Gildas Kubicke

Fast method to compute scattering by a buried object under a randomly rough surface: PILE combined with FB-SA

A fast, exact numerical method based on the method of moments (MM) is developed to calculate the scattering from an object below a randomly rough surface. Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)] have recently developed the PILE (propagation-inside-layer expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. From the inversion of the impedance matrix by block (in which two impedance matrices of each interface and two coupling matrices are involved), this method allows one to calculate separately and exactly the multiple-scattering contributions inside the layer in which the inverses of the impedance matrices of each interface are involved. Our purpose here is to apply this method for an object below a rough surface. In addition, to invert a matrix of large size, the forward-backward spectral acceleration (FB-SA) approach of complexity O(N) (N is the number of unknowns on the interface) proposed by Chou and Johnson [Radio Sci.33, 1277 (1998)] is applied. The new method, PILE combined with FB-SA, is tested on perfectly conducting circular and elliptic cylinders located below a dielectric rough interface obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.

Scattering by an object above a randomly rough surface from a fast numerical method: Extended PILE method combined with FB-SA

In this paper, a fast exact numerical method, based on the method of moments, is developed to calculate the scattering by an object above a rough surface. N. Déchamps et al. have recently developed the PILE (Propagation-Inside-Layer Expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. This method allows us to calculate separately and exactly the multiple scattering contributions inside the layer. This is done with a decomposition by block of the impedance matrix (the inverse of the impedance matrix of each interface and two coupling matrices are involved). The purpose of this paper is to extend the PILE method to the more general case of two illuminated surfaces and to apply it to an object located above a rough surface. In addition, to invert a matrix of large size, the Forward–Backward Spectral Acceleration (FB-SA) approach of complexity 𝒪(N) proposed by Chou and Johnson is applied. The new method, extended PILE combined with FB-SA, is tested on Perfectly Conducting (PC) circular and elliptic cylinders located above a rough surface (dielectric or PC) obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.

Method of Moments for 2D Scattering Problems: Basic Concepts and Applications

In this book, the method of moments (MoM) is addressed to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Because the problem is considered two-dimensional (2D), the integral equations (IEs) are scalar and only the transverse electric (TE) and transverse magnetic (TM) polarizations are considered (no cross polarizations occur). Chapter 1 analyzes how the MoM with the point matching method and pulse basic functions is applied to convert the IEs into a linear system. In addition, chapter 1 presents the statistical parameters necessary to generate Gaussian random rough surfaces. Chapter 2 compares the MoM with the exact solution of the field scattered by a circular cylinder in free space, and with the physical optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM combined with the efficient E-PILE method, of the scattering from two illuminated scatterers and how the E-PILE algorithm can be hybridized with asymptotic or rigorous methods valid for the scattering from a single scatterer(alone). Chapter 4 presents the same results as in Chapter 3 but for an object above a random rough surface or for a coated (circular or elliptical) cylinder. In the last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks.

Propagation-inside-layer-expansion method combined with physical optics for scattering by coated cylinders, a rough layer, and an object below a rough surface.

In this article, the fields scattered by coated cylinders, a rough layer, and an object below a rough surface are computed by the efficient propagation-inside-layer-expansion (PILE) method combined with the physical optics (PO) approximation to accelerate the calculation of the local interactions on the non-illuminated scatterer, which is assumed to be perfectly conducting. The PILE method is based on the method of moments, and the impedance matrix of the two scatterers is then inverted by blocks from a Taylor series expansion of the inverse of the Schur complement. Its main interest is that it is rigorous, with a simple formulation and a straightforward physical interpretation. In addition, one of the advantages of PILE is to be able to hybridize methods (rigorous or asymptotic) valid for a single scatterer. Then, in high frequencies, the hybridization with PO allows us to significantly reduce the complexity in comparison to a direct lower-upper inversion of the impedance matrix of the two scatterers without loss in accuracy.

A Fast Hybrid Method for Scattering From a Large Object With Dihedral Effects Above a Large Rough Surface

A new hybrid numerical method is described for scattering from an electrically large perfectly-conducting object with dihedral effects above a very long one-dimensional rough surface (two-dimensional problem). Such a problem involves a large number of unknowns and cannot be solved easily with a conventional method of moments by using a direct LU inversion. Thus, to solve this issue, the Extended-PILE method is combined with the forward-backward spectral acceleration (FBSA) for the local interactions on the rough surface and with the second-order physical optics (PO2) approximation for the local interactions on the object. Classically objects under test do not present dihedral effects and in the high frequency domain the first-order PO (PO1) provides the main contribution. In opposite, in this paper since a cross is considered, the second-order inner reflections contribute significantly and the PO2 must be included. By assuming a Gaussian process with a Gaussian height spectrum, this new hybrid method, E-PILE+FBSA+PO2, is tested against the rigorous E-PILE+ FBSA method (direct LU inversion on the object) as functions of the object inclination, the polarization and the incidence angle.

3-D Scattering From a PEC Target Buried Beneath a Dielectric Rough Surface: An Efficient PILE-ACA Algorithm for Solving a Hybrid KA-EFIE Formulation

An efficient hybrid KA-EFIE formulation is deployed to analyze the electromagnetic (EM) scattering from a 3-D perfectly electric conducting (PEC) object buried beneath a 2-D dielectric rough surface. In this approach, the electric and magnetic current densities on the rough surface are analytically obtained through the current-based Kirchhoff approximation (KA), whereas the electric current density on the buried object is rigorously determined by solving the electric field integral equation (EFIE) using the Galerkins method of moments (MoM) with Rao-Wilton-Glisson (RWG) basis functions. The KA-EFIE matrix system is then efficiently solved by the iterative propagation-inside-layer-expansion (PILE) method combined with the algebraic adaptive cross approximation (ACA). The current densities on the dielectric rough surface are thereafter used to handle the bistatic normalized radar cross-section (NRCS) patterns. The proposed hybrid approach allows a significant reduction in computation time and memory requirements compared to the rigorous Poggio-Miller-Chang-Harrington-Wu (PMCHW)-EFIE formulation which requires solving a large MoM matrix equation. Moreover, the hybridization of the ACA algorithm with the PILE method improves further the computational cost thanks to the rank-deficient propriety of the coupling matrices. To validate the hybrid approach, we compare its results with those of the rigorous PMCHW-EFIE approach.

Improvement of Iterative Physical Optics Using the Physical Optics Shadow Radiation

The prediction of Radar Cross Section (RCS) of complex targets which present shadowing efiects is an interesting challenge. This paper deals with the problem of shadowing efiects in the computation of electromagnetic scattering by a complex target using Iterative Physical Optics (IPO). The original IPO is limited to cavities applications, but a generalized IPO can be applied to arbitrary geometries. This paper proposes a comparison between the classical PO approach and a physical approach based on shadow radiation (around forward direction) with PO approximation for the consideration of shadowing efiects in generalized IPO. Based on the integral equations, a rigorous demonstration of this physical shadowing is provided. Then simulation results illustrate the interest of using physical shadowing both from the transmitter and towards the receiver, compared to the classical approach. Computing electromagnetic signature of complex targets presenting shadowing efiects is a complex problem for which many solutions have been proposed. Each of these solutions presents beneflts and drawbacks, and two difierent kinds of methods can be used for arbitrary shaped cavities: rigorous numerical methods and asymptotic methods. Numerical methods, like Method of Moments (MoM), can be used to calculate RCS (Radar Cross Section) of targets with a good precision. These methods, which do not apply any approximation (but approximation linked to meshing), are known to provide excellent results, but their complexity is high. MoM has a complexity of O(N 3 ), N being the number of unknowns (which is equal to the number of non boundary edges of a meshed target). Thus, in case of great targets dimensions (compared to wavelength), these methods are generally not used, due to their computing time and memory requirement. Nevertheless, MoM will be used in this paper as a reference method. To overcome this issue, asymptotic methods have been developed and can be used in high- frequency domain for arbitrarily shaped targets with a reduced complexity. These methods are based on Geometrical Optics (GO), based on ray trajectories, and/or Physical Optics (PO), using surface currents to calculate scattered flelds. When multiple re∞ections occur, PO is generally preferred to GO, as GO is less precise, particularly in case of highly curved geometries. Iterative Physical Optics (IPO) (1{3) is an asymptotic method based on PO. The method has been originally developed to calculate RCS of cavities (1) and has been generalized to arbitrary geometries (4). This method can be described by an algorithm in 4 steps:

Rigorous Prediction of the Ground Wave Above Flat and Rough Highly-Conducting One-Dimensional Sea Surfaces in HF-VHF Band

For horizontally and vertically polarized line sources in HF-VHF band, a detailed analysis of the propagation over one-dimensional highly-conducting smooth and rough sea surfaces is addressed from an efficient rigorous numerical method: the method of moments combined with the BMIA-CAG approach and with the impedance boundary condition (Leontovitch approximation). This method can treat a huge problem, typically, ranging from 200 000 to 300 000 for the number of unknowns on the surface, which allows us to show, for the TM polarization, the ground wave propagation over a long distance. The contribution of the surface wave is then exhibited for a smooth sea surface and compared with the Collin asymptotic formulation deduced from the Sommerfeld integral. The surface roughness effect on the propagation is also investigated.

Design of a stealth wind turbine

A hybridization method of Geometrical Optics and Physical Optics (POGO) has been developed to calculate the radar cross section (RCS) of electrically large targets. The GO technique takes high order interactions into account while the PO technique allows to get rid of caustics problems. This hybrid technique is well suited to calculate the field radiated by meteorological radars and backscattered by wind turbines. These radars, having to estimate the clouds speed by calculating the Doppler effects, are very sensitive to moving targets as explained in [1].

Extended propagation-inside-layer expansion method combined with the forward-backward method to study the scattering from an object above a rough surface.

In this Letter, a fast red rigorous numerical method, based on the method of moments, is developed to calculate the scattering from an object above a rough surface for three-dimensional problems (3D). G. Kubické has recently developed the extended propagation-inside-layer expansion (E-PILE) method to calculate the scattering from an object above a rough surface for two-dimensional problems. This method allows us to calculate separately and exactly the interactions between the object and the rough surface. The purpose of this paper is to extend the E-PILE method to a 3D problem. In addition, to invert a matrix of large size, the forward-backward (FB) method is applied to calculate the local interactions on the rough surface.