Hybrid and concurrent algorithms for nonlinear magnetic field problems

To solve the magnetostatic field equations in nonlinear materials, the classical Newton method and its variants are more efficient but not as robust as the Picard-Banach simple iterations method. In order to obtain a better algorithm we propose and analyze several techniques for combining these two methods. The combination is done either sequentially (based on the switching between the methods or on the weighting of the solutions as in the original "triangle search method"), or in parallel (based on concurrent agents).