Computer simulation of wave scattering from three-dimensional conducting random surfaces

Numerical simulation studies had been carried out by the conjugate gradient method to compute the solutions of the field integral equation for three-dimensional, perfectly conducting, Gaussian, random rough surfaces. The rate of convergence of the conjugate gradient method was fundamentally controlled by the root mean square (rms.) surface slope. Solutions computed using this method result in a significant reduction in CPU running time compared to those using direct methods, such as the Gaussian Elimination method. The validity of the numerical results of backscattering coefficients is verified by comparing simulation results with Kirchhoff theory, small perturbation theory, and Integral Equation methods at their valid regions. The efficiency and versatility of the numerical simulation algorithm as a practical tool to study rough surface scattering is demonstrated.     

Electromagnetic imaging for shape and variable conductivity

We consider the inverse problem of determining both the shape and the conductivity of a two-dimensional (2D) conducting scatterer from the knowledge of the far-field pattern of TM waves by solving the ill-posed nonlinear equation. Based on the boundary condition and measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. Satisfactory reconstructions are achieved by the genetic algorithm. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effect of Gaussian noise on the reconstruction results is investigated. The numerical results show that multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 433–440, 2004.     

Light scattering from anisotropic, randomly rough, perfectly conducting surfaces

An approach is introduced for performing rigorous numerical simulations of electromagnetic wave scattering from randomly rough, perfectly conducting surfaces. It is based on a surface integral technique, and consists of determining the unknown electric surface current densities from which the electromagnetic field everywhere can be determined. The method is used to study the scattering of a p-polarized beam from an anisotropic Gaussian, randomly rough, perfectly conducting surface. It is demonstrated that the surface anisotropy gives rise to interesting and pronounced signatures in the angular intensity distribution of the scattered light. The origins of these features are discussed.     

Electromagnetic wave scattering from the sea surface in the presence of wind wave patterns

The study is concerned with electromagnetic wave (EM) scattering by a random sea surface in the presence of coherent wave patterns. The coherent patterns are understood in a broad sense as the existence of certain dynamical coupling between linear Fourier components of the water wave field. We show that the presence of weakly nonlinear wave patterns can significantly change the EM scattering compared to the case of a completely random wave field. Generalizing the Random Phase Approximation (RPA) we suggest a new paradigm for EM scattering by a random sea surface.

The specific analysis carried out in the paper synthesizes the small perturbation method for EM scattering and a weakly nonlinear approach for wind wave dynamics. By investigating, in detail, two examples of a random sea surface composed of either Stokes waves or horse-shoe (‘crescent-shaped’) patterns the mechanism of the pattern effect on scattering is revealed. Each Fourier harmonic of the scattered EM field is found to be a sum of contributions due to different combinations of wave field harmonics. Among these ‘partial scatterings’ there are phase-dependent ones and, therefore, the intensity of the resulting EM harmonic is sensitive to the phase relations between the wind wave harmonics. The effect can be interpreted as interference of partial scatterings due to the co-existence of several phase-related periodic scattering grids. A straightforward generalization of these results enables us to obtain, for a given wind wave field and an incident EM field, an a priori estimate of whether the effects due to the patterns are significant and the commonly used RPA is inapplicable. When the RPA is inapplicable, we suggest its natural generalization by re-defining the statistical ensemble for water surface. First, EM scattering by an ‘elementary’ constituent pattern should be considered. Each such scattering is affected by the interference because the harmonics comprising the pattern are dynamically linked. Then, ensemble averaging, which takes into account the distribution of the pattern parameters (based on the assumption that the phases between the patterns are random), should be carried out. It is shown that, generally, this interference does not vanish for any statistical ensemble due to dynamical coupling between water wave harmonics. The suggested RPA generalization takes into account weak non-Gaussianity of water wave field m contrast to the traditional RPA which ignores it.     

Electromagnetic scattered field time series from finite difference time domain trained time delay neural network

This paper uses time delay neural network (TDNN) for predicting electromagnetic (EM) fields scattered from dielectric objects (cylinder, cylinder‐hemisphere, and cylinder‐cone) using: (a) FDTD generated initial field data for similar conducting objects and (b) Statistical information for the nature of fields. Statistical data indicated that the scattered field nature is close to deterministic. The TDNN structure determination uses statistical data for fixing the number of delays and tabular technique to obtain the number of hidden neurons. The TDNN training uses the Levenberg‐Marquardt (LM) algorithm. The model outputs follow standard FDTD results closely.     

Electromagnetic design of microwave filters using the finite element method

We present two complex microwave filter designs using the finite element method (FEM). A metallic cavity, loaded by low-loss dielectric plates is first optimized to obtain a high unloaded quality factor resonator. An original synthesis approach is then proposed to design a three-pole dielectric loaded cavity filter. The FEM is also applied to characterize a filter element, a dielectric resonator (DR) coupled on a whispering gallery mode (WGM) to two microstrip lines. A generalized [S] matrix is computed. Different elements are then put together to generate complex filtering responses. © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 167–179, 1997.     

GPU-based rendering of point-sampled water surfaces

Particle-based simulations are widely used to simulate fluids. We present a real-time rendering method for the results of particle-based simulations of water. Traditional approaches to visualize the results of particle-based simulations construct water surfaces that are usually represented by polygons. To construct water surfaces from the results of particle-based simulations, a density function is assigned to each particle and a density field is computed by accumulating the values of the density functions of all particles. However, the computation of the density field is time consuming. To address this problem, we propose an efficient calculation of density field using a graphics processing unit (GPU). We present a rendering method for water surfaces sampled by points. The use of the GPU permits efficient simulation of optical effects, such as refraction, reflection, and caustics.     

An algorithm for construction of iso-valued surfaces for finite elements

Finite element analysis of 3D phenomena gives as a result a set of function values specified on the nodes of the mesh. Various modes of graphical representation of such results are possible, including contour plots on cross-sections and surfaces of constant field values. In this paper, we propose an algorithm for the generation of such models. The continuous surfaces representing constant field values are obtained element-by-element by linear interpolation of nodal values. The normalized gradient of computed values is used for surface smoothing and shading. The method uses shaded polygon and shaded triangle strip primitives to meet with industry standards for graphical equipment.     

Feature-based design and finite element mesh generation for functional surfaces

This paper describes an approach to feature-based design and feature-based mesh generation for multi-featured functional surfaces. Unlike standard free-form parametric surface representation where the parametric surface patch plays the key role in both surface design and finite element mesh generation, we propose an approach to these two tasks which proceeds from the level of a complete feature (for example, a pocket or channel). The result is a more direct method for modeling functional surface characteristics and a more efficient feature-based implementation of Delaunay surface triangulation.     

A multigrid finite element method for reaction-diffusion systems on surfaces

We develop a multigrid finite element approach to solve PDE’s on surfaces. The multigrid approach involves the same weights for restriction and prolongation as in the case of planar domains. Combined with the concept of parametric finite elements the approach thus allows to reuse code initially developed to solve problems on planar domains to solve the corresponding problem on surfaces. The method is tested on a non-linear reaction-diffusion system on stationary and evolving surfaces, with the normal velocity of the evolving surface depending on the reaction-diffusion system. As a reference model the Schnakenberg system is used, offering non-linearity and algebraic simplicity on one hand, and quantitative reference data on the other hand.     

A goal-oriented hp-adaptive finite element approach to radar scattering problems

The paper presents application of an hp-adaptive finite element method for scattering of electromagnetic waves. The main objective of the numerical analysis is to determine the characteristics of the scattered waves indicating the power being scattered at a given direction––i.e. the radar cross-section (RCS). This is achieved considering the scattered far-field which defines RCS and which is expressed as a linear functional of the solution. Techniques of error estimation for the far-field are considered and an h-adaptive strategy leading to the fast reduction of the error of the far-field is presented. The simulations are performed with a three-dimensional version of an hp-adaptive finite element method for electromagnetics based on the hexahedral edge elements combined with infinite elements for modeling the unbounded space surrounding the scattering object.     

Combined finite volume–finite element method for shallow water equations

This paper is concerned with solving the viscous and inviscid shallow water equations. The numerical method is based on second-order finite volume–finite element (FV–FE) discretization: the convective inviscid terms of the shallow water equations are computed by a finite volume method, while the diffusive viscous terms are computed with a finite element method. The method is implemented on unstructured meshes. The inviscid fluxes are evaluated with the approximate Riemann solver coupled with a second-order upwind reconstruction. Herein, the Roe and the Osher approximate Riemann solvers are used respectively and a comparison between them is made. Appropriate limiters are used to suppress spurious oscillations and the performance of three different limiters is assessed. Moreover, the second-order conforming piecewise linear finite elements are used. The second-order TVD Runge–Kutta method is applied to the time integration. Verification of the method for the full viscous system and the inviscid equations is carried out. By solving an advection–diffusion problem, the performance assessment for the FV–FE method, the full finite volume method, and the discontinuous Galerkin method is presented.     

Incident energy dependence of the scattering dynamics of water molecules on silicon and graphite surfaces: the effect on tangential momentum accommodation

The scattering dynamics of water molecules on solid surfaces was investigated using the molecular beam technique. In contrast to the experiments previously reported in the literature, the range of incident energy was chosen to cover the typical kinetic energies of gas molecules in equilibrium at room temperature (35–130 meV). Even in such a narrow energy range, the angular distribution of scattered molecules is heavily affected by the incident energy, exhibiting both a nearly cosine distribution and a lobular distribution, which has a clear peak close to the specular direction. Interestingly, the tangential momentum accommodation coefficients (TMACs) estimated from the scattering experiments show opposite energy dependences on graphite (0001) and silicon (100) surfaces. As the incident energy increases, the TMAC decreases on the graphite surface, whereas it increases on the silicon surface. These trends can be attributed to the relatively large adsorption energy of water molecules on these surfaces and the atomic-scale surface corrugation, although a rigorous understanding requires further analysis by molecular dynamics simulations. Our findings suggest the need for an elaborate slip-flow model that takes account of the incident energy effect to accurately analyze water vapor flow in micro/nanostructures, which is ubiquitous in nature and engineering applications.     

Time domain electromagnetic scattering using finite elements and perfectly matched layers

We consider a model for the interrogation of a planar Debye medium by a non-harmonic microwave pulse from an antenna source in free space, and we compute the reflected solution using finite elements in the spatial variables and finite differences in the time variable. Perfectly matched layers (PMLs) and an absorbing boundary condition are used to damp waves interacting with artificial boundaries imposed to allow finite computational domains. We present simulation results showing that numerical reflections from interfaces at PML boundaries can be controlled.     

A scattering model for perfectly conducting random surfaces I. Model development

Abstract

The standard integral equation for the surface current is solved iterativcly to obtain an estimate of the surface current on a perfectly conducting randomly rough surface. The far-zone scattered fields and the backscattering coefficients for vertical, horizontal and cross-polarizations are then computed using this current estimate. The polarized backscattering coefficients are explicit functions of the surface parameters and reduce to the Kirchhoff solution in the high-frequency region and to the first-order perturbation solution in the low-frequency region. The cross-polarized scattering coefficient reduces to the second-order perturbation result in the low-frequency region and to zero in the high-frequency limit. A comparison is made with scattering measurements taken under laboratory conditions on a random surface with ka equal to 0-44 and kl equal to 3-25 ( l is the correlation length) It is found that better agreement is obtained with the current model than with the first-order perturbation model in predicting polarized scattering. It is also shown that the separation between VV and HH polarizations decreases gradually with frequency and approaches zero in the high-frequency limit     

Noise over water surfaces in Landsat TM images

A coherent pattern of system noise observable on all visible wavebands of Landsat Thematic Mapper images over homogeneous surfaces such as waterbodies is regarded as serious enough to impair visual interpretation and affect image analysis results. The noise is removable using iterative median filtering in the spatial domain, which requires much less processing time than removal by frequency domain Fourier transform. The significance of the error introduced to the images by the noise is evaluated in terms of water quality parameters in the study area, and methods for removal of the noise are described.     

Electromagnetic scattering by an array of conducting strips by an integral equation technique

Scattering of electromagnetic waves by an array of perfectly conducting infinitesimally thin strips is analyzed by a numerical procedure based on an integral equation formulation. The solution of the integral equation gives the induced surface current from which the reflected and transmitted waves are conveniently computed. Results are compared against other numerical results available in the literature which demonstrate the accuracy of the proposed method Further results are presented which show interesting physical phenomena.     

Light scattering from filaments

Photorealistic visualization of a huge number of individual filaments like in the case of hair, fur, or knitwear is a challenging task: Explicit rendering approaches for simulating radiance transfer at a filament get totally impracticable with respect to rendering performance and it is also not obvious how to derive efficient scattering functions for different levels of (geometric) abstraction or how to deal with very complex scattering mechanisms. We present a novel uniform formalism for light scattering from filaments in terms of radiance, which we call the bidirectional fiber scattering distribution function (BFSDF). We show that previous specialized approaches, which have been developed in the context of hair rendering, can be seen as instances of the BFSDF. Similar to the role of the BSSRDF for surface scattering functions, the BFSDF can be seen as a general approach for light scattering from filaments, which is suitable for deriving approximations in a canonic and systematic way. For the frequent cases of distant light sources and observers, we deduce an efficient far field approximation (bidirectional curve scattering distribution function, BCSDF). We show that on the basis of the BFSDF, parameters for common rendering techniques can be estimated in a non-ad-hoc, but physically-based way     

Nonreactive atom/molecule-surface scattering within the finite basis wave packet method

A quantum wave packet code for studying nonreactive scattering of closed-shell atoms or diatomic molecules from a rigid surface is described. The time evolution relies on the Chebychev propagator. Up to 5 collider degrees of freedom, 3 in translation and 2 in rotation, are treated in a pseudospectral way with the momentum or finite basis representation as the primary space. Potential matrix elements are efficiently evaluated by means of sequential 1D transformations between momentum and coordinate spaces. Fast Fourier transforms are performed for the translational and azimuthal coordinates whereas a Gauss-Legendre transform is used for the polar coordinate. This pseudospectral strategy minimizes memory requirements because no off-diagonal Hamiltonian matrix elements need to be stored. In addition, a wide variety of physical systems can be studied since no particular functional form is imposed for the interaction potential.     

FERM3D: A finite element R-matrix electron molecule scattering code

FERM3D is a three-dimensional finite element program, for the elastic scattering of a low energy electron from a general polyatomic molecule, which is converted to a potential scattering problem. The code is based on tricubic polynomials in spherical coordinates. The electron-molecule interaction is treated as a sum of three terms: electrostatic, exchange, and polarization. The electrostatic term can be extracted directly from ab initio codes (GAUSSIAN 98 in the work described here), while the exchange term is approximated using a local density functional. A local polarization potential based on density functional theory [C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785] describes the long range attraction to the molecular target induced by the scattering electron. Photoionization calculations are also possible and illustrated in the present work. The generality and simplicity of the approach is important in extending electron-scattering calculations to more complex targets than it is possible with other methods.

Program summary

Title of program:FERM3DCatalogue identifier:ADYL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYL_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested:Intel Xeon, AMD Opteron 64 bit, Compaq AlphaOperating systems or monitors under which the program has been tested:HP Tru64 Unix v5.1, Red Hat Linux Enterprise 3Programming language used:Fortran 90Memory required to execute with typical data:900 MB (neutral CO₂), 2.3 GB (ionic CO₂), 1.4 GB (benzene)No. of bits in a word:32No. of processors used:1Has the code been vectorized?:NoNo. of lines in distributed program, including test data, etc.:58 383No. of bytes in distributed program, including test data, etc.:561 653Distribution format:tar.gzip fileCPC Program library subprograms used:ADDA, ACDPNature of physical problem:Scattering of an electron from a complex polyatomic molecular target.Method of solution:Solution of a partial differential equation using a finite element basis, and direct sparse linear solvers.Restrictions on the complexity of the problem:Memory constraints.Typical running time:2 hours.Unusual features of the program:

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very extensive use of memory,

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requires installation of Lapack, Blas, a direct sparse solver library (SuperLU, freely available, or Pardiso, which requires a license, but is free of charge for academic use), and optionally the Cernlib and Arpack libraries, freely available,

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requires input from quantum chemistry programs (Gaussian, Molpro or PC Gamess).