Hierarchical Bases Preconditioners for the Electric Field Integral Equation on Multiply Connected Geometries

Abstract

This paper presents a formulation that allows to use hierarchical basis preconditioners applicable to the electric field integral equation (EFIE) on multiply connected geometries without searching for global loops. Currently available hierarchical basis preconditioners need an explicit representation of global loops. Finding these requires a computational complexity exceeding the linearithmic complexity of fast matrix-vector multiplication methods. Instead of using an explicit representation of global loops, we utilize Helmholtz projectors to regularize the EFIE separately on the solenoidal, non-solenoidal, and harmonic Helmholtz subspaces. Thereby, we avoid the explicit recovery of the global loops and maintain the leading complexity of fast multiplication methods. Numerical results prove the effectiveness of the proposed approach.