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Construction of Differential Material Matrices for the Orthogonal Finite-Integration Technique With Nonlinear Materials

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3 Author(s)
De Gersem, H. ; Inst. fur Theor. Elektromagn. Felder, Tech. Univ. Darmstadt, Darmstadt ; Munteanu, I. ; Weiland, T.

The linearization of an electromagnetic formulation by the Newton method can be expressed similarly as for the linear case, by introducing differential material matrices. For the case of the finite-integration technique applied to an orthogonal grid, the chord material matrix is diagonal whereas the differential material matrices includes off-diagonal bands, representing the cross-directional coupling introduced by the nonlinearity. An approximative Newton method based on a unidirectional differential material matrix yields a diagonal matrix, which has a higher computational efficiency but may lead to a degenerated convergence.

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Magnetics, IEEE Transactions on  (Volume:44 ,  Issue: 6 )