Analysis of Electrically Large Problems Using the Augmented EFIE With a Calderón Preconditioner

Calderón preconditioned electric-field integral equation (CP-EFIE) is very efficient in analyzing electromagnetic problems with a moderate electrical size. For the analysis of electrically large problems with closed surfaces, the CP-EFIE, however, suffers from the well-known spurious internal resonance problem because both the EFIE and the Calderón preconditioner are singular at resonant frequencies. In this paper, the resonance problem of the Calderón preconditioner is removed by using a complex wavenumber, and that of the EFIE is eliminated by enforcing the boundary condition n̂ · D = ρ
_s
to the EFIE, resulting in the so-called augmented EFIE (AEFIE). It is shown that the proposed Calderón preconditioned AEFIE is a resonant-free formulation, and has a fast convergence rate for an iterative solution. Numerical examples are given to demonstrate the good accuracy and fast convergence of the proposed approach for the analysis of electrically large problems. The multilevel fast multipole algorithm (MLFMA) is employed to reduce the computational and storage complexities of the iterative solution.