On the Schwarz Method for the Eddy Currents Model

We investigate an iterative solver for the reduced eddy currents model set in open domains. Its formulation is the result of the coupling of a variational problem restricted to a truncated domain with a transparent condition at the fictitious boundary. The non-local boundary condition is derived using simple/double layer potentials. Applying a splitting technique yields an iterative algorithm that requires to solve, at each iteration, a local Neumann boundary value problem on the current potential. A re-interpretation of the algorithm as a Schwarz method enables a tractable convergence analysis which is the core subject of the paper. Using suitable variational tools, we establish an exponential convergence of the iterative solver. Some analytical and numerical examples are presented to check the theoretical findings and the relevance of our procedure.