Near-Field-Based Preconditioning Technique in the Incomplete-Leaf MLFMA for Nonuniformly Discretized Electromagnetic Scattering Problems

The potential of incomplete tree structures, previously used in the context of the multilevel fast multi pole algorithm, on developing an effective preconditioning technique for multiscale electromagnetic problems is analyzed. The preconditioning technique is based on the sparse near-field matrix constructed by the near-field clustering definition of the incomplete tree structures for multiscale geometries. The proposed preconditioner is applied to solutions of matrix systems obtained via method-of-moments discretization of potential integral equations since the conditioning of the calculated matrices deteriorates as the problem size grows or the number of unknowns increases. The effectiveness and robustness of the preconditioning technique are demonstrated by numerical experiments on a complex target.