Steepest Descent Fast Multipole Method Research Articles

Multiple-incidence and multifrequency for profile reconstruction of random rough surfaces using the 3-D electromagnetic fast multipole model

A fast algorithm for reconstructing the profile of random rough surfaces using electromagnetic scattering data is presented. The algorithm is based on merging a fast forward solver and an efficient optimization technique. The steepest descent fast multipole method is used as the three-dimensional fast forward solver. A rapidly convergent descent method employing a "marching-on" strategy for processing multifrequency and multi-incidence angle data is introduced to minimize an underlying cost function. The cost function represents the error between true (synthetic) and simulated scattered field data. Several key issues that impact the accuracy in reconstructing the rough profile are examined in this work, e.g., the location and number of receivers, the incident and scattered directions, the surface roughness, and details regarding the manner in which sensitivity information is computed in the inversion scheme. The results show that using the multiple-incidence (one angle at a time) and the multifrequency (one frequency at a time) strategies lead to improve the profile reconstruction.

Statistical distributions of fields in urban environment based on Monte Carlo simulations of Maxwell equations

We studied wave propagation in an urban environment based on Monte Carlo simulations of Maxwell's equations. The multilevel steepest descent fast multipole method (ML/SD/FMM) is used in the computations. The building profile is about 2 km in length and the frequency is 900 MHz. Numerical results are statistically analyzed to study the spatial variations, including fast fading, shadow fading, and range dependence. The results are compared with the Rayleigh, Rician, and lognormal distributions.

Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces

A rigorous electromagnetic model has been used to analyze the scattering from two dielectric shallow objects buried under the two-dimensional (2-D) random rough ground (3-D scattering problem) as a means of predicting false alarms. The method of moments (MoM) accelerated by the steepest descent fast multipole method (SDFMM) is used to compute the equivalent electric and magnetic surface currents on all scatterers (i.e., the rough ground and the two buried objects). The roughness parameters influence the scattering interference mechanism of the two objects, however, a large separation distance (e.g., several correlation lengths) showed stronger effect for small ground roughness.

Scattering from multiple objects buried beneath two-dimensional random rough surface using the steepest descent fast multipole method

Generalized formulations are presented to analyze the electric field scattered from multiple penetrable shallow objects buried beneath two-dimensional random rough surfaces. These objects could have different materials, shapes, or orientations. In addition, their separation distance may range from a fraction of a wavelength to several wavelengths. The fast algorithm, steepest descent fast multipole method (SDFMM), is used to compute the unknown electric and magnetic surface currents on the rough ground surface and on the buried objects. Parametric investigations are presented to study the effect of the objects proximity, orientations, materials, shapes, the incident waves polarization, and the ground roughness on the scattered fields. A significant interference is observed between the objects when they are separated by less than one free space wavelength. Even when the clutter due to the rough ground is removed, the return from the second object, can be dominating causing a possible false alarm in detecting the target. The results show that the distortion in target signature significantly increases with the increase of both the proximity to a clutter item and the ground roughness.

Monte Carlo simulations for clutter statistics in minefields: AP-mine-like-target buried near a dielectric object beneath 2-D random rough ground surfaces

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on the target and on the clutter object. A comprehensive numerical investigation of two clutter sources; the ground roughness and the nearby benign object, is presented based on using more than 800 random rough surface realizations which could not be achieved without using fast algorithms such as the SDFMM. The statistics of the scattered near-electric fields are computed using the Monte Carlo simulations for both polarizations. For the parameters used here, the results show that the average and the standard deviation of the target signature represent 5-7% and 3-3.5% of the total scattered signal, respectively, while they represent 16-20% and 7-12% of the signal for the clutter object, respectively. This study indicates the high possibility of a false alarm during the detection process when the target is located nearby a realistic object such as a piece of a tree root.

The multiple interaction model for nonshallow scatterers buried beneath 2-d random rough surfaces

The multiple interaction model is hybridized with the robust Steepest Descent Fast Multipole Method (SDFMM) to compute the signature of nonshallow penetrable scatterers buried beneath two-dimensional random rough surfaces. The most attractive feature of the multiple interaction model with using the SDFMM is removing the quasi-planar structure constraint for analyzing nonquasi-planar scatterers. The results show that the buried object's signature is largely due to the first interaction mechanism; however, the contribution of each additional interaction is explicitly calculated, though they may become insignificant especially for lossy background soil.

Parallel implementation of the steepest descent fast multipole method (SDFMM) on a Beowulf cluster for subsurface sensing applications

We present the parallel, MPI-based implementation of the SDFMM computer code using a thirty-two node Intel Pentium-based Beowulf cluster. The SDFMM is a fast algorithm that is a hybridization of the method of moments (MoMs), the fast multipole method (FMM), and the steepest descent integration path (SDP), which is used to solve large-scale linear systems of equations produced in electromagnetic scattering problems. An overall speedup of 7.2 has been achieved on the 32-processor Beowulf cluster and a significant reduced runtime is achieved on the 4-processor 667 MHz Alpha workstation.

Monte Carlo simulations of electromagnetic wave scattering from a random rough surface with three-dimensional penetrable buried object: mine detection application using the steepest-descent fast multipole method.

We present a statistical study of the electric field scattered from a three-dimensional penetrable object buried under a two-dimensional random rough surface. Monte Carlo simulations using the steepest-descent fast multipole method (SDFMM) are conducted to calculate the average and the standard deviation of the near-zone scattered fields. The SDFMM, originally developed at the University of Illinois at Urbana-Champaign, has been modified to calculate the unknown surface currents both on the rough ground and on the buried object that are due to excitation by a tapered Gaussian beam. The rough ground medium used is an experimentally measured typical dry Bosnian soil with 3.8% moisture, while the buried object represents a plastic land mine modeled as an oblate spheroid with dimensions and burial depth smaller than the free-space wavelength. Both vertical and horizontal polarizations for the incident waves are studied. The numerical results show that the TNT mine signature is almost 5% of the total field scattered from the ground. Moreover, relatively recognizable object signatures are observed even when the object is buried under the tail of the incident beam. Interestingly, even for the small surface roughness parameters considered, the standard deviation of the object signature is almost 30% of the signal itself, indicating significant clutter distortion that is due to the roughness of the ground.

Three-dimensional subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method

The electromagnetic scattering from a three-dimensional (3D) shallow object buried under a two-dimensional (2D) random rough dielectric surface is analyzed. The buried object can be a perfect electric conductor (PEC) or can be a penetrable dielectric with size and burial depth comparable to the free-space wavelength. The random rough ground surface is characterized with Gaussian statistics for surface height and for surface autocorrelation function. The Poggio, Miller, Chang, Harrington, and Wu (PMCHW) integral equations are implemented and extended. The integral equation-based steepest descent fast multipole method (SDFMM), that was originally developed at UIUC, has been used and the computer code based on this algorithm has been successfully modified to handle the current application. The significant potential of the SDFMM code is that it calculates the unknown moment method surface electric and magnetic currents on the scatterer in a dramatically fast, efficient, and accurate manner. Interactions between the rough surface interface and the buried object are fully taken into account with this new formulation. Ten incident Gaussian beams with the same elevation angle and different azimuth angles are generated for excitation as one possible way of having multiple views of a given target. The scattered electric fields due to these ten incident beams are calculated in the near zone and their complex vector average over the multiple views is computed. The target signature is obtained by subtracting the electric fields scattered from the rough ground only from those scattered from the ground with the hurled anti-personnel mine.

Modeling Clutter from Bosnian and Puerto Rican Rough Ground Surfaces for GPR Subsurface Sensing Applications Using the SDFMM

The Steepest Descent Fast Multipole Method (SDFMM) is used to analyze the distorting effect of random rough ground surfaces on scattered and transmitted electromagnetic waves. Two well-measured loamy soils: Bosnian and Puerto Rican clay loam are investigated, each with a variety of surface roughness. This study is important in understanding the effects of different soil properties and is meant to be an a priori phase of investigating scattering from buried targets under the rough ground. In this work, we investigated the scattering from rough soil ground without buried objects. The SDFMM is an integral equation-based fast algorithm that is well suited for two-dimensional penetrable rough surfaces (3-D scattering) in the frequency domain. The scattered and transmitted near electric field of an incident Gaussian beam are calculated at different locations above and below the mean plane of the dielectric rough interface. The receiver locations above are chosen to simulate GPR measurement protocols. The obtained numerical results show that the scattered field undergoes more distortion than the transmitted field from both soil types. Moreover, the transmitted fields into the higher dielectric constant Puerto Rican soil experience more distortion than those transmitted into Bosnian soil.

Two-dimensional rough surface couplers for broadband quantum-well infrared photodetectors

Rough surfaces are proposed as a class of couplers for achieving high absorption in broadband quantum-well infrared photodetectors (QWIPs). The performance of these structures is predicted numerically using the steepest-descent fast-multipole method, a recently developed fast electromagnetic analysis technique. This method permits the efficient and accurate solution of the electric-field integral equation governing scattering from a quasiplanar structure. The scattered optical electric-field component along the growth direction at the device layer can be used to predict the QWIP absorption. It is demonstrated that rough-surface couplers exhibit very high absorption sustained over large spectral ranges, in contrast to quasirandom or periodic gratings that are characterized by tradeoffs between peak absorption and spectral range. It is expected that the excellent spectral absorption characteristics of rough-surface couplers will make them particularly suitable for broadband QWIP applications.

A combined steepest descent-fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces

A new technique, the steepest descent-fast multipole method (SDFMM), is developed to efficiently analyze scattering from perfectly conducting random rough surfaces. Unlike other prevailing methods, this algorithm has linear computational complexity and memory requirements, making it a suitable candidate for analyzing scattering from large rough surfaces as well as for carrying out Monte Carlo simulations. The method exploits the quasiplanar nature of rough surfaces to efficiently evaluate the dyadic Green's function for multiple source and observation points. This is achieved through a combination of a Sommerfeld steepest descent integral and a multilevel fast multipole-like algorithm based on inhomogeneous plane wave expansions. The fast evaluation of the dyadic Green's function dramatically speeds up the iterative solution of the integral equation for rough surface scattering. Several numerical examples are presented to demonstrate the efficacy and accuracy of the method in analyzing scattering from extremely large finite rough surfaces.

Efficient electromagnetic analysis of two-dimensional finite quasi-random gratings for quantum well infrared photodetectors

In this work, a recently developed full-wave electromagnetic analysis technique is applied to the simulation of two-dimensional finite quasi-random gratings for quantum well infrared photodetectors. This steepest descent fast multipole method is a mathematically rigorous technique that permits the rapid and accurate solution of the electric field integral equation governing scattering from a quasi-planar structure. In the present application, it enables the efficient and accurate simulation of scattering by finite two-dimensional grating structures interfacing with GaAs. Grating absorption is predicted by evaluating the scattered optical electric field component at the device layer along the growth direction. Numerical examples illustrating the functional dependence of the absorption on grating parameters and wavelength are discussed. The simulation approach presented here should prove to be a useful tool for the a priori design of novel aperiodic, quasi-random and rough surface two-dimensional gratings for infrared imaging applications.