Fast Iterative Schemes for the Solution of Eddy Current Problems Featuring Multiple Conductors by Integral Formulations

Integral formulations lead to full matrices that, despite the use of efficient low-rank approximation techniques, are impossible to be solved when the number of unknowns is large enough. To overcome this limitation, we propose a novel direct-iterative hybrid technique to solve eddy currents by taking advantage of the domain splitting into disjoint conductors: each subproblem is solved via direct solvers on each subdomain, whereas the Krylov subspace techniques are applied to compute the mutual effects between the substructures iteratively. In this way, the entries related to the mutual contributions between the subdomains are not stored. In particular, this article focuses on testing the convergence of the iterative method.