Zhiqin Zhao

Analysis of scattering from very large three-dimensional rough surfaces using MLFMM and ray-based analyses

Several techniques are considered for the analysis of electromagnetic scattering from rough ocean surfaces. A rigorous Multi-level Fast Multipole Method (MLFMM) is employed, as well as a high-frequency ray-based solution. The MLFMM analysis is implemented in scalable form, allowing consideration of scattering from very large surfaces (in excess of 100/spl lambda//spl times/100/spl lambda/, where A represents the electromagnetic wavelength). Plane-wave incidence is assumed, and a key aspect of the MLFMM study involves investigating techniques for rough-surface truncation. The rough surface is modeled as a target placed in the presence of an infinite half-space background; to minimize edge effects, the surface is smoothly tapered into the planar half space. We also consider the technique of employing a resistive taper on the edges of the rough surface. These two truncation techniques are compared in accuracy, memory requirements (RAM), and in computational time (CPU). The MLFMM results are used to validate an approximate ray-based high-frequency model that allows rapid analysis of large surfaces. The computational results are compared to measured forward-scattering data from scaled laboratory measurements, used to simulate scattering from an ocean surface.

Low-grazing-angle microwave scattering from a three-dimensional spilling breaker crest: a numerical investigation

The microwave backscattering from a three-dimensional (3-D) target approximating the rough crest of a gently spilling water wave at low grazing angle illumination has been numerically examined. The target surfaces were synthesized from the direct two-dimensional (2-D) measurement of the time evolution of the upwave-downwave cross-section of a wave-tank breaker. The reference scattering was found using the multilevel fast multipole algorithm implemented with impedance boundary conditions and resistive surface loading to suppress nonphysical edge diffraction. The scattering was compared with the predictions of the two-scale model and a synthesis of the 3-D backscattering from individual 2-D calculations. Specular reflection from a bulge feature that appeared on the crest prior to breaking dominated the backscattering at both polarizations, overwhelming even the strong vertical polarization Bragg scattering that appeared in the corresponding scattering from the individual 2-D profiles used to synthesize the 3-D target. The scattering from the surface including the bulge could be accurately modeled using a coherent addition of the scattering from the 2-D profiles. The two-scale model performed poorly whenever there are steep sections on the surface that provide significant quasi-specular back-reflection. Accuracy improved when the specular points were eliminated and the dominant scattering roughness was fully illuminated, but was still sensitive to the surface-roughness scale-separation threshold used in its application.

Resistive suppression of edge effects in MLFMA scattering from finite conductivity surfaces

The use of resistive loading to suppress edge-diffraction effects in three-dimensional numerical multilevel fast multipole algorithm calculation of scattering from arbitrary rough surfaces has been considered. The effectiveness of the loading is similar to that obtained in earlier work using a two-dimensional moment method applied to surfaces that are infinitely uniform in the azimuthal direction. The loading dramatically reduces the direct back-diffraction from the edges. However, current perturbations induced by the loading can introduce significant errors if the local angle of incidence on the leading-edge loaded area exceeds approximately 70/spl deg/. The loading is effective with finite conductivity surfaces modeled using impedance boundary conditions. The method is particularly suitable for use at high incidence (low grazing) with surfaces where the leading and trailing edges on which the loading is applied may be naturally angled downward from horizontal without affecting the scattering.

Rapid Prolate Pseudospectral Differentiation and Interpolation with the Fast Multipole Method

Pseudospectral methods utilizing prolate spheroidal wave functions as basis functions have been shown to possess advantages over the conventional pseudospectral methods based on trigonometric and orthogonal polynomials. However, the spectral differentiation and interpolation steps of the prolate pseudospectral method involve matrix-vector products, which, if evaluated directly, entail O(N2) memory requirement and computational complexity (where N is the number of unknowns utilized for discretization and interpolation). In this work we show that the fast multipole method (FMM) can be used to reduce the memory requirement and computational complexity of the prolate pseudospectral method to O(N). Example simulation results demonstrate the speed and accuracy of the resulting fast prolate pseudospectral solver.

Resistive treatment of edges in MLFMA LGA scattering from finite conductivity 2D surfaces

Several approaches have been used to reduce or eliminate the effects of artificial surface-truncation edges on the numerically calculated scattering from rough surfaces. Some approaches become quite expensive at low grazing angles (LGA). We consider the suppression of edge effects using resistive loading in the numerical scattering from two-dimensionally rough surfaces. The multi-level fast multipole approach (MLFMA) (see Song, J.M. and Chew, W.C., Microwave and Optical Technology Letters, vol.10, no.1, p.14-19, 1995) is applied to two-dimensional surfaces that approximate breaking water waves. Two different resistive-loading schemes are considered. In the first, the loading is applied only to the front and back edges (in range) of the wave, and the azimuthal edges are suppressed using a Gaussian illumination window. In the second, the resistive loading is applied to both the range and azimuthal edges. In both cases, where applicable, the results are verified through a comparison with the results of the 1D MM/GTD approach (see West, J.C., IEEE Trans. on GRS, vol.38, no.4, p.1609-16, 2000).

Volumetric fast multipole method for modeling Schrödinger's equation

A volume integral equation method is presented for solving Schrodingers equation for three-dimensional quantum structures. The method is applicable to problems with arbitrary geometry and potential distribution, with unknowns required only in the part of the computational domain for which the potential is different from the background. Two different Greens functions are investigated based on different choices of the background medium. It is demonstrated that one of these choices is particularly advantageous in that it significantly reduces the storage and computational complexity. Solving the volume integral equation directly involves O(N2) complexity. In this paper, the volume integral equation is solved efficiently via a multi-level fast multipole method (MLFMM) implementation, requiring O(NlogN) memory and computational cost. We demonstrate the effectiveness of this method for rectangular and spherical quantum wells, and the quantum harmonic oscillator, and present preliminary results of interest for multi-atom quantum phenomena.

Extended GO modeling of microwave backscattering from measured breaking wave crests

In previous work, an extension to geometrical optics (EGO) that allows the application to reflecting surfaces that have radii of curvature less than the electromagnetic was used to model the microwave backscattering from numerically simulated breaking water wave crests. The same approach has now been applied to plunging wave crest profiles that were directly measured in a wave tank, and the modeled backscattering compared to reference scattering found using moment-method based numerical techniques. When considering the directly measured two-dimensional cross-sections of the breaker, EGO successfully predicts the reduction in the vertically polarized backscatter (VV) observed in the reference scattering through the interference of reflections from the breaker jet itself and the cavity under the jet. A similar reduction is not seen at horizontal polarization (HH), giving a large HH-to-VV ratio at certain times in the breaking process. A three-dimensional scattering profile was synthesized from the 2-D measurements. The EGO-modeled interference of reflections from several different points on the 3-D wave yields a deep null in the VV backscattering that matches the null observed in the reference scattering. Again no interference null is observed in the HH scattering.

Active Learning Applied to RCS Computations With Nonuniform Sampling Using Different Objective Functions

An active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements. This method is used to optimally select those frequencies and angles that would be most informative, resulting in nonuniform sampling and often a reduced number of points (vis-agrave-vis uniform sampling). In this paper we focus on jointly two-dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering. The method consists of two basic steps. One step involves estimation of model parameters using a least-square (LS) algorithm. The next step is to optimally choose the next point (frequency and thetas) for analysis by the computational model or experiment. This new point is selected with the goal of reducing uncertainty in the parametric model (quantified via the Fisher information matrix). Iterating these two steps, a sequence of numerical computations or measurements are performed, each at the most informative point for learning the parameters of the associated simpler parametric model. This idea is demonstrated here in the context of reducing the number of points (frequencies and orientations) at which a computational model must be employed. And in order to avoid repeatedly gathering samplings at the edge of the input space, an alternative objective function is applied which makes the actively selected points closer to a region of interest

Two-scale analysis of LGA scattering from a 3-D spilling breaker crest

Scattering from the crests of intermediate-scale breaking waves with wavelengths on the order of a meter has been suggested as a significant contributor to sea-surface microwave backscattering at low grazing angle (LGA) illumination. Recently, West and Ja (Radio Sci., vol.37, no.4, p. 7-1-7-12, 2002) used the two-scale scattering model (TSM) to examine the scattering from the 2D measurements of the crest of a low energy spilling breaker wave-tank wave. The roughness was divided into large-scale and small-scale components using a moving average filter, and the deterministic TSM field equations of Guissard and Sobieski were used to find the field directly. These were compared with reference scattering found using a 2D computational EM technique. In this work, a 3D crest profile (rough in 2D) is synthesized from the 2D wave tank measurements. TSM is again applied, and the is field compared with reference scattering found using the multilevel fast multipole algorithm (MLFMA).