Calderon multiplicative preconditioner based on curvilinear elements for fast analysis of electromagnetic scattering

Abstract

In this study, an efficient Calderon multiplicative preconditioner (CMP) based on the curvilinear elements is proposed for preconditioning electric field integral equation (EFIE) for three-dimensional electromagnetic problems. The curvilinear CMP are constructed by the curvilinear Buffa–Christinansen (BC) basis functions and curvilinear Rao–Wilton–Glisson (CRWG) basis functions, both of which can be presented as a linear combination of CRWG basis functions acting on barycentrically refined triangular meshes. Therefore the implementation of the curvilinear CMP-preconditioned EFIE allows direct application to the existing method of moments (MoM) code using CRWG basis functions and can be combined with the multilevel fast multipole algorithm (MLFMA) for electrically large problems and low-frequency fast multipole algorithm (LF-FMA) for low-frequency problems. The Caldron identities of the curvilinear CMP can lead to the fast convergence rate of iterative solvers for EFIE solutions, independently of the discretisation density. The numerical results demonstrate that the curvilinear CMP scheme with both MLFMA and LF-FMA lead to significant reduction of both the iteration number and the CPU time of monostatic radar cross-section (RCS) calculation.