Accelerated integral equation techniques for solving EM wave propagation and scattering problems

This dissertation focuses on the development of the robust, efficient and accurate numerical methods of EM wave propagation and scattering from urban, rural areas and random rough surfaces. There are four main contributions of this dissertation. - The Improved Tabulated Interaction Method (ITIM) is proposed to compute EM wave propagation over lossy terrain profiles using a coupled surface integral equation formulation. The ITIM uses a common set of basis functions in conjunction with a simple matching technique to compress the original system to a reduced system containing considerably smaller number of unknowns and therefore provide a very efficient and accurate method. - Initial efforts in using the full-wave method to compute EM wave propagation over urban areas. The un-accelerated full-wave method has a massive computational burden. In order to reduce the computational complexity, Generalized Forward Backward Method (GFBM) is applied (note that the conventional Forward Backward Method diverges in this scenario). - The Improved Forward Backward Method with Spectral Acceleration (FBM-SA) is proposed to solve the problem of 2D wave scattering from random lossy rough surfaces. - An efficient and accurate iterative method is proposed for computing the 3D wave scattering from 2D dielectric random rough surfaces. The proposed method referred to as the Block Forward Backward Method improves the convergence of the 3D FBM, makes it converge for the case of 2D dielectric surfaces. In addition the Spectral Acceleration is also modified and combined with the BFBM to reduce the computational complexity of the proposed method

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

Electromagnetic Wave Theory and Applications

Contains reports on twelve research projects.Joint Services Electronics Program (Contract DAALO3-86-K-0002)National Science Foundation (Grant ECS 85-04381)National Aeronautics and Space Administration/Goddard Space Flight Center (Contract NAG5-270)National Aeronautics and Space Administration/Goddard Space Flight Center (Contract NAG5-725)U.S. Navy - Office of Naval Research (Contract N00014-83-K-0258)U.S. Navy - Office of Naval Research (Contract N00014-86-K-0533)U.S. Army - Research Office Durham (Contract DAAG29-85-K-0079)International Business Machines, Inc.National Aeronautics and Space Administration/Goddard Space Flight Center (Contract NAG5-269)Simulation TechnologiesSchlumberger-Doll Researc

Microwave remote sensing of earth terrain

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1984.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.Vita.Bibliography: leaves 307-318.by Robert Tong-Ik Shin.Ph.D

Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with/without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational e±ciency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91459/1/xduan_1.pd

Electromagnetic Wave Theory and Applications

Contains table of contents for Section 3, research summary and reports on six research projects.Joint Services Electronics Program (Contract DAAL 03-86-K-0002)Joint Services Electronics Program (Contract DAAL 03-89-C-0001)U.S. Navy - Office of Naval Research (Contract N00014-86-K-0533)National Science Foundation (Contract ECS 86-20029)U.S. Army Research Office (Contract DAAL03 88-K-0057)International Business Machine CorporationSchlumberger-Doll ResearchNational Aeronautics and Space Administration (Contract NAG 5-270)U.S. Navy - Office of Naval Research (Contract N00014-83-K-0258)National Aeronautics and Space Administration (Contract NAG 5-769)U.S. Army Corps of Engineers - Waterways Experimental Station (Contract DACA39-87-K-0022)Simulation TechnologiesU.S. Air Force - Rome Air Development Center (Contract F19628-88-K-0013)U.S. Navy - Office of Naval Research (Contract N00014-89-J-1107)Digital Equipment Corporatio

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135885/1/srtan_1.pd

Parameter Optimization of a Discrete Scattering Model by Integration of Global Sensitivity Analysis Using SMAP Active and Passive Observations

Active and passive microwave signatures respond differently to the land surface and provide complementary information on the characteristics of the observed scenes. The objective of this paper is to explore the synergy of active radar and passive radiometer observations at the same spatial scale to constrain a discrete radiative transfer model, the Tor Vergata (TVG) model, to gain insights into the microwave scattering and emission mechanisms over grasslands. The TVG model can simultaneously simulate the backscattering coefficient and emissivity with a set of input parameters. To calibrate this model, in situ soil moisture and temperature data collected from the Maqu area in the northeastern region of the Tibetan Plateau, interpolated leaf area index (LAI) data from the Moderate Resolution Imaging Spectroradiometer LAI eight-day products, and concurrent and coincident Soil Moisture Active Passive (SMAP) radar and radiometer observations are used. Because this model needs numerous input parameters to be driven, the extended Fourier amplitude sensitivity test is first applied to conduct global sensitivity analysis (GSA) to select the sensitive and insensitive parameters. Only the most sensitive parameters are defined as free variables, to separately calibrate the active-only model (TVG-A), the passive-only model (TVG-P), and the active and passive combined model (TVG-AP). The accuracy of the calibrated models is evaluated by comparing the SMAP observations and the model simulations. The results show that TVG-AP can well reproduce the backscattering coefficient and brightness temperature, with correlation coefficients of 0.87, 0.89, 0.78, and 0.43 and root-mean-square errors of 0.49 dB, 0.52 dB, 7.20 K, and 10.47 K for σ HH⁰ , σ VV⁰ , TBH, and TBV, respectively. In contrast, TVG-A and TVG-P can only accurately model the backscattering coefficient and brightness temperature, respectively. Without any modifications of the calibrated parameters, the error metrics computed from the validation data are slightly worse than those of the calibration data. These results demonstrate the feasibility of the synergistic use of SMAP active radar and passive radiometer observations under the unified framework of a physical model. In addition, the results demonstrate the necessity and effectiveness of applying GSA in model optimization. It is expected that these findings can contribute to the development of model-based soil moisture retrieval methods using active and passive microwave remote sensing data

Robust simulation methodology for surface-roughness loss in interconnect and package modelings

In multigigahertz integrated-circuit design, the extra energy loss caused by conductor surface roughness in metallic interconnects and packagings is more evident than ever before and demands explicit consideration for accurate prediction of signal integrity and energy consumption. Existing techniques based on analytical approximation, despite simple formulations, suffer from restrictive valid ranges, namely, either small or large roughness/frequencies. In this paper, we propose a robust and efficient numerical-simulation methodology applicable to evaluating general surface roughness, described by parameterized stochastic processes, across a wide frequency band. Traditional computation-intensive electromagnetic simulation is avoided via a tailored scalar-wave modeling to capture the power loss due to surface roughness. The spectral stochastic collocation method is applied to construct the complete statistical model. Comparisons with full wave simulation as well as existing methods in their respective valid ranges then verify the effectiveness of the proposed approach. © 2009 IEEE.published_or_final_versio

Design Data Collection with Skylab Microwave Radiometer-Scatterometer S-193, Volume 1

The author has identified the following significant results. Observations with S-193 have provided radar design information for systems to be flown on spacecraft, but only at 13.9 GHz and for land areas over the United States and Brazil plus a few other areas of the world for which this kind of analysis was not made. Observations only extended out to about 50 deg angle of incidence. The value of a sensor with such a gross resolution for most overland resource and status monitoring systems seems marginal, with the possible exception of monitoring soil moisture and major vegetation variations. The complementary nature of the scatterometer and radiometer systems was demonstrated by the correlation analysis. Although radiometers must have spatial resolutions dictated by antenna size, radars can use synthetic aperture techniques to achieve much finer resolutions. Multiplicity of modes in the S-193 sensors complicated both the system development and its employment. An attempt was made in the design of the S-193 to arrange optimum integration times for each angle and type of measurement. This unnecessarily complicated the design of the instrument, since the gains in precision achieved in this way were marginal. Either a software-controllable integration time or a set of only two or three integration times would have been better