Fast directional multilevel algorithm combined with Calderon multiplicative preconditioner for stable electromagnetic scattering analysis

Abstract

In this article, a new method called fast directional multilevel algorithm (FDMA) is proposed for three-dimensional electromagnetic problems. Combined with the Caldron identities of Calderon multiplicative preconditioner (CMP), the new algorithm has a fast convergence rate of iterative solvers and is stable at low frequency for the electrical field integral equation solutions. Like the fast multipole method, octree structure is used in our proposed algorithm. However, the new algorithm does not require the implementation of multipole expansions of the Green's function but based only on kernel evaluations. It does not suffer from low-frequency breakdown when the discretization density is high. The numerical results demonstrate that the CMPpreconditioned FDMA leads to significant reduction of both the iteration number and the computer processing use (CPU) time for radar cross section (RCS) calculation.

Augmented EFIE with Adaptive Cross Approximation Algorithm for Analysis of Electromagnetic Problems

“…A well-conditioned EFIE (WEFIE) to overcome the shortcomings of the EFIE has been proposed in [15][16][17][18][19][20][21][22][23]. Due to the fact that the square of the EFIE operator does not have eigenvalues accumulating at zero or infinity, the WEFIE can give rise to a well-conditioned EFIE system independently of the discretization density [15,[17][18][19].…”

“…Due to the fact that the square of the EFIE operator does not have eigenvalues accumulating at zero or infinity, the WEFIE can give rise to a well-conditioned EFIE system independently of the discretization density [15,[17][18][19]. An efficient Calderón preconditioner is introduced based on the Calderón identities for scattering by perfect electric conductor (PEC) [16,[20][21][22][23]. The Calderón preconditioner is made purely multiplicative by using the Buffa-Christiansen (BC) basis functions.…”