On the Relationship Between Multiple-Scattering Macro Basis Functions and Krylov Subspace Iterative Methods

A mathematical link is provided between the Krylov subspace iterative approach based on the full orthogonalization method (FOM) and the macro basis functions (MBF) approach based on a multiple-scattering methodology. The link refers to the subspaces created by those methods as well as to the orthogonality conditions which they satisfy. Both approaches are applied to the same method-of-moments (MoM) system of equations that is preconditioned based on a closest-interaction rule, and where blocks of the MoM impedance matrix are compressed using a rank-revealing method. MBF and FOM approaches are compared numerically, with a special attention given to accuracy, for perfectly conducting objects, comprising an array of tapered-slot antennas, spheres and an aircraft. The respective advantages of both methods are briefly discussed and further prospects are given.