Vorlesungen uber theoretische Physik Von Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376 + 4 plates. 18 D. marks. Band 3: Elektrodynamik. Pp. xvi + 368. 18 D. marks. Band 6: Partielle Differentialgleichungen der Physik. Pp. xiii + 332. 18 D. marks. (Wiesbaden: Dieterich'sche Verlagsbuchhandlung, 1947–1949.)

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Lectures on Theoretical Physics

The forward-backward method has been shown to be an effective iterative technique for the computation of scattering from one-dimensional rough surfaces, often converging rapidly even for very large surface heights. However, previous studies with this method have computed interactions between widely separated points on the surface exactly, resulting in anO(N2) computational algorithm that becomes intractable for large rough surface sizes, as are required when low grazing incidence angles are approached. An acceleration algorithm for more rapidly computing interactions between widely separated points in the forward-backward method is proposed in this paper and results in an O(N) algorithm with increasing surface size. The approach is based on a spectral domain representation of source currents and the Green's function and is developed for both perfectly conducting and impedance boundary surfaces. The method is applied in a Monte Carlo study of low grazing incidence backscattering from very rough (up to 10 m/s wind speed) ocean-like surfaces at 14 GHz and is found to require only a small fraction of the CPU time required by other competing methods; such as the banded matrix iterative approach/canonical grid and fast multipole methods.

A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward-backward method

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. Dechamps 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.

Fast method to compute scattering by a buried object under a randomly rough surface: PILE 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. Dechamps 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 &#x1d4aa;(N) proposed by Chou and Johnson is applied. The new method, extended PILE combined with FB-SA, is tested on Perfectly C...

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

We derive an analytic scattering model for 3D bistatic scattering from a dihedral using geometrical optics (GO) and physical optics (PO). We use GO to trace ray reflections, and we evaluate the PO integral(s) for the field scattered by each plate of the dihedral. Multiple cases of reflection geometry are considered to account for effects of the dihedral plate size and antenna aspect angles. The complex-valued (amplitude and phase) scattering response is derived. The resulting parametric scattering model is presented in terms of the vertical and horizontal co-polarization and cross-polarization responses that correspond to the outputs of industry-standard numerical prediction codes. Comparing the derived model to available codes for method of moments (MoM), shooting and bouncing rays (SBR), and parametric models (PM), we demonstrate that the derived solution achieves the same accuracy as SBR, approximates MoM, is more accurate than PM, and does so in fast computation time comparable to a PM.

Analytic Physical Optics Solution for Bistatic, 3D Scattering From a Dihedral Corner Reflector

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.

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

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.

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

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 Galerkin’s 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.

Gildas Kubicke

Papers

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

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

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

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

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