Study of multilevel Green's function interpolation method for efficient analysis of large-scale electromagnetic problems

Abstract

The purpose of this research work is to study efficient algorithms for the analysis of electromagnetic problems. Solving these electromagnetic problems, which are usually large-scale, is a big challenge for the simulation tools due to their high computational requirements. Various fast methods have been proposed in recent years; among which, a kernel independent approach named multilevel Green's function interpolation method (MLGFIM) has been developed to address large-scale electromagnetic problems. This method achieves a computational efficiency of O(NlogN) and has a memory requirement of O(N). Because of its flexibility for multilayered and sparsely distributed multibody problem simulation, MLGFIM can be applied to a wide range of applications, including antenna design, radar cross section (RCS) calculation, electromagnetic compatibility analysis, and frequency selective surface simulation. For this study, we first investigate the suitability of MLGFIM for parallel computing. A parallelized MLGFIM algorithm using message-passing interface is developed. This algorithm, which is based on hybrid integral equation, is applied to accelerate the analysis of metallic objects composed of open surface, closed surface, and coexisting open and closed surfaces. Some issues are discussed to achieve an efficient parallelization of MLGFIM. In addition, extended radial basis function (RBF) interpolation method, in which a polynomial term is augmented, is introduced for the Green's function interpolation. This method guarantees that the interpolation coefficients are uniquely determined. The comparison of Bessel (BE) RBFs of different orders shows that interpolation using BE RBF of order zero can achieve better interpolation accuracy than previously used BE RBF when the group length is shorter than a wavelength. Numerical examples, such as the bistatic RCS of the structure consisting of a sphere over a square patch, and the electric field in a reverberation chamber, have been given to validate the accuracy and show the efficiency of the parallelized MLGFIM algorithm. Apart from applying parallel computing, it is more important to enhance the efficiency of MLGFIM itself. The key factor influencing the efficiency of the full-wave MLGFIM is the implementation of an appropriate interpolation scheme to efficiently approximate the Green's function. A new interpolation grid pattern, called boundary clustered staggered Tartan grid (BCSTG), is proposed to improve the performance of the Green's function interpolation. By adopting BCSTG, the required number of interpolation points is greatly reduced. And consequently, the efficiency of MLGFIM is significantly enhanced. In addition to being capable of analyzing metallic objects, the improved MLGFIM can also simulate composite metallic and dielectric objects using Poggio-Miller-Chang-Harrington-Wu-Tsai integral equations. Given that the implementation of large group interpolation requires a large number of interpolation points, ill-conditioning problems are always encountered in this case. The compromise of making the basis functions relatively less smooth has been used in the previous RBF interpolations to address this problem. A stable RBF approach, called RBF-QR algorithm is proposed to resolve the ill-conditioning issue without such a compromise. The RBF-QR algorithm exhibits better interpolation performance compared with the previous methods. In addition, to remedy the weakness of grid pattern (viz., oversampling of interpolation points lower the interpolation efficiency), a hybrid interpolation pattern consisting of BCSTG and Halton points is adopted in MLGFIM. With the proposed interpolation scheme, the finite periodic structures, which are always large in size, can be solved efficiently through MLGFIM. Finally, the MLGFIM is applied to simulate the infinite periodic structures. The Floquet theorem is adopted so that only the unknowns within a unit cell need to be considered. The problem is formulated using the volume surface integral equation for homogeneous dielectric and metallic objects. The periodic Green's function used in the integral equation is accelerated by the Ewald's transformation. The periodic Green's functions for different periodic structures are different (viz., the interpolated functions are different), so that the numerical experiment should be repeated in the preprocessing stage of MLGFIM to determine the optimum shape of RBFs when the problem type is changed, for instant, an increase in the structure periodicity. This makes the MLGFIM cumbersome for the simulations of periodic structures. We address this problem by using the aforementioned RBF-QR method because it is insensitive to the shape of RBFs. Consequently, MLGFIM becomes more robust for the analysis of infinite periodic structures. Numerical examples are given to validate the effectiveness of this method.

Date of Award	14 Feb 2014
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Chi Hou CHAN (Supervisor)