The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes (Articolo in rivista)

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  • The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes (Articolo in rivista) (literal)
Anno
  • 2011-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1016/j.jcp.2010.09.007 (literal)
Alternative label
  • Lipnikov K., Manzini G., Brezzi F., Buffa A. (2011)
    The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
    in Journal of computational physics (Print); Elsevier, Amsterdam (Paesi Bassi)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Lipnikov K., Manzini G., Brezzi F., Buffa A. (literal)
Pagina inizio
  • 305 (literal)
Pagina fine
  • 328 (literal)
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  • 230 (literal)
Rivista
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  • 24 (literal)
Note
  • Scopu (literal)
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) - CNR, via Ferrata 1, I-27100 Pavia, Italy; Centro di Simulazione Numerica Avanzata (CeSNA)-IUSS Pavia, v.le Lungo Ticino Sforza 56, I-27100 Pavia, Italy; Istituto Universitario di Studi Superiori, Pavia, Italy (literal)
Titolo
  • The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes (literal)
Abstract
  • We extend the mimetic finite difference (MFD) method to the numerical treatment of magnetostatic fields problems in mixed div-curl form for the divergence-free magnetic vector potential. To accomplish this task, we introduce three sets of degrees of freedom that are attached to the vertices, the edges, and the faces of the mesh, and two discrete operators mimicking the curl and the gradient operator of the differential setting. Then, we present the construction of two suitable quadrature rules for the numerical discretization of the domain integrals of the div-curl variational formulation of the magnetostatic equations. This construction is based on an algebraic consistency condition that generalizes the usual construction of the inner products of the MFD method. We also discuss the linear algebraic form of the resulting MFD scheme, its practical implementation, and discuss existence and uniqueness of the numerical solution by generalizing the concept of logically rectangular or cubic meshes by Hyman and Shashkov to the case of unstructured polyhedral meshes. The accuracy of the method is illustrated by solving numerically a set of academic problems and a realistic engineering problem. (literal)
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