Application of Hierarchical Two-Level Spectral Preconditioning Method for Electromagnetic Scattering from the Rough Surface

D Z Ding,G M Li,Y Y An,R S Chen

doi:10.1155/2014/752418

Abstract

The higher-order hierarchical Legendre basis functions combining the electrical field integral equations (EFIE) are developed to solve the scattering problems from the rough surface. The hierarchical two-level spectral preconditioning method is developed for the generalized minimal residual iterative method (GMRES). The hierarchical two-level spectral preconditioner is constructed by combining the spectral preconditioner and sparse approximate inverse (SAI) preconditioner to speed up the convergence rate of iterative methods. The multilevel fast multipole method (MLFMM) is employed to reduce memory requirement and computational complexity of the method of moments (MoM) solution. The accuracy and efficiency are confirmed with a couple of numerical examples.

Highlights

The study of electromagnetic scattering from an object above a rough surface has a large number of applications, for example, in remote sensing, radar surveillance, and so on [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
The height value must be very small compared to the electromagnetic wave length in the small perturbation method (SPM), the radius of the surface must be larger than a wavelength in the Kirchhoff approximation (KA), the slope must be small and the height must be moderate for the first order in the small slope approximation (SSA)
The hierarchical two-level spectral preconditioning technique based on higher order hierarchical Legendre basis functions is presented for solving electrical field integral equations (EFIE) for scattering from conducting objects

Summary

Introduction

The study of electromagnetic scattering from an object above a rough surface has a large number of applications, for example, in remote sensing, radar surveillance, and so on [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. Jorgensen et al proposed a new set of higher order hierarchical Legendre basis functions for a quadrilaterals element for integral equations solved with MoM [24]. The system matrix in MoM from the divergenceconforming higher order basis functions is often an illconditioned matrix and result in the low convergence of the Krylov iterative method. Inherited from the basic idea of the traditional two-grid cycle of the multigrid methods [33, 34], the high frequency components of the iteration error belong to the subspace spanned by the eigenvectors associated with the large eigenvalues of the system matrix and can be represented on a fine grid defined by the higher order basis functions. We apply similar ideas to improve the quality of a prescribed SAI preconditioner based on the higher order hierarchical basis functions. The time factor e−iωt is assumed and suppressed throughout this paper

Theory and Formulation

Numerical Experiments

Conclusions