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This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromagnetic field problems in nonlinear media. The hybrid technique is based on new theoretical results regarding the similarities between the Picard-Banach fixed-point (polarization) method and the Newton method. At each iteration, the solution is obtained as a linear combination of the old solution, and the new Picard-Banach and Newton solutions. The numerical solutions are calculated through à`t riangle'' (bidimensional) minimization of the residual or of the energy functional. The goal of this combination is to increase the robustness of the iterative method, without losing the quadratic speed of convergence in the vicinity of the solution. The proposed method generalizes and unifies in a single algorithm the overrelaxed Picard-Banach and the underrelaxed Newton methods.

A benchmark problem of a thin film magnetic recording write head, proposed by the Storage Research Consortium (SRC) in Japan, is simulated with implicit time-domain formulations for nonlinear three-dimensional magneto-quasi-static problems based on the finite integration technique (FI 2 TD). Several numerical schemes adapted to this framework are presented to achieve the required solutions. The write head fields are simulated with good agreement to the measurements.

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