Penetrable Objects Research Articles

Conforming Testing of Electromagnetic Surface-Integral Equations for Penetrable Objects

The necessity of conforming testing procedures in developing accurate and reliable surface-integral-equation-based solvers for homogeneous penetrable objects is demonstrated. It is shown that only in Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation with a conforming testing procedure, the interface conditions become properly tested for both the tangential and normal field components. Numerical experiments illustrate that the use of a nonconforming testing procedure can lead to a significant decrease on the solution accuracy or erroneous diverging results.

A model for the pore size distribution in random and isotropic mixtures of cylindrical fibres and circular disks

A model for the distribution of pore sizes in systems of randomly distributed cylindrical fibers and circular disks is developed that derives from simple excluded-volume considerations. The dimensions of the particles with finite hard cores are mapped onto those of a hypothetical system of fully penetrable objects in a manner that preserves the overall core-occupied volume fraction and specific surface area. This mapping enables us to obtain estimates for the pore size distribution, and for the first and second moments of the pore sizes, as functions of the particle volume fraction and mixture composition in terms of closed-form, analytical expressions.

Solutions of plasmonic structures using the multilevel fast multipole algorithm

We consider accurate full-wave solutions of plasmonic problems using the multilevel fast multipole algorithm (MLFMA). Metallic structures at optical frequencies are modeled by using the Lorentz-Drude model, formulated with surface integral equations, and analyzed iteratively via MLFMA. Among alternative choices, the electric and magnetic current combined-field integral equation (JMCFIE) and the combined tangential formulation (CTF), which are popular integral-equation formulations for penetrable objects, are discretized with the conventional Rao-Wilton-Glisson functions and used to model plasmonic structures. We discuss electromagnetic interactions in plasmonic media and show how far-field interactions may be omitted for improving the efficiency without sacrificing the accuracy of results. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:335–341, 2016.

Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers

We present a projection based regularization parameter choice approach within the framework of the linear sampling method for the reconstruction of acoustically penetrable objects. Using the Golub–Kahan bidiagonalization algorithm and the Lanczos tridiagonalization process we form appropriate subspaces which generate a sequence of regularized solutions. As a result two new and efficient methods are developed and used for the solution of problems that involve large linear systems of equations. The effectiveness of our approach is illustrated with reconstructions of three dimensional objects.

Analysis of Transient EM Scattering From Penetrable Objects by Time Domain Nonconformal VIE

A marching-on-in-time (MOT)-based nonconformal volume integral equation (VIE) is proposed to analyze the transient electromagnetic scattering from the inhomogeneous penetrable objects. The gradient–gradient operator is acted on the Green’s function to realize the nonconformal tetrahedral meshes discretization. Half Schaubert–Wilton–Glisson (SWG) basis functions are chosen for the trail and test spatial functions, meanwhile the piecewise polynomial Lagrange interpolation functions are applied for temporal expansion. In addition, the quasi-explicit scheme is introduced to accelerate the calculation of conventional implicit MOT system. Numerical results are given to demonstrate the flexibility and validity of the proposed scheme.

DGTD Analysis of Electromagnetic Scattering From Penetrable Conductive Objects With IBC

To avoid straightforward volumetric discretization, a discontinuous Galerkin time-domain (DGTD) method integrated with the impedance boundary condition (IBC) is presented in this paper to analyze the scattering from objects with finite conductivity. Two situations are considered. 1) The skin depth is smaller than the thickness of the conductive volume. 2) The skin depth is larger than the thickness of a thin conductive sheet. For the first situation, a surface impedance boundary condition (SIBC) is employed, wherein the surface impedance usually exhibits a complex relation with the frequency. To incorporate the SIBC into DGTD, the surface impedance is first approximated by rational functions in the Laplace domain using the fast relaxation vector-fitting (FRVF) technique. Via inverse Laplace transform, the time-domain DGTD matrix equations can be obtained conveniently in integral form with respect to time t. For the second situation, a transmission IBC (TIBC) is used to include the transparent effects of the fields. In the TIBC, the tangential magnetic field jump is related with the tangential electric field via the surface conductivity. In this work, a specifically designed DGTD algorithm with TIBC is developed to model the graphene up to the terahertz (THz) band. In order to incorporate the TIBC into DGTD without involving the time-domain convolution, an auxiliary surface polarization current governed by a first-order differential equation is introduced over the graphene. For open-region scattering problems, the DGTD algorithm is further hybridized with the time-domain boundary integral (TDBI) method to rigorously truncate the computational domain. To demonstrate the accuracy and applicability of the proposed algorithm, several representative examples are provided.

A Hybrid Scheme With Nyström Discretization for Solving Transient Electromagnetic Scattering by Conducting Objects

The interaction of transient electromagnetic (EM) waves with objects can be formulated by the integral equation approach in time domain. For conducting objects or homogeneous penetrable objects, the time-domain surface integral equations (TDSIEs) can be applied. Traditionally, the TDSIEs are solved by combining the method of moments (MoM) in spatial domain and a march-on-in-time (MoT) scheme in temporal domain. The MoM usually requires conforming meshes with a well-designed basis function and the MoT may suffer from a stability problem. In this work, we propose a hybrid scheme in which the Nystrom method is used in spatial domain while the MoM with Laguerre function as basis and testing functions is employed with a march-on-in-degree (MoD) manner in the temporal domain. The Nystrom method does not require any basis and testing functions and can use nonconforming meshes in spatial domain, whereas the MoM with Laguerre function as basis and testing functions can fully eliminate the stability problem in temporal domain. Numerical examples for EM scattering by typical conducting objects are presented to demonstrate the scheme and its merits have been verified.

Quasi‐local multitrace boundary integral formulations

In the context of time harmonic wave scattering by piecewise homogeneous penetrable objects, we present a new variant of the multitrace boundary integral formulation, that differs from the local multitrace approach of (Jerez‐Hanckes and Hiptmair, 2012) [13] by the presence of regularization terms involving boundary integral operators and localized at junctions i.e. points where at least three subdomains abut. We prove well‐posedness and quasioptimal convergence of conforming Galerkin discretizations for this new formulation, and present numerical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2043–2062, 2015

Street environment change detection from mobile laser scanning point clouds

Mobile laser scanning (MLS) has become a popular technique for road inventory, building modelling, infrastructure management, mobility assessment, etc. Meanwhile, due to the high mobility of MLS systems, it is easy to revisit interested areas. However, change detection using MLS data of street environment has seldom been studied. In this paper, an approach that combines occupancy grids and a distance-based method for change detection from MLS point clouds is proposed. Unlike conventional occupancy grids, our occupancy-based method models space based on scanning rays and local point distributions in 3D without voxelization. A local cylindrical reference frame is presented for the interpolation of occupancy between rays according to the scanning geometry. The Dempster–Shafer theory (DST) is utilized for both intra-data evidence fusion and inter-data consistency assessment. Occupancy of reference point cloud is fused at the location of target points and then the consistency is evaluated directly on the points. A point-to-triangle (PTT) distance-based method is combined to improve the occupancy-based method. Because it is robust to penetrable objects, e.g. vegetation, which cause self-conflicts when modelling occupancy. The combined method tackles irregular point density and occlusion problems, also eliminates false detections on penetrable objects.

Fast quantitative microwave imaging with resolvent kernel extracted from measurements

A quantitative imaging method is proposed based on microwave measurements where a direct inversion in real space is employed. The electrical properties of penetrable objects are reconstructed using a resolvent kernel in the forward model, which is extracted from calibration measurements. These measurements are performed on two known objects: the reference object (RO) representing the scatterer-free measurement and the calibration object representing a small scatterer embedded in the RO. Since the method does not need analytical or numerical approximations of the forward model, it is particularly valuable in short-range imaging, where analytical models of the incident field do not exist while the fidelity of the simulation models is often inadequate. The experimentally determined resolvent kernel inherently includes the particulars of the measurement setup, including all transmitting and receiving antennas. The inversion is fast, allowing for quasi-real-time image reconstruction. The proposed technique is demonstrated and validated through examples using simulated and experimental data. Its performance with noisy data is also examined. The concept of experimentally determined resolvent kernel in the forward model may be valuable in other imaging modalities such as ultrasound, photonic imaging, electrical-impedance tomography, etc.

Challenges in developing efficient Calderon preconditioners for resonating or high material contrast penetrable objects

Calderon preconditioning is a recently proposed technique for improving conditioning of ill-conditioned matrices arising from discretization of surface integral equations. In electromagnetics the method has been developed for both perfectly conducting and homogeneous penetrable objects. In the case of penetrable objects the large variety of possible material parameters poses additional challenges on the efficiency of the preconditioner. We demonstrate with numerical experiments that problems may appear in particular at high material parameter values, at the physical resonances of the object, and at negative or zero material parameters. As realistic examples of objects with zero or negative material parameters we consider plasmonic nanoparticles at optical wavelengths.

Local multiple traces formulation for high-frequency scattering problems

We present an efficient method to solve high-frequency scattering problems by heterogeneous penetrable objects in two dimensions. This is achieved by extending the so-called Local Multiple Traces Formulation, introduced recently by Hiptmair and Jerez-Hanckes, to purely spectral discretizations employing weighted Chebyshev polynomials. Together with regularization strategies to handle boundary integral operators singularities, matrix entries are quickly computed via the Fast Fourier Transform. The resulting Fredholm first-kind formulation is free from spurious resonances, and though ill-conditioned, it possesses built-in Calderón-type preconditioners. Numerical results obtained for different settings validate our claims and greatly motivate future research in this direction.

Calderón Preconditioned PMCHWT Equations for Analyzing Penetrable Objects in Layered Medium

We study Calderón preconditioners for analyzing electromagnetic scattering by penetrable objects in a layered medium. To account for the scattering effects of the multilayered background, the layered medium Green's function is adopted in the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) method. However, similar to the free-space case, the spectrum of the resulting equation is undesirable. This leads to a slow convergence of an iterative solver, especially when the geometry is densely meshed. To improve the convergence, a highly effective preconditioner is proposed. Different from its free-space counterpart, the preconditioning operator is constructed based on the Calderón identities for inhomogeneous medium. To reduce the relatively high construction cost of the preconditioning operator, several alternative simplified schemes are proposed and analyzed. Finally, the performances of different preconditioners are examined and compared carefully through different numerical examples. It is shown that the convergence of the PMCHWT system in a layered medium can be significantly improved by using the proposed Calderón preconditioners.

Prediction of negative radiation forces due to a Bessel beam.

The mechanism of generating backward dragging forces on objects standing in the path of a single, translationally invariant, symmetric acoustic Bessel beam is studied. This paper aims to provide mechanical and structural conditions for the emergence of negative axial forces based on the elastodynamic response of acoustically penetrable objects and beam's nonparaxiality parameter. An extensive numerical study has been performed for various liquid and solid elastic cases to illustrate the validity of the proposed eigenfrequency-based conditions. Results have revealed the existence of a complex but interpretable link between the emergence of negative radiation forces on spheres illuminated by zero-order Bessel beams and the eigenfrequencies of the particle. Considerable progress has been made in elucidating these relationships, which may lead to the development of predictable and robust single-beam acoustic handling devices.

Radar Imaging of Impenetrable and Penetrable Targets From Finite-Duration Pulsed Signatures

A straightforward time-domain imaging technique for shape reconstruction of both impenetrable and penetrable objects is described. For a class of finite-duration incident waveforms, the ramp cross-sectional area function is recovered from the radar signature of a target through the stable integration procedure. The results presented in this paper can be readily applied to identification of targets from their radar signatures directly in time domain. A number of illustrative examples is presented.

Extended Linear Embedding via Green's Operators for Analyzing Wave Scattering from Anisotropic Bodies

Linear embedding via Green’s operators (LEGO) is a domain decomposition method particularly well suited for the solution of scattering and radiation problems comprised of many objects. The latter are enclosed in simple-shaped subdomains (electromagnetic bricks) which are in turn described by means of scattering operators. In this paper we outline the extension of the LEGO approach to the case of penetrable objects with dyadic permittivity or permeability. Since a volume integral equation is only required to solve the scattering problem inside a brick and the scattering operators are inherently surface operators, the LEGO procedureper secan afford a reduction of the number of unknowns in the numerical solution with the Method of Moments and subsectional basis functions. Further substantial reduction is achieved with the eigencurrents expansion method (EEM) which employs the eigenvectors of the scattering operator as local entire-domain basis functions over a brick’s surface. Through a few selected numerical examples we discuss the validation and the efficiency of the LEGO-EEM technique applied to clusters of anisotropic bodies.

Time-Domain Single-Source Integral Equations for Analyzing Scattering From Homogeneous Penetrable Objects

Single-source time-domain electric- and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia et al. alongside the high-order divergence- and quasi curl-conforming (DQCC) basis functions of Valdes et al. The combination of these two sets allows for a well-conditioned mapping from div- to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme.

Computations of Electromagnetic Wave Scattering From Penetrable Composite Targets Using a Surface Integral Equation Method With Multiple Traces

We present a surface integral equation domain decomposition method (SIE-DDM) for time harmonic electromagnetic wave scattering from bounded composite targets. The proposed SIE-DDM starts by partitioning the composite object into homogeneous sub-regions with constant material properties. Each of the sub-regions is comprised of two sub-domains (the interior of the penetrable object, and the exterior free space), separated on the material interface. The interior and the exterior boundary value problems are coupled to each other through the Robin transmission conditions, which are prescribed on the material/domain interface. A generalized combined field integral equation is employed for both the interior and the exterior sub-domains. Convergence studies of the proposed SIE-DDM are included for both single homogeneous objects and composite penetrable objects. Furthermore, a complex large-scale simulation is conducted to demonstrate the capability of the proposed method to model multi-scale electrically large targets.

A Numerical Procedure for the Analysis of EMC/EMI Problems in Radio Communication Systems Operating in Complex Environments

An efficient combined full-wave/high-frequency procedure useful to evaluate the spatial distribution of the electromagnetic field excited by radio sources operating in complex environments is presented. The procedure is based on a full-wave technique for the evaluation of the field distribution excited within a volume surrounding the radiating sources, and a dedicated high-frequency technique useful to model the propagation and interaction of the electromagnetic field with electrically penetrable objects forming the operative environment. In this way, it is possible to determine, with a reduced computational burden, the field distribution from the source location to the far-field region while keeping a high numerical accuracy. Using the proposed procedure, it is possible to evaluate the performance of mobile radio communication systems taking into account the impact of the operative environment, which is in turn essential to identify safety areas in compliance with the electromagnetic compatibility (EMC) regulations. Numerical examples aimed to predict potential EMC/EMI issues which could be caused by a mobile communication system operating in a complex scenario modeling a crisis area are also reported.

Electric and magnetic combined source integral equations for electromagnetic transmission problems

Abstract Various combined source integral equation (CSIE) formulations are developed for the analysis of electromagnetic scattering by three-dimensional arbitrarily shaped homogeneous penetrable objects. The considered CSIE formulations include the classical “electric” CSIE proposed by Mautz and Harrington in 1979, and its dual “magnetic” CSIE as well as mixed “electric–magnetic” and “magnetic–electric” CSIE formulations. Novel discretization schemes by utilizing the primary (Rao–Wilton–Glisson, RWG) and the dual (Buffa–Christiansen, BC) functions are applied to convert the integral equations into matrix equations. These schemes avoid the numerical problems that would appear if the CSIE formulations were discretized with the conventional Galerkin method using the RWG functions only.