Efficient Solution of Skin-Effect Problems by Means of the GMRES-Accelerated FEM-BEM Method

This paper shows that the global system of linear equations in the hybrid finite element method/boundary element method (FEM-BEM) solution of open-boundary skin effect problems can be efficiently solved by means of the generalized minimal residual (GMRES) solver. This solver is applied virtually to the reduced system of equations in which the unknowns are the nodal values of the normal derivative of the magnetic vector potential on the fictitious truncation boundary. In each step of the GMRES algorithm, the solution of the FEM equations is performed by means of the standard complex conjugate gradient solver, whereas the BEM equations are not solved but used to perform fast matrix-by-vector multiplications. The BEM equations are written in a nonconventional way, by making the nodes for the potential noncoinciding with the nodes for its normal derivative.