Selected projection methods to improve the convergence of non‐linear problems

Short computation times required for the design and numerical optimisation of electromagnetic devices with the finite element method are obtained using an adaptive mesh refinement algorithm. Less time is spent on the initial mesh generation, while the time needed for refinement is negligible when special data structures are used. But an even more significant reduction in total computation time is achieved with the initialisation of the solution on the generated mesh. Fewer Newton steps are required to solve non‐linear problems compared to a zero initial solution, while the time needed for the projection of the solution is far less than the time needed for a Newton step.