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 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.