Preconditioning of the second-kind boundary integral equations for 3D eddy current problems

Starting from the time-harmonic Maxwell equations at low-frequency eddy current approximation the H– formulation is presented. An equivalent system of boundary integral equations of the second kind on the conductor surface (resp. the conductor=dielectric) is derived. Discretizing these equations with a boundary element method (BEM) yields a block linear equation system   A1 B1 0 ˜B 2 A2   j = b1 b2 with a fully populatedsti@ness matrix. This system is non-symmetric and, for large = 0 (of interest in practice) ill-conditioned. Iterative solvers like GMRES converge very slowly, in general. We propose a new preconditioner which depends on . We present numerical results with a serial andparallel version of this preconditioner also on large industrial eddy current problems with complex geometry. The performance of preconditioned GMRES is found to be practically independent of = 0.