An approach for the efficient solution of the time-dependent linear Boltzmann equation

Matthias Schlottbom, Mike A. Botchev, Herbert Egger

    Research output: Contribution to conferenceAbstract

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    Abstract

    Kinetic equations have proven to be useful models in different applications as, e.g., neutron transport,
    gas dynamics, semiconductors, photon propagation, opinion dynamics or biological network
    formation. One of the key challenges in the numerical simulation of kinetic equations is their highdimensionality.
    For instance, in neutron transport, the solution depends in general on three spatial,
    three angular and one temporal variable. Based on the mixed variational formulation analyzed in
    [1] we will present a strategy for the design of efficient numerical approximation schemes. The formulation
    of [1] incorporates boundary conditions in a weak sense. Unfortunately, the bilinear form
    corresponding to the boundary conditions couples spatial and angular variables in a non-smooth way
    rendering a tensor product approximation not straight-forward. As a remedy we introduce an absorbing
    layer and consider a perturbed variational problem which leads to matrices with tensor product
    structure. Hence, even in the full tensor product approximation, the resulting discrete operators can
    be stored efficiently. We provide corresponding error estimates for our approach.
    Original languageEnglish
    Pages356-356
    Publication statusPublished - 28 Sep 2017
    EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway
    Duration: 25 Sep 201729 Sep 2017

    Conference

    ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017
    Abbreviated titleENUMATH
    CountryNorway
    CityVoss
    Period25/09/1729/09/17

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  • Cite this

    Schlottbom, M., Botchev, M. A., & Egger, H. (2017). An approach for the efficient solution of the time-dependent linear Boltzmann equation. 356-356. Abstract from European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway.