Geometrically based preconditioner for the Fast Multipole Method using rooftop basis functions and Galerkin testing procedure

The simulation of radiation problems typically involves localized excitation of a small and refined portion of the mesh representing the antenna. Due to this fact and the implicit units imbalance of problems comprising wire and surface elements, the convergence of the iterative solutions often shows a bad behavior. In this work, a preconditioning scheme is presented which moderates the strong dominance of the self-coupling of wire or surface antennas and weights the matrix equation to renormalize the respective units of wire and surface coupling terms.