Fast algorithm for scattering from planar arrays of conducting patches

Cataloged from PDF version of article.A direct (noniterative) algorithm for the solution of the electromagnetic scattering from three-dimensional planar arrays of conducting patches is developed. For an N-unknown problem, the computational complexity of this new solution technique is shown to be O(N2 log2N), which is considerably lower than the O(N3) computational complexity of the conventional direct solution techniques. The advantages of the reduction in the computational complexity is pronounced in the solution of large electromagnetics problems, such as scattering from large and finite arrays of patches, synthesis and analysis of finite-sized frequency selective surfaces (FSS’s), and radiation and scattering from large phased-array antennas, to name a few

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure

Scattering of Ocean Surfaces in Microwave Remote Sensing by Numerical Solutions of Maxwell Equations

Sea-surface scattering has long been studied using various analytical methods. These analytical methods include the two scale method (TSM), the small-slope approximation (SSA), the small-perturbation method (SPM), the Advanced Integral Equation Method (AIEM), and the Geometrical/Physical Optics (GO/PO) method. These analytical methods rely on making approximations and assumptions in the modelling process. Some of these assumptions undermine their applicability in a wide range of situations. The input for analytical methods are usually the ocean spectrum. In real implementations, there are 2 sources of uncertainty in such approaches: (1) the analytical methods have a limited range of applicability to the surface scattering problem; the approximations made in these methods are questionable and (2) the various ocean spectra are another source of uncertainty. We earlier applied a numerical method in 3-dimensions (NMM3D) to the scattering problem of soil surfaces. Through comparison with measured data, we established the accuracy and applicability of NMM3D. We see a drastic increase of ocean remote sensing applications in recent years. It is thus feasible to extend NMM3D to the sea-surface scattering problem. Compared to soil, sea water has a much higher permittivity, e.g., 75+61i at L-band. The large permittivity dictates the need for using a much denser mesh for the sea surface. In addition, the root mean square (rms) height of the sea surface is large under moderate to high ocean wind speeds, which requires a large simulation area to account for the influence of long scale wave like gravity waves. Compared to the two-scale model commonly used for the ocean scattering problem, NMM3D does not need an ad-hoc split wavenumber in the ocean spectrum. Combined with a fast computational algorithm, it was shown that NMM3D can produce accurate results compared to measured data like the Aquarius missions. TSM could also match well with Aquarius provided with a pre-selected splitting wavenumber. But it was observed that the result of TSM changes with different splitting wavenumbers. It is seen that TSM is fairly heuristic while NMM3D can serve as an exact method for the scattering problem. On the other hand, through our study of NMM3D, we found that with a fine grid, the final impedance matrix converges slowly and also it becomes hard to perform simulations for a large surface. This has provoked us to (1) solve low convergence problem for a dense mesh and (2) resolve difficulties in simulations of large surfaces. Inspired by the existing impedance boundary condition (IBC) method, we proposed a neighborhood impedance boundary condition (NIBC) method to solve the slow convergence problem caused by the dense grid. Different from IBC where the surface electric field and the surface magnetic field are related locally, NIBC relates the surface electric field to the magnetic field within a preselected bandwidth BW. Through numerical simulations, we found that the condition number can be reduced using NIBC. Errors of NIBC are controllable through changing BW. We applied NIBC to various wind speeds and surface types and found NIBC to be quite accurate when surface currents only suffer an error norm of less than 1%.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145797/1/qiaot_1.pd

Fast Algorithm for Scattering from Planar Arrays of Conducting Patches

A direct (noniterative) algorithm for the solution of the electromagnetic scattering from three-dimensional planar arrays of conducting patches is developed. For an N-unknown problem, the computational complexity of this new solution technique is shown to be O(N2 log2N), which is considerably lower than the O(N3) computational complexity of the conventional direct solution techniques. The advantages of the reduction in the computational complexity is pronounced in the solution of large electromagnetics problems, such as scattering from large and finite arrays of patches, synthesis and analysis of finite-sized frequency selective surfaces (FSS's), and radiation and scattering from large phased-array antennas, to name a few

FURTHER INVESTIGATION ON MAGNETICALLY INDUCED SUBSEQUENT FAULT AND STUDY ON ELECTROMAGNETIC SCATTERING OF OBJECTS BURIED BELOW A RANDOM ROUGH SURFACE

This dissertation contains two subjects: further development of numerical technique for the analysis of magnetically induced subsequent fault (MISFault) in overhead power lines and its implementation into a software upgrade; and first-phase of study on the electromagnetic scattering from objects buried below a random rough surface making use of the multidomain pseudospectral time domain (PSTD) method and Monte-Carlo simulation. An initial electric fault can result in strong magnetic torque on the overhead power line conductors, which will make them swing and may bring them to close proximity or in contact with one another, causing a subsequent fault. In Chapter 2, Computer simulations for the analysis of the subsequent fault in transition spans, which are often required in power line topology, are developed. A dynamic analysis of swing movement of power line conductors subsequent to an initial fault is presented to track the smallest distance between the conductors. In Chapter 3, the simulation is implemented into the upgrade of the MISFault analysis software. Its functions are depicted in details. The MISFault software is being used by Duke Energy Company and is expected to be useful to a utility for eliminating the magnetically induced subsequent faults. The multidomain pseudospectral time domain (PSTD) method has been developed and successfully applied to solve a variety of electromagnetic scattering problems in the past decade. It is a novel algorithm with improvement over traditional FDTD method. In Chapter 4, a multidomain PSTD algorithm is developed to investigate the scattering from a 2-D cylinder in free space. Sample numerical results are presented and validated. Then, the theoretical derivations are extended for the analysis of scattering from 2-D objects buried below a random rough surface

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

Study on Electromagnetic Scattering of Cylinders Buried in a Half Space with Random Rough Surfaces of Finite/Infinite Length

Analysis of electromagnetic scattering of buried objects is a subject of great interest due to its practical importance in both military and civil applications, such as subsurface investigation and target detection. In reality, the earth is of layered structure of random rough interfaces, which leads to a greatly increased complexity of the analysis. However, it is necessary to incorporate the nature of random rough surface and the layered structure because they both have substantial impact on the scattered signature and hence affect the study of inverse scattering and detection of buried objects. In this dissertation, a Monte-Carlo multidomain pseudospectral time domain (MPSTD) method is developed for investigating the scattering from cylinders buried below a random rough surface separating two half spaces under various conditions. As a prelude, the formulation of multidomain PSTD algorithm is presented. Then, this formulation is extended and combined with the Monte-Carlo approach to analyze the scattering of an object buried below a random rough surface of finite length. In the analysis, special attention is paid to the treatments of the random rough surface including its profile generation, matching with CGL points, and subdomain patching. Next, the scattering of a cylinder buried below a random rough surface of infinite length is studied and a two-step computation model based on the Monte-Carlo MPSTD method is developed. Further, in order to better simulate the real situation, the analysis is then extended to study the scattering from one or more cylinders embedded in a layered half space with random rough surfaces. Finally, a near-zone field to far-zone field transformation technique is developed and presented. Sample numerical results under different conditions, involving random rough surface of various roughness, lower half space with different permittivities, and cylinders of circular and rectangular shapes are presented, validated, and analyzed. Throughout this research, a numerical technique based on Monte-Carlo method and MPSTD approach has been developed and validated for investigating cylinders buried in a half space with random rough surfaces. It is observed that the roughness of the random rough surface and the electromagnetic properties of the lower half space can significantly affect the scattered signature of the buried object

Time-Domain Physical Optics Method for the Analysis of Wide-Band EM Scattering from Two-Dimensional Conducting Rough Surface

Time-domain physical optics (TDPO) method is extended to investigate electromagnetic (EM) scattering from two-dimensional (2D) perfectly electrically conducting (PEC) rough surface in both time domain and frequency domain. The scheme requires relatively small amounts of computer memory and CPU time, and has advantage over the Kirchhoff Approximation (KA) method in obtaining transient response of rough surface by a program run. The 2D Gaussian randomly rough surface is generated by Monte Carlo method and then is partitioned into small triangle facets through the meshing preprocess. The accuracy of TDPO is validated by comparing the numerical results with those obtained by the KA method in both backward and specular directions. The transient response and its frequency distribution of radar cross section (RCS) from rough surface is shown, respectively. The scattering results from rough surface with different size in the specular direction are given. The influence of the root mean square height (σ) and correlation length (l) on electromagnetic scattering from PEC rough surface is discussed in detail. Finally, the comparisons of backscattering results at different incident angles are presented and analyzed