An Embedded Iterative Scheme in Electromagnetism

In this paper we describe an embedded iterative scheme based on the GMRES method and implemented in combination with the Fast Multipole Method for the solution of large electromagnetic scattering problems expressed in an integral formulation. In our scheme, we use a Frobenius-norm minimization preconditioner to speed-up the inner iterations, and the M-V products within the inner and the outer solvers are carried out at different accuracy. We describe the implementation of the preconditioner in a multipole and parallel out-of-core solver for distributed memory computer architectures, and report on results on the scalability of the iterative solver on large industrial and academic models. We show that the proposed technique enables to significantly reduce the computational cost of the simulation. In particular, we are able to solve a linear system with more than one million unknowns arising from a simulation on a real aircraft.