Triangle search method for nonlinear electromagnetic field computation

This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromag netic field problems in nonlinear media. The hybrid technique is based on n ew 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 ca lculated through a "triangle" (bidimensional) minimization of the residual or of the energy functional: The goal of this combination is to increase th e robustness of the iterative method, without losing the quadratic speed of convergence in the vicinity of the solution. The proposed method generaliz es and unifies in a single algorithm the overrelaxed Picard-Banach and the underrelaxed Newton methods.