Two-level solver for nonlinear magnetic field problems using the p-version of the fem

In this work we present an approach for solving nonlinear magnetostatic fields by utilizing the p-version of the FEM. The hierarchical H(curl)-conforming elements enable a natural splitting in lower order Nédélec-type shape functions and higher order ones. We develop a two-level solver analogous to the multigrid method, where the initial solution of the nonlinear problem on the lower order space is inserted into the higher order one, thus reducing the computational effort. Due to the explicit representation of gradients in the shape functions, the higher order space can be solved robustly using a simple Schwarz-type preconditioned Krylov method. The efficiency of the proposed method is demonstrated by TEAM benchmark problems.