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

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