Algebraic formulation of nonlinear surface impedance boundary condition coupled with BEM for unstructured meshes

This paper deals with nonlinear eddy currents problems introducing a novel surface impedance boundary conditions (SIBC). The SIBC is formulated in the algebraic framework giving to the field problem a circuital interpretation. In this way, the material behavior of the conductive computational domain is described by a network of lumped components. This paper shows that this matrix can be defined analytically in the case of linear magnetic characteristic or numerically when the material is nonlinear. It is shown that by mapping the magnetic nonlinearity into the circuit matrix the nonlinearity of the problem is smoothed and, therefore, a simple iterative scheme can be used. The SIBC is coupled to a BEM (for the region surrounding) giving rise to a hybrid solution. The method has been tested in terms of efficiency and accuracy. The use of the Schur complement of the solution matrix has allowed to decrease the solution time of an order of magnitude. A block triangular preconditioner is finally proposed in the case of highly distorted elements of the mesh. The preconditioner is based on the sparsification of the BEM matrix and its performance are analyzed considering a benchmark problem and a real problem (a wireless power transfer system).