Equivalent Surface Current Densities Research Articles

Wave scattering from random sets of closely spaced objects through linear embedding via Green's operators

In this paper we present the application of linear embedding via Green's operators (LEGO) to the solution of the electromagnetic scattering from clusters of arbitrary (both conducting and penetrable) bodies randomly placed in a homogeneous background medium. In the LEGO method the objects are enclosed within simple-shaped bricks described in turn via scattering operators of equivalent surface current densities. Such operators have to be computed only once for a given frequency, and hence they can be re-used to perform the study of many distributions comprising the same objects located in different positions. The surface integral equations of LEGO are solved via the Moments Method combined with Adaptive Cross Approximation (to save memory) and Arnoldi basis functions (to compress the system). By means of purposefully selected numerical experiments we discuss the time requirements with respect to the geometry of a given distribution. Besides, we derive an approximate relationship between the (near-field) accuracy of the computed solution and the number of Arnoldi basis functions used to obtain it. This result endows LEGO with a handy practical criterion for both estimating the error and keeping it in check.

INVERSE EQUIVALENT SURFACE CURRENT METHOD WITH HIERARCHICAL HIGHER ORDER BASIS FUNCTIONS, FULL PROBE CORRECTION AND MULTILEVEL FAST MULTIPOLE ACCELERATION

An inverse equivalent surface current method working with equivalent electric and/or magnetic surface current densities on appropriately chosen Huygens surfaces is investigated. The considered model with triangular surface meshes is compatible with the models known from method of moments (MoM) solutions of surface integral equations. Divergence conforming current basis functions of order 0.5 and of order 1.5 are considered, where the order 0.5 functions are the well-known Rao-Wilton-Glisson basis functions. Known near-fleld samples typically obtained from measurements are mapped on the unknown equivalent surface current densities utilizing the radiation integrals of the currents as forward operator, where the measurement probe in∞uence is formulated in a MoM like weighting integral. The evaluation of the forward operator is accelerated by adaptation of the multilevel fast multipole method (MLFMM) to the inverse formulation, where the MLFMM representation is the key to full probe correction by employing only the far-fleld patterns of the measurement probe antennas. The resulting fully probe corrected algorithm is very ∞exible and e-cient, where it is found that the computation speed is mostly dependent on the MLFMM conflguration of the problem and not that much on the particular equivalent current expansion as long as the expansion is able to represent the currents su-ciently well. Inverse current and far-fleld pattern results are shown for a variety of problems, where near-fleld samples obtained from simulations as well as from realistic measurements are considered.

Numerical solution of the CFIE using vector bases and dual interlocking meshes

A numerical solution of the combined-field integral equation for wave scattering from homogeneous dielectric bodies is proposed. The approach uses a simultaneous representation of the equivalent surface current densities in both curl-conforming and divergence-conforming bases, defined on a dual interlocking mesh representing the scatterer surface. The dual-mesh based approach is stable at internal resonances and allows the use of the optimum type of basis function for each integral operator within the combined field equation. The procedure can also be used to obtain a radiation boundary condition for differential equation formulations.

MEG Forward Problem Formulation Using Equivalent Surface Current Densities

We present a formulation for the magnetoencephalography (MEG) forward problem with a layered head model. Traditionally the magnetic field is computed based on the electric potential on the interfaces between the layers. We propose to express the effect of the volumetric currents in terms of an equivalent surface current density on each interface, and obtain the magnetic field based on them. The boundary elements method is used to compute the equivalent current density and the magnetic field for a realistic head geometry. We present numerical results showing that the MEG forward problem is solved correctly with this formulation, and compare it with the performance of the traditional formulation. We conclude that the traditional formulation generally performs better, but still the new formulation is useful in certain situations.

Theory and implementation of dielectric resonator antenna excited by a waveguide slot

Excitation of dielectric resonator antennas (DRAs) by waveguide slots is proposed as an alternative to traditionally used excitation mechanisms in order to enhance the frequency bandwidth of slotted waveguide radiators and to control the power coupled to the DRA. The analysis is based on the numerical solution of coupled integral equations discretized using the method of moments (MoM). The dielectric resonator (DR) is modeled as a body-of-revolution based on the integral equation formulation for the equivalent electric and magnetic surface current densities. The analysis of an infinite or a semi-infinite waveguide containing longitudinal or transverse narrow slots uses the appropriate dyadic Green's function resulting in closed-form analytical expressions of the MoM matrix. The scattering parameters for a slotted waveguide loaded with a dielectric resonator antenna disk are calculated and compared with finite-difference time-domain results. Bandwidth enhancement is achieved by the proper selection for the antenna parameters.

Optimum design of tapered slot antenna profile

The optimum design of the tapered slot antenna (TSA) profile and geometry is achieved through its modeling by a stepline terminated in free space intrinsic impedance. The impedance matching of the TSA input impedance (obtained by the transmission matrix properties) to the generator impedance is achieved by minimizing an error criterion constructed as the magnitude squared of the difference between the generator and input impedances over the desired bandwidth. The attenuation constant of the stepline is computed by the broadside radiation of TSA (which is an endfire antenna) and the longitudinal power flow. The spectral domain immitance approach is used to compute the broadside radiation, by first determining the electric field components in the slot by the Galerkin's method and then obtaining the equivalent magnetic surface current densities. The power flow in the endfire direction of TSA may be computed by the Poynting's vector in the substrate. The attenuation constant is calculated for various values of slot width. Finally, the minimization procedure gives the slotline widths and lengths.

A numerical study of scattering from an object above a rough surface

A numerical model is applied in a Monte Carlo study of scattering from a three-dimensional penetrable object above a lossy dielectric rough interface. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. Both time-and frequency-domain results are investigated to illustrate the relative importance of coherent and incoherent scattering effects in the sample problem considered. Results show that a four-path model using a reduced-reflection coefficient can be reasonable for coherent scattering predictions and that incoherent object/surface interaction effects can make significant contributions to received cross sections.

Hybrid/sup 2/: combining the three-dimensional hybrid finite element-boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction

The fully three-dimensional (3-D) hybrid finite element (FE)-boundary integral (BI) technique is extended by further hybridization with the uniform geometrical theory of diffraction (UTD) resulting in a so-called hybrid/sup 2/ FE-BI-UTD approach. The formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar-multilayered medium. The arbitrarily shaped inhomogeneous objects are discretized by finite elements, whereas, the electrically-large obstacles are described by the UTD and both of these models are included into an integral equation derived from the equivalence principle for planar-multilayered media. Thus, full-electromagnetic coupling is realized between all parts of the formulation. The integral equation is implemented using mixed potentials with appropriate Green's functions derived from Sommerfeld integral representations for planar-multilayered media. The UTD contributions are accounted for by corresponding modifications of the Green's functions and the FE technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects. After presenting the formulation of this novel fully 3-D hybrid/sup 2/ technique, the implemented computer code is validated against conventional hybrid FE-BI computations and a wireless base station antenna is analyzed in several situations of complex real world, microcell environments.

Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns.

3D numerical analysis of AC travelling magnetic fields problems by the indirect BIEM

In this paper, the indirect boundary integral equation method (BIEM) is applied to the 3D analysis of an electromagnetic system with a time-varying excitation in the presence of material motion. To do this, a fundamental Green's function for the convection-diffusion equation is derived. Using the Green's function, both effects of the time-varying magnetic field and the material motion are reflected on numerical solutions. The integral representation of the eddy current and the electromagnetic force is developed in terms of the equivalent magnetic surface current density and the equivalent magnetic surface charge density. The validity of the proposed method is examined by comparing the numerical results of the magnetic levitation force with the experimental values.

Passive magnetic bearings: The conic-shaped bearing

An analytical and numerical method, based on the equivalent surface current density theory for magnetic field modelling has been used for characterizing the behaviour of some basic configurations of axially and radially magnetized ring-shaped magnetic bearings, also superimposed in a conic shape. The forces and stiffnesses versus the geometric and magnetic characteristics of rings have been calculated also in relation to the possible stability of conic bearings.

Numerical analysis of eddy current NDT for a tube with cracks using 3D indirect BIEM

In this paper, the 3-dimensional indirect boundary integral equation method (BIEM) is applied to the numerical analysis of eddy current non-destructive testing (NDT) for a tube with cracks. The indirect BIEM is developed in terms of the equivalent surface current density and equivalent surface charge density on the interface. The existence and type of the crack in the pipe can be determined from the distortion of the magnetic charge density distribution. The impedance signal is calculated from the equivalent surface charge density without calculating the self inductance. The axisymmetric and the 90-degree circular outer crack problems are calculated as an example. The result shows the usage of the indirect BIEM in the area of eddy current NDT.

Uniform Asymptotic Po Diffraction Coefficients for an Anisotropic Impedance Half-Plane

Uniform asymptotic Physical Optics diffraction coefficients for an anisotropic half-plane illuminated at oblique incidence are given in this paper. From the electromagnetic viewpoint such a structure is characterized by suitable anisotropic impedance boundary conditions. The principal axes of anisotropy can be not coincident with the half-plane edge. The solution is obtained by using a Physical Optics approximation of the equivalent surface current densities on the half-plane and by performing an uniform asymptotic evaluation of the radiation integral. Some numerical results are reported to demonstrate the effectiveness of the proposed approach.

3-D FEM/BEM-hybrid approach based on a general formulation of Huygens' principle for planar layered media

Huygens' principle is used to exclude inhomogeneous regions and ideal conducting regions from planar layered structures. The fields in the inhomogeneous regions are modeled by the finite-element method (FEM) with tetrahedral edge elements in terms of the electric-field strength E/spl I.oarr/. The fields in the layered structure are described by an integral representation of the electric-field strength E/spl I.oarr/ in terms of equivalent electric and magnetic Huygens' surface current densities for the inhomogeneous regions, and in terms of electric Huygens' surface current densities for ideal conducting regions. It is formulated with the help of electromagnetic (EM) potentials resulting in low-order singular integral kernels to facilitate the numerical handling of the integral representation. A general formulation of the integral representation is given for observation points lying in the Huygens' surface. As compared to the homogeneous-space case, additional terms in the integral representation have to be considered if parts of the Huygens' surface lie in an interface of layers with different material properties. An integral equation is formulated and discretized by a Galerkin testing procedure (boundary-element method), together with the finite-element (FE) system resulting in an unequivocal discretized description of the entire field problem. The method is validated with the help of a canonical test problem. Further numerical results are presented for dielectric resonators coupled to microstrip circuits.

Application of modal expansion and method of moments to study electromagnetic scattering from a rectangular cavity recessed in a three‐dimensional conducting surface

The problem of electromagnetic (EM) scattering from an aperture backed by a rectangular cavity recessed in a three‐dimensional (3‐D) conducting body is analyzed using the modal expansion inside and the integral equation method outside the cavity. Assuming (1) an equivalent electric surface current density flowing on the 3‐D conducting surface of the object including the cavity aperture and (2) an equivalent magnetic surface current density flowing over the aperture, only the scattered fields outside the cavity are determined . The EM fields inside the cavity are determined using the waveguide modal expansion functions. Making the total tangential electric and magnetic fields across the aperture continuous and subjecting the total tangential electric field on the outer conducting 3‐D surface of the object to zero, a set of coupled integral equations is obtained. The equivalent electric and magnetic surface currents are then obtained by solving the coupled integral equation using the method of moments (MoM). The numerical results on scattering from rectangular cavities embedded in various 3‐D objects are compared with the results obtained by other numerical techniques.

A novel method for the characterization of LSE-type dielectric waveguides

A novel method is developed to calculate the propagation characteristics of dielectric ridge structures in high-frequency monolithic integrated circuits. The electric field in the dielectric ridge is expressed in terms of a polarization current from which an equivalent surface current density is defined. Generalized boundary conditions are enforced in order to provide a simple integral equation. Results derived by this modified integral equation approach give excellent agreement with other numerical methods. The main advantage of this technique is that it greatly simplifies the analysis of three-dimensional complex structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Current distribution in exciting coil conductors in cross-field heating systems

The current distribution in the exciting coils of double-sided iron-backed cross-field heating systems is analyzed. The finite-difference method is used to calculate the internal resistance of the winding. The internal resistance is used as a criterion in studying the effect of the load on the winding current distribution. The concept of equivalent surface current density shows the influence of such parameters as the winding cross section and the skin depth. Equivalent surface current density is obtained by placing virtual current sources at the interface of the winding conductor and the air gap. Impedance values calculated using the two methods are in agreement.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Novel basis function for the equivalent magnetic current in the method of moments solution of dielectric scattering problems

In the method of moments surface formulation of dielectric scattering problems, two sets of basis functions are required for the equivalent electric and magnetic surface current density. In the Letter a novel simple basis function for the magnetic current is presented which is approximately spatially orthogonal to the widely used basis function developed by Rao et al.

Electromagnetic scattering from conductor‐coated material bodies

AbstractA moment method solution is presented to compute electromagnetic scattering from material bodies. The bodies are supposed to be homogeneous, arbitrarily shaped and lossy; they can be coated with very thin perfect conductors in some parts. A formulation of the scattering problem is made in terms of the equivalent surface current densities for which mixed potentials are used. The equivalent currents are expanded in the space‐domain by a triangular expansion function on the triangulated surfaces of the scatterer. The Galerkin procedure is carried out to test boundary integral equations and reduce the functional form of the equations to a partitioned matrix equation. The solution is applied to the scattering problem of a dielectric slab, a thin conductor coated by absorber material and a rectangular patch on a grounded dielectric slab. The computed backscattering radar cross‐section and surface current densities of the structures are presented and some of the results are compared with experimental data.

Perfectly conducting diffraction grating formalisms extended to good conductors via the surface impedance boundary condition

The surface impedance boundary condition is used to include the effect of high conductivity of meals in the integral theory of perfectly conducting gratings. As an intuitive approach, the diffraction formalism proposed by Petit for the treatment of infinitely conducting gratings in P polarization is extended to highly conducting materials by introducing the concept of equivalent surface current density. Then, integral equations for both polarizations are deduced in a mathematically rigorous way. The new method is used to calculate the efficiencies of sinusoidal gratings at infrared and visible light, and the numerical results are compared with those obtained using Maxwell boundary conditions and also with the perfect conductivity model.