Accelerated iterative solvers for the solution of electromagnetic scattering and wave propagation propagation problems

The aim of this work is to contribute to the development of accelerated iterative methods for the solution of electromagnetic scattering and wave propagation problems. In spite of recent advances in computer science, there are great demands for efficient and accurate techniques for the analysis of electromagnetic problems. This is due to the increase of the electrical size of electromagnetic problems and a large amount of design and analytical work dependent on simulation tools. This dissertation concentrates on the use of iterative techniques, which are expedited by appropriate acceleration methods, to accurately solve electromagnetic problems. There are four main contributions attributed to this dissertation. The first two contributions focus on the development of stationary iterative methods while the other two focus on the use of Krylov iterative methods. The contributions are summarised as follows: • The modified multilevel fast multipole method is proposed to accelerate the performance of stationary iterative solvers. The proposed method is combined with the buffered block forward backward method and the overlapping domain decomposition method for the solution of perfectly conducting three dimensional scattering problems. The proposed method is more efficient than the standard multilevel fast multipole method when applied to stationary iterative solvers. • The modified improvement step is proposed to improve the convergence rate of stationary iterative solvers. The proposed method is applied for the solution of random rough surface scattering problems. Simulation results suggest that the proposed algorithm requires significantly fewer iterations to achieve a desired accuracy as compared to the conventional improvement step. • The comparison between the volume integral equation and the surface integral equation is presented for the solution of two dimensional indoor wave propagation problems. The linear systems resulting from the discretisation of the integral equations are solved using Krylov iterative solvers. Both approaches are expedited by appropriate acceleration techniques, the fast Fourier transform for the volumetric approach and the fast far field approximation for the surface approach. The volumetric approach demonstrates a better convergence rate than the surface approach. • A novel algorithm is proposed to compute wideband results of three dimensional forward scattering problems. The proposed algorithm is a combination of Krylov iterative solvers, the fast Fourier transform and the asymptotic waveform evaluation technique. The proposed method is more efficient to compute the wideband results than the conventional method which separately computes the results at individual frequency points

Accelerated direct solution of the method-of-moments linear system

This paper addresses the direct (noniterative) solution of the method-of-moments (MoM) linear system, accelerated through block-wise compression of the MoM impedance matrix. Efficient matrix block compression is achieved using the adaptive cross-approximation (ACA) algorithm and the truncated singular value decomposition (SVD) postcompression. Subsequently, a matrix decomposition is applied that preserves the compression and allows for fast solution by backsubstitution. Although not as fast as some iterative methods for very large problems, accelerated direct solution has several desirable features, including: few problem-dependent parameters; fixed time solution avoiding convergence problems; and high efficiency for multiple excitation problems [e.g., monostatic radar cross section (RCS)]. Emphasis in this paper is on the multiscale compressed block decomposition (MS-CBD) algorithm, introduced by Heldring , which is numerically compared to alternative fast direct methods. A new concise proof is given for the N2 computational complexity of the MS-CBD. Some numerical results are presented, in particular, a monostatic RCS computation involving 1 043 577 unknowns and 1000 incident field directions, and an application of the MS-CBD to the volume integral equation (VIE) for inhomogeneous dielectrics.Peer Reviewe

Accelerated direct solution of the method-of-moments linear system

This paper addresses the direct (noniterative) solution of the method-of-moments (MoM) linear system, accelerated through block-wise compression of the MoM impedance matrix. Efficient matrix block compression is achieved using the adaptive cross-approximation (ACA) algorithm and the truncated singular value decomposition (SVD) postcompression. Subsequently, a matrix decomposition is applied that preserves the compression and allows for fast solution by backsubstitution. Although not as fast as some iterative methods for very large problems, accelerated direct solution has several desirable features, including: few problem-dependent parameters; fixed time solution avoiding convergence problems; and high efficiency for multiple excitation problems [e.g., monostatic radar cross section (RCS)]. Emphasis in this paper is on the multiscale compressed block decomposition (MS-CBD) algorithm, introduced by Heldring , which is numerically compared to alternative fast direct methods. A new concise proof is given for the N2 computational complexity of the MS-CBD. Some numerical results are presented, in particular, a monostatic RCS computation involving 1 043 577 unknowns and 1000 incident field directions, and an application of the MS-CBD to the volume integral equation (VIE) for inhomogeneous dielectrics.Peer Reviewe