "Society for Industrial and Applied Mathematics Publications",
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    A Space-Time Finite Element Method for Neural Field Equations with Transmission Delays. / Polner, Monika; van der Vegt, J.J.W.; van Gils, S.A.

    In: SIAM journal on scientific computing, Vol. 39, No. 5, 21.12.2017, p. B797–B818.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - A Space-Time Finite Element Method for Neural Field Equations with Transmission Delays

    AU - Polner, Monika

    AU - van der Vegt, J.J.W.

    AU - van Gils, S.A.

    PY - 2017/12/21

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    AB - We present and analyze a new space-time nite element method for the solutionof neural eld equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on the spatial domain and the functionsinvolved, such as connectivity and delay functions. The use of a space-time discretization, with basis functions that are discontinuous in time and continuous in space (dGcG-FEM), is a natural way to deal with space-dependent delays, which is important for many neural eld applications. Inthis paper we provide a detailed description of a space-time dGcG-FEM algorithm for neural delay equations, including an a priori error analysis. We demonstrate the application of the dGcG-FEM algorithm on several neural eld models, including problems with an inhomogeneous kernel.

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    KW - Transmission delays

    KW - Discontinuous Galerkin finite element methods

    KW - Space-time methods

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    SP - B797–B818

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