Numerical procedures for the solution of nonlinear electromagnetic problems

A typical nonlinear three-dimensional eddy current problem is analyzed using dual finite element formulations in terms of the two-component vector potential. Each of the two formulations enforces one of the Maxwell equations exactly. In this way, the numerical error is concentrated in the constitutive equations, allowing for an estimation of local and global errors. The authors assess how the performances of the methods are affected by choice of the gauge, substructuring of the problem. and choice of the iterative algorithm for the treatment of the nonlinearity. In agreement with previous results, it was found that the choice of the tree does affect the properties of the systems of equations