A new Whitney-based material operator for the finite-integration technique on triangular grids

Author

Schuhmann, Rolf ; Schmidt, Peter ; Weiland, Thomas

Author_Institution

Comput. Electromagn. Lab. (TEMF), Technische Hochschule Darmstadt, Germany

Volume

38

Issue

2

fYear

2002

fDate

3/1/2002 12:00:00 AM

Firstpage

409

Lastpage

412

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

Keywords

Maxwell equations; eigenvalues and eigenfunctions; electromagnetic fields; integration; interpolation; Maxwell´s equations; Whitney-based material operator; discretization scheme; dual points; finite-integration technique; interpolating functions; matrix operator; primary cell; stability; symmetric material matrices; triangular grids; Eigenvalues and eigenfunctions; Finite element methods; Integral equations; Magnetic flux; Magnetic materials; Maxwell equations; Stability; Sufficient conditions; Symmetric matrices; Voltage;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.996109

Filename

996109