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  4. The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
 
research article

The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes

Lipnikov, K.
•
Manzini, G.
•
Brezzi, F.
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2011
Journal of Computational Physics

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. © 2010.

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Type
research article
DOI
10.1016/j.jcp.2010.09.007
Author(s)
Lipnikov, K.
Manzini, G.
Brezzi, F.
Buffa, Annalisa  
Date Issued

2011

Publisher

Elsevier

Published in
Journal of Computational Physics
Volume

230

Issue

2

Start page

305

End page

328

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
MNS  
Available on Infoscience
April 3, 2017
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/136338
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