Triangle search method for nonlinear electromagnetic field computation

Source abstract

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 a “triangle” (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.