Volume Integral Equation Method Research Articles

Optimization of plasma parameters for effective attenuation of microwaves in specified frequency range

AbstractIn this article, a plasma‐metal model is studied as an electromagnetic absorber for stealth application. Epstain distribution is considered for plasma and the electromagnetic reflection of the structure is analyzed by the Green's function volume integral equation method. The attenuation of microwaves in plasma depends on microwave frequency, plasma electron density, spatial distribution of plasma, collision frequency, and plasma thickness. Using a metaheuristic optimization method, it is possible to change the parameters simultaneously in the specified domains to obtain conditions for which microwaves can be absorbed effectively in the specified frequency. In this paper, optimized plasma parameters related to ideal attenuation in desired frequency band are determined by this method. The advantage of this method is that the intervals related to the plasma parameters are selecting according to the practical conditions and in many cases prevent the production of high volume with high density plasma to achieve effective attenuation. The proposed method can be useful for designing adjustable devices in stealth applications. Proper management of power consumption in these devices is one of the results of adjustment.

Decreasing the memory of the discontinuous Galerkin volume integral equation method for scattering from inhomogeneous dielectric objects.

A memory-efficient implementation scheme for the discontinuous Galerkin volume integral equation method (DGVIE) using Schaubert-Wilton-Glisson (SWG) basis functions is proposed to analyze electromagnetic scattering from inhomogeneous dielectric objects. For this proposed scheme, almost no half-SWG basis functions are needed for the elements separating nonconformal meshes, while these half-SWG basis functions are indispensable for the conventional DGVIE-SWG method. This is realized by applying the divergence-free condition of the electric displacement vector explicitly for nonconformal meshes separating neighboring subdomains of an inhomogeneous dielectric body. Therefore, the number of unknowns of the conventional DGVIE method can be further reduced. As a result, the memory of the proposed DGVIE method is only about half of the conventional one for inhomogeneous dielectric problems. Meanwhile, the total solution time has been reduced by the use of the proposed scheme. Particularly, the proposed DGVIE-SWG method is efficient in memory usage not only for inhomogeneous dielectric cases with high contrast ratio but also for cases with relatively low contrast ratio.

A Parallel 3D Spatial Spectral Volume Integral Equation Method for Electromagnetic Scattering from Finite Scatterers

A Parallel 3D Spatial Spectral Volume Integral Equation Method for Electromagnetic Scattering from Finite Scatterers

Parallel volume integral equation method for three-dimensional multiple inclusion problems

Parallel volume integral equation method for three-dimensional multiple inclusion problems

Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters

This article presents a novel method to accurately simulate electromagnetic scattering at homogeneous polygonal cylinders with arbitrary material properties. A single source equivalence approach is invoked, allowing to substitute the background medium for the inner material of the scatterer, provided an equivalent surface current density is introduced. We construct the pertinent differential surface admittance operator by means of the Fokas method, establishing a map between the known Dirichlet boundary values and their unknown Neumann counterparts. However, to allow for lossy materials, we extend the Fokas method to complex wavenumbers. The novel formalism, employing pulse-shaped local basis functions, natively supports combined magnetic and dielectric contrast, accurately captures the skin effect, and is conveniently integrated in traditional boundary integral equation formulations. The correctness and versatility of our technique are verified for various examples by means of analytical validation and through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.

An Efficient Volume Integral Equation Method for Analysis of Boresight Error of a Radome with Minor Ablation

In this paper, an efficient method based on volume integral equation is developed to analyze the effects of ablation of a radome on the boresight error. To avoid recalculating the whole impedance matrix when the permittivity of the radome or the shape of the top portion is slightly changed due to ablation, the radome is divided into unaffected and affected parts and the volume equivalent current instead of the displacement current is used as the unknown. This permits us to reassemble rather than recalculate the impedance matrix when the ablation condition is altered. Moreover, a viable preconditioning technique is introduced and integrated with the multilevel fast multipole algorithm (MLFMA) to cope with the electrically large antenna-radome system (ARS). Simulation results are provided for the boresight error (BSE) and boresight error slope (BSES) of the ARS at some different ablation states. The present approach is considerably faster than using the conventional methods.

Volume Integral Equation Method Solution for Spheroidal Inclusion Problem.

In this paper, the volume integral equation method (VIEM) is introduced for the numerical analysis of an infinite isotropic solid containing a variety of single isotropic/anisotropic spheroidal inclusions. In order to introduce the VIEM as a versatile numerical method for the three-dimensional elastostatic inclusion problem, VIEM results are first presented for a range of single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under uniform remote tensile loading. We next considered single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under remote shear loading. The authors hope that the results using the VIEM cited in this paper will be established as reference values for verifying the results of similar research using other analytical and numerical methods.

Algorithm for inversion of resistivity logging-while-drilling data in 2D pixel-based model

Multi-frequency and multi-component extra-deep azimuthal resistivity measurements with depth of investigation of a few tens of meters provide advanced possibilities for mapping of complex reservoir structures. Inversion of the induction measurements set becomes an important technical problem. We present a regularized Levenberg–Marquardt algorithm for inversion of resistivity measurements in a 2D environment model with pixel-based resistivity distribution. The cornerstone of the approach is an efficient parallel algorithm for computation of resistivity tool signals and its derivatives with respect to the pixel conductivities using volume integral equation method. Numerical tests of the suggested approach demonstrate its feasibility for near real time inversion.

A 2-D differential surface admittance operator for combined magnetic and dielectric contrast

In this paper, we present a novel technique to accurately model scattering phenomena at two-dimensional circular and rectangular structures consisting of arbitrary homogeneous materials, including magnetic media in particular. The proposed formalism utilizes a differential surface admittance operator, which invokes a single source equivalence theorem to replace the inside material by its surrounding medium, while introducing an equivalent surface current density. The arbitrary magnetic contrast can be combined with an arbitrary electrical conductivity. As such, the skin effect is rigorously taken into account, making our method ideally suited for broadband modeling of good conductors as well. It is demonstrated that an appropriate choice of the basis functions for the discretized problem is critical to obtain a convergent result when magnetic contrast is introduced. The method is analytically validated for the case of a circular cylinder and additional numerical results illustrate the correctness of the technique for (combinations of) rectangular cylinders, through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.

Characteristic basis function method based on mixed discretization for analyzing scattering from electrically large inhomogeneous objects

The characteristic basis function method (CBFM) based on the mixed discretization (MD) is firstly proposed to analyze the electromagnetic scattering from electrically large inhomogeneous objects. The discontinuous Galerkin volume integral equation (DGVIE) method which employs nonconformal discretization permits to independently discretize the various component regions of the inhomogeneous object depending on its local shape or dielectric permittivity. Moreover, by the means of the CBFM, the low-level basis functions employed in the DGVIE method are converted into high-level basis functions, dramatically reducing the number of basis functions for modeling. In addition, the conformal discretization which is superior in dealing with homogenous regions is mixed with the nonconformal discretization to further cut down the number of the basis functions. Numerical results show that the CBFM based on mixed discretization (MD-CBFM) generates much less unknowns in contrast to several conventional methods. Several composite inhomogeneous examples are given to demonstrate the accuracy and efficiency of the proposed method.

Direct solution of the volume integral equation for electromagnetic scattering from dielectric objects with negative permittivity.

In this paper, electromagnetic scattering from dielectric objects with negative permittivity is solved by the volume integral equation (VIE)-hierarchical matrix (H-matrix)-based fast direct solver. To improve solution efficiency, a coarsening algorithm for the H-matrix is used, and the key parameter for the admissible condition is optimized through numerical experiments. Finally, the discontinuous Galerkin (DG) VIE (DGVIE) method is developed for the fast direct solver. It is shown that scattering from inhomogeneous dielectric objects with negative permittivity and with multiscale structure can be analyzed efficiently by the DGVIE-H-matrix-based fast direct solver.

Cutoff Wavenumbers of Multilayered Gyrotropic Circular Waveguides

A coupled-field volume integral equation (CFVIE) method is developed for the calculation of the normalized cutoff wavenumbers of circular metallic walled waveguides having concentric continuously varying highly inhomogeneous gyrotropic (i.e., gyroelectric and gyromagnetic) infill. The normalized cutoff wavenumbers are obtained as the roots of a determinantal equation formed by solving the CFVIEs using the cylindrical Dini series expansion (CDSE) method where the unknown fields inside the waveguide are expanded by entire domain orthogonal Dini-type vectorial basis functions. To account for the electric boundary condition (BC) on waveguide's circular perfect electric conducting (PEC) surface, two modified 2-D tensorial Green's functions (GFs), expanded in cylindrical vector wave functions (CVWFs), are employed in the kernels of the CFVIEs. These modified 2-D tensorial GFs are constructed by enforcing, on their dyadic form, the satisfaction of the electric BC. The CDSE, along with the modified 2-D tensorial GFs, allow for the analytical integration of the volumetric-type integrals and the reduction of the CFVIEs to a set of algebraic equations. We exhaustively demonstrate the validity of the CFVIE-CDSE by a series of comparisons on the normalized cutoff wavenumbers: we first construct the solutions for obtaining the normalized cutoff wavenumbers in homogeneous gyrotropic waveguides by the separation of variables method (SVM), and second, we employ HFSS commercial software for two-layered isotropic and three-layered gyroelectric loaded waveguides. We characterize the type of modes, i.e., TE/TM or hybrid HE/EH, for each configuration presented, and discuss the efficiency of the CFVIE-CDSE method.

Numerical solution of the integral equations of the electromagnetic field in geosteering problems

Extra-deep azimuthal resistivity measurements improve the depth of investigation up to 30 m from the wellbore. Interpretation of electromagnetic logging data in the neighbourhood of a well becomes an important technical problem. We present an efficient parallel method for computation of induction tool responses with multiple transmitter–receiver configurations in 2D pixel-based anisotropic model crossed by an arbitrary well trajectory. The cornerstone of the approach is volume integral equation method. We consider the conductivity distribution as a sum of background and anomalous conductivities. Background conductivity is 1D-layered. Anomalous conductivity has arbitrary 2D distribution. Electromagnetic fields are the superposition of background and anomalous fields. Background fields are calculated exactly using rigorous analytical solution for 1D-layered background model. With this approach, the 2D pixel-based model is treated as an extension of the 1D-layered model. The anomalous fields are required only in pixels with conductivity different from the conductivity of the 1D-layered model. Anomalous fields are calculated using convergent series of integral operators [1]. The approach takes into account conductivity anisotropy and allows obtaining both the exact solution and the fast approximate one. The convergence of approximate solution is investigated on some synthetic examples.

Fast Fourier transform-volume integral: a smart approach for the electromagnetic design of complex systems in large fusion devices

A volume integral (VI) equation method based on the fast Fourier transform (FFT) is proposed for the electromagnetic simulation of complex systems in large magnetic confinement fusion (MCF) devices. Such FFT-VI allows for dramatically reducing the time and the human effort required to adapt the CAD input files to models suited for electromagnetic simulations. Moreover, with FFT-VI the mesh generation is performed automatically and is very efficient and robust. The adoption of the FFT allows for significantly reducing the computation time and the memory requirements, therefore making simulations with several millions of unknowns feasible. Numerical results show that, in terms of numerical performances, the FFT-VI method applied to challenging electromagnetic problems in representative MCF devices is markedly superior with respect to the state of the art VI techniques. A sample implementation of FFT-VI is made publicly available.

Three-Dimensional Volume Integral Equation Method for Solving Isotropic/Anisotropic Inhomogeneity Problems

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM is introduced for the analysis of an unbounded isotropic solid composed of isotropic/anisotropic inhomogeneity of arbitrary shape. The authors hope that the volume integral equation method can be used to compute critical values of practical interest in realistic models of composites composed of strong anisotropic and/or heterogeneous inhomogeneities of arbitrary shapes.

An Entire Domain CFVIE-CDSE Method for EM Scattering on Electrically Large Highly Inhomogeneous Gyrotropic Circular Cylinders

A coupled-field volume integral equation (CFVIE) method for electromagnetic (EM) scattering on electrically large, highly inhomogeneous gyrotropic circular cylinders, under normal incidence, is developed in this work. The CFVIEs are solved by the cylindrical Dini series expansion (CDSE) method where the unknown fields are expanded by entire domain orthogonal vectorial basis functions. The main advantage of the present method is that it permits the scatterer to have continuously varying highly inhomogeneous gyrotropic characteristics, i.e., the constitutive parameters of the cylinder can be highly inhomogeneous in both gyroelectric and gyromagnetic tensors. Initially, the 2-D Green's function (GF) is expanded in a tensorial form using the cylindrical vector wave functions (CVWFs). Then, by employing the CDSE for the unknown fields, the 2-D volumetric integrals are carried out analytically, reducing the CFVIEs to a set of algebraic equations. The method is validated by comparisons with the exact solution based on the separation of variables method (SVM) for homogeneous gyroelectric/gyromagnetic cylinders, with HFSS commercial software for three-layered gyroelectric cylinders, as well as with the recently developed hybrid projection method (HPM) for electrically large continuously varying highly inhomogeneous isotropic cylinders. Results for combined gyroelectric-continuously varying highly inhomogeneous isotropic cylinders are presented and discussed.

Loops and Meshes Formulations for 3-D Eddy-Current Computation in Topologically Non-Trivial Domains With Volume Integral Equations

The volume integral equation method based on the current vector potential approximated by means edge element basis function is a well-established approach for 3-D eddy currents computation. The application of the method is straightforward when simply connected geometries and no connection with external circuits are involved. In this case, in fact, the solving system is easily obtained based on tree-cotree decomposition of the primal graph. However, when multiply connected geometries or external generators are considered, “additional” degrees of freedom, not related to interior cotree edges of the primal graph, need to be identified and involved to assure the consistency of the numerical solution. In this article, the link between the volume integral equation method and the circuit is investigated in detail, and the circuit view is used as a guide for systematically finding the additional degrees of freedom arising in case of multiply connected geometries and/or external circuits. In particular, the dual graph is introduced as the support of the circuit and it is shown that this is the natural frame for taking the topology into account. For multiply connected geometries, the additional degrees of freedom are related to loop currents crossing one only time (or an odd number of times) any cutting surface making the domain simply connected, and are found by applying a minimum path algorithm on the dual graph forming the circuit. In case of conducting domain connected to an external generator, an extended dual graph is introduced for finding the further additional degrees of freedom. This article also researches into the possibility to replace the usual current density of the elements, obtained via facet-element shape functions and exactly matching the current of the faces, with a uniform current density obtained by means of a minimum error procedure and approximately matching the current of the faces. The use of this uniform current density, besides improving the calculation time and the accuracy of the coupling coefficients, also allows the extension of the volume integral equation method to discretizations of the problem domain made of arbitrarily shaped polyhedral elements.

Magnetic switching of Kerker scattering in spherical microresonators

Abstract Magneto-optical materials have become a key tool in functional nanophotonics, mainly due to their ability to offer active tuning between two different operational states in subwavelength structures. In the long-wavelength limit, such states may be considered as the directional forward- and back-scattering operations, due to the interplay between magnetic and electric dipolar modes, which act as equivalent Huygens sources. In this work, on the basis of full-wave electrodynamic calculations based on a rigorous volume integral equation (VIE) method, we demonstrate the feasibility of obtaining magnetically-tunable directionality inversion in spherical microresonators (THz antennas) coated by magneto-optical materials. In particular, our analysis reveals that when a high-index dielectric is coated with a magneto-optical material, we can switch the back-scattering of the whole particle to forward-scattering simply by turning off/on an external magnetic field bias. The validity of our calculations is confirmed by reproducing the above two-state operation, predicted by the VIE, with full-wave finite-element commercial software. Our results are of interest for the design of state-of-the-art active metasurfaces and metalenses, as well as for functional nanophotonic structures, and scattering and nanoantennas engineering.

Theoretical analysis of compact cylindrical microlenses for terahertz photoconductive antennas in the photomixer regime

A terahertz photoconductive antenna placed on the back side of a semiconductor slab with and without a compact cylindrical semiconductor microlens on the front side is studied theoretically. The antenna is operated as a photomixer giving narrowband radiation at 1 THz. Radiation patterns and emitted powers are found to oscillate with slab thickness as a consequence of multiple-reflection interference. It is further shown that an antireflection layer on the lens may eliminate these oscillations to a large extent. In the absence of a lens, most of the radiation is trapped inside the semiconductor slab, and the radiation pattern is far from that of a pencil-beam. Both light trapping and radiation patterns are shown to be significantly improved by a very compact lens with a size smaller than a cubic wavelength. The improvements on outcoupling of radiation in a predominantly forward direction versus lens radius and height are mapped out. The calculated outcoupling efficiency of the antenna-lens system takes into account the Purcell effect and radiation trapped in the semiconductor slab. The antenna-lens system is modeled rigorously by using the Green’s function volume integral equation method in a form that exploits cylindrical symmetry.

Volume Integral Equation Methods for Axisymmetric Problems With Conductive and Magnetic Media

Two new different integral equation methods for the study of axisymmetric harmonic electromagnetic problems are presented. Both proposed formulations allow the modeling of conductive and magnetic media, and inhomogeneous media can be considered as well. Thanks to the use of low-rank approximation techniques, a drastic reduction in the required memory and computational cost is achieved with a truly negligible loss of accuracy. The numerical features of the two proposed integral methods are widely discussed and compared. Moreover, most of the considerations hold for the case of 3-D integral methods. Sample implementations of the two formulations are made publicly available.