A new Whitney-based material operator for the finite-integration technique on triangular grids. Schuhmann, R.; Schmidt, P.; and Weiland, T. IEEE Transactions on Magnetics, 38(2):409–412, IEEE, March, 2002.
doi  abstract   bibtex   
We propose a new matrix operator for the material relations within the finite-integration technique. It is based on the assumption of Whitney-type basis functions in the cells of a triangular two-dimensional grid. To ensure the symmetry of the new operator, we introduce the positions of the dual points in each primary cell as additional degrees of freedom in the derivation of the discretization scheme. It is shown that there exists one unique position, which leads to symmetric material matrices - a sufficient condition for the stability of the method. In addition, the analysis may help to understand the differences between finite-integration and finite-element schemes on triangular grids
@Article{         Schuhmann_2002aa,
  abstract      = {We propose a new matrix operator for the material relations within the finite-integration technique. It is based on the assumption of Whitney-type basis functions in the cells of a triangular two-dimensional grid. To ensure the symmetry of the new operator, we introduce the positions of the dual points in each primary cell as additional degrees of freedom in the derivation of the discretization scheme. It is shown that there exists one unique position, which leads to symmetric material matrices - a sufficient condition for the stability of the method. In addition, the analysis may help to understand the differences between finite-integration and finite-element schemes on triangular grids},
  author        = {Schuhmann, Rolf and Schmidt, Peter and Weiland, Thomas},
  doi           = {10.1109/20.996109},
  file          = {Schuhmann_2002aa.pdf},
  issn          = {0018-9464},
  journal       = {IEEE Transactions on Magnetics},
  keywords      = {field,whitney,fem},
  langid        = {english},
  month         = mar,
  number        = {2},
  pages         = {409--412},
  publisher     = {IEEE},
  title         = {A new Whitney-based material operator for the finite-integration technique on triangular grids},
  volume        = {38},
  year          = {2002},
  shortjournal  = {IEEE Trans. Magn.}
}
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