P. L. Rui

A Novel Hierarchical Two-Level Spectral Preconditioning Technique for Electromagnetic Wave Scattering

A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations solved by method of moments. The hierarchical two-level spectral preconditioning technique is developed for the generalized minimal residual iterative method, in which the multilevel fast multipole method is used to accelerate matrix-vector product. The sparse approximate inverse (SAI) preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two-level manner defined on the lower order basis functions. The spectral preconditioner is combined with SAI preconditioner to obtain a hierarchical two-level spectral preconditioner. Numerical experiments indicate that the new preconditioner can significantly reduce both the iteration number and computational time.

Fast analysis of electromagnetic scattering of 3-D dielectric bodies with augmented GMRES-FFT method

The problem of electromagnetic scattering by three-dimensional dielectric bodies is formulated in terms of a weak formulation of the domain-integral equation. Applying Galerkins method with rooftop functions as basis and testing functions, the integral equation can be solved by the Krylov-subspace iterative fast Fourier transform (FFT) methods. However, poor convergence is observed when the relative permittivity of the scatterer becomes large. In order to relieve this trouble, an augmented generalized minimum residual method (AGMRES) is presented. Comparisons between several typical iterative methods are made to show the efficiency of our proposed method.

Spectral Two-Step Preconditioning of Multilevel Fast Multipole Algorithm for the Fast Monostatic RCS Calculation

A new spectral two-step preconditioning of multilevel fast multipole algorithm (MLFMA) is proposed to solve large dense linear systems with multiple right-hand sides arising in monostatic radar cross section (RCS) calculations. The first system is solved with a deflated generalized minimal residual (GMRES) method and the eigenvector information is generated at the same time. Based on this eigenvector information, a spectral preconditioner is defined and combined with a previously constructed sparse approximate inverse (SAI) preconditioner in a two-step manner, resulting in the proposed spectral two-step preconditioner. Restarted GMRES with the newly constructed spectral two-step preconditioner is considered as the iterative method for solving subsequent systems and the MLFMA is used to speed up the matrix-vector product operations. Numerical experiments indicate that the new preconditioner is very effective with the MLFMA and can reduce both the iteration number and the computational time significantly.

A Spectral Multigrid Method Combined With MLFMM for Solving Electromagnetic Wave Scattering Problems

A new spectral multigrid method (SMG) combined with the multilevel fast multipole method (MLFMM) is proposed for solving electromagnetic wave scattering problems. The MLFMM is used to speed up the matrix-vector product operations and the SMG is employed to accelerate the convergence rate of the Krylov iteration. Unlike traditional algebraic multigrid methods (AMG), the spectral multigrid method is an algebraic two-grid cycle built on a preconditioned Krylov iterative method that is used as the smoother, and the grid transfer operators are defined using the spectral information of the preconditioned matrix. Numerical experiments indicate that this class of multigrid method is very effective with the MLFMM and can reduce both the iteration number and the overall simulation time significantly.

Application of SSOR preconditioned GMRESR algorithm for FEM Analysis of Helmholtz Equations

In this paper, an efficient variant of the generalized minimal residual method, which is the GMRESR iterative method has been proposed and demonstrated to solve the large, sparse matrix equation obtained from an ungauged formulation of FEM analysis Helmholtz Equations. The performance of variable preconditioning for GMRESR method is further improved by using an efficient symmetric successive over-relaxation (SSOR) preconditioning for the inner GMRES method. Several electromagnetic structures are analyzed and good convergence improvement is achieved in terms of both the iteration number and CPU time

Three-Dimensional Weak-Form GMRESIR-FFT for EM Scattering

A weak-form GMRESIR-FFT method is developed for iterative solution of 3D volume electric field integral equation. Approximate eigenvectors are employed by using implicit restarting scheme to alleviate the ill effect of restarting in GMRES iteration process, and hence improves convergence. Numerical experiments are conducted, which show that GMRESIR-FFT is more efficient and robust than the conventional CG-FFT and BCG-FFT methods

Scattering of 3D Dielectric Body by GMRES and LGMRES Weak-Form FFT Methods

This paper aims to develop a fast and robust algorithm for three-dimensional problems, especially for large-permittivity case. We adopt the generalized minimum residual (GMRES) and loose GMRES to replace the CG or BCG method to solve the integral equation, and investigate their efficiency in the application. We show that all methods produce accurate results and when the contrast is high, the loose GMRES has a superior behavior among the different iterative methods

An Effective Sparse Approximate Inverse Preconditioner for Vector Finite Element Analysis of 3D EM Problems

In this paper, we consider a new approach to choose the priori sparsity pattern, and present a pre- and post-filtration technique for sparse approximate inverse (SAI) implementation to alleviate this difficulty. Experiment shows that these tricks are very effective when combined with conjugate gradient (CG) method to solve 3D electromagnetic field (EM) problems

Three-Dimensional Weak-Form DRGMRES-NUFFT for Volume Integral Equations

In this paper, the deflated restarting GMRES (DRGMRES) iterative method, combined with the nonuniform FFT (NUFFT) algorithms, is first proposed to solve 3D weak-form volume electric field integral equations in electromagnetic scattering problems. Numerical experiments for problems with both large and small regions are conducted, which shows the advantage of the NUFFT over the conventional FFT methods and the efficiency of DRGMRES for improving convergence of the standard GMRES

Fast analysis of microstrip antenna array by use of the adaptive integral method (AIM) combined with the loose GMRES method

The large-scale microstrip antenna array is analyzed by use of the adaptive integral method (AIM). The resulting integral equations are then solved by the loose generalized minimal residual (LGMRES) method to accelerate iteration. One typical microstrip antenna array is analyzed and the good results demonstrate the validity of the proposed algorithm. Our numerical calculations show that the LGMRES can converge about 6 times faster than the conjugate gradient (CG) method.