Finite Element-boundary Integral Method Research Articles

Enhancing the Modeling Capability of the FE-BI Method for Simulation of Cavity-Backed Antennas and Arrays

The modeling capability of the finite element-boundary integral (FE-BI) technique is expanded for the analysis and design of cavity-backed antennas and arrays consisting of complex, inhomogeneous, and anisotropic materials. The adaptive integral method (AIM) is implemented to accelerate the evaluation of the time-consuming boundary integrals. The modeling of anisotropic materials, impedance boundary conditions, and resistive boundary conditions is also addressed. Validation examples and comparison data are presented to demonstrate the acceleration and memory reduction achieved as a result of this enhancement.

Numerical Simulation of BOR Scattering and Radiation Using a Higher Order FEM

Numerical simulations of body-of-revolution geometries for scattering and radiation problems are presented. The formulation consists of a finite element-boundary integral (FE-BI) method which is based on a finite element method that uses higher order nodal-based scalar basis functions for the azimuthal field component and higher order edge-based vector basis functions for the transverse field. This formulation, when combined with a symmetric FE-BI hybridization scheme, yields a final system of equations that is more accurate than earlier first-order formulations. Numerical examples are given to demonstrate the accuracy and capabilities of the higher order solution

Full-wave electromagnetic and thermal modeling for the prediction of heat-dissipation-induced RF-MEMS switch failure**This work was supported in part by the National Science Foundation under grant no ECS-01152222.

We propose an extended finite element-boundary integral method (EFE-BI) to model the electromagnetic (EM) behavior of RF-MEMS switches over a wide frequency range from UHF to terahertz. Our new method integrates EM with finite element heat transfer analysis to extract heat dissipation on the micrometer-scale switch beam due to the non-uniform radio frequency (RF) current distribution. The developed EFE-BI technique is an extension of the standard finite element-boundary integral (FE-BI) method to allow for accurate characterization of RF-MEMS structures whose entire size is a small fraction of a wavelength (λ/250 or less) and may contain dimensions in the order of λ/50 000 or less. Our model predictions exhibit good agreement with experimental results obtained independent of the current study.

Application of the inner–outer flexible GMRES-FFT method to the analysis of scattering and radiation by cavity-backed patch antennas and arrays

The finite element-boundary integral (FE-BI) method is applied for the analysis of scattering and radiation by cavity-backed patch antenna and arrays. In this investigation, the FE-BI formulations have been implemented using brick element volumes and it allows for a particular use of the efficient FFT-based iterative solver. The inner–outer flexible GMRES algorithm is applied to solve the equation with a higher convergence speed when compared with the standard GMRES algorithm.

Design of a frequency selective structure with inhomogeneous substrates as a thermophotovoltaic filter

In this paper, the design of a thermophotovoltaic (TPV) filter with high-pass characteristics is presented. The filter is in the form of a frequency selective structure (FSS) with cascaded inhomogeneous dielectric substrates. The goal is to allow for more design flexibility using dielectric periodic structures to deliver a sharper filter response. Therefore, the primary focus is to design a periodic material substrate composition (supporting FSS elements) using a topology optimization technique known as the density method. The design problem is formulated as a general nonlinear optimization problem and sequential linear programming is used to solve the optimization problem with the sensitivity analysis based on the adjoint variable method for complex variables. A key aspect of the proposed design method is the integration of optimization tools with a fast simulator based on the finite element-boundary integral method. The capability of the design method is demonstrated by designing the material distribution for a TPV filter subject to pre-specified bandwidth and compactness criteria.

Pareto optimal design of absorbers using a parallel elitist nondominated sorting genetic algorithm and the finite element-boundary integral method

Microwave absorbing structures have many applications including the lining of anechoic chambers and the reduction of electromagnetic interference. Pareto optimization is an important tool in the design of absorbers, since most absorbers must be designed keeping both performance and economy in mind. In this paper, a new elitist strategy is implemented into the nondominated sorting genetic algorithm (NSGA) to effectively and efficiently design broadband high performance electromagnetic absorbers. The absorbers are analyzed using the finite element boundary integral method, and the optimization is accelerated with parallel processing. Numerical tests demonstrate that the elitist NSGA proposed in this paper converges faster that the standard NSGA and other classical techniques for a wide variety of absorber design problems. Finally, this efficient elitist NSGA is applied to design complex polygonal absorbers. Numerical results not only demonstrate the robustness of the design algorithm, but also reveal some important information and advantages related to absorber designs based on Pareto optimization.

Scattering of Three-Dimensional Chiral Objects above a Perfect Conducting Plane by Hybrid Finite Element Method

Electromagnetic scattering from three-dimensional chiral objects above a perfectly electric or magnetic conducting plane (PEC and PMC) is analyzed by the hybrid finite element-boundary integral (FEM-BI) method. The chiral image principle is used to transform the original single chiral target in half space into two chiral targets with the same permittivity and permeability yet conjugate chirality parameters. Numerical examples demonstrate that the FEM-BI method provides a flexible and powerful solution of multiple scattering from inhomogeneous chiral objects. Both near field distribution and radar cross section (RCS) of chiral objects illuminated by plane waves are provided to demonstrate the effectiveness of the hybrid method.

Efficient electromagnetic near-field computation by the multilevel fast multipole method employing mixed near-field/far-field translations

Method of moments (MoM) solutions of electromagnetic surface integral equations provide the desired amplitudes of the equivalent surface currents on the Huygens' surfaces around the involved objects, where the solution process is nowadays routinely accelerated by fast integral methods such as the multilevel fast multipole method (MLFMM). Computation of radiated or scattered electromagnetic fields produced by these currents requires integration over the Huygens' surfaces and can easily become extremely time-consuming for large numbers of observation points. In this contribution, integration of electromagnetic near-fields is accelerated by a postprocessing MLFMM approach, where near-field and far-field translations are combined in order to achieve optimum performance. The proposed approach has been applied in the postprocessing stage of a finite element boundary integral (FEBI) method with fast integral equation solution by MLFMM, saving a large amount of postprocessing computation time. The formulation of the proposed acceleration is presented and numerical results are shown.

Dual-Polarized Frequency-Tunable Composite Left-Handed Slab

A dual-polarized frequency-tunable composite left-handed slab (CLS) is proposed. The CLS consists of periodic split-ring resonators (SRRs) along with thin wires. Two orthogonal SRR/wire arrays are utilized for dual-polarization purposes. Polarization-selectivity and frequency-tuning are achieved by means of on/off switches placed between the rings of the SRR. By opening all of the switches for one array and closing them for the other, the left-handed behavior can be switched on and off, respectively. Frequency-tuning performance is then achieved by turning on/off the switches in the former array. Transmission characteristics of the composite structure are predicted using a fast periodic array simulator based on the hybrid finite element-boundary integral (FE-BI) method in conjunction with the fast spectral domain algorithm (FSDA). Numerical results demonstrate dual-polarization and frequency-tuning performance of the proposed switching configuration.

Topology optimization of dielectric substrates for filters and antennas using SIMP

In this paper a novel design procedure based on the integration of full wave Finite Element Analysis (FEA) and a topology design method employing Sequential Linear Programming (SLP) is introduced. The employed design method is the Solid Isotropic Material with Penalization (SIMP) technique formulated as a general non-linear optimization problem. SLP is used to solve the optimization problem with the sensitivity analysis based on the adjoint variable method for complex variables. A key aspect of the proposed design method is the integration of optimization tools with a fast simulator based on the finite element-boundary integral (FE-BI) method. The capability of the design method is demonstrated by two design examples. First, we developed a metamaterial substrate with arbitrary material composition and subject to a pre-specified antenna bandwidth enhancement. The design is verified and its performance is evaluated via measurements and simulation. As a second example, the material distribution for a Thermo-Photovoltaic (TPV) filter subject to pre-specified bandwidth and compactness criteria is designed. Results show that the proposed design method is capable of designing full three-dimensional volumetric material textures and printed conductor topologies for filters and patch antennas with enhanced performance.

Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry

In this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons with the finite elementboundary integral method are given in terms of accuracy and computing resources. We also discuss preconditioning, parallelization of the multilevel fast multipole method and propose higher-order basis for curvilinear quadrilaterals and volumetric basis functions for curvilinear hexahedra. The latter have the desirable property of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications. keyword: Radar scattering, magnetic materials, volume integral equations, finite-element boundary-integral method, fast multipole method, parallelization, antenna radiation, preconditioning, curvilinear elements, higherorder basis functions.

Modeling Conformal Antennas on Metallic Prolate Spheroid Surfaces Using a Hybrid Finite Element Method

In this paper, the hybrid finite element-boundary integral (FE-BI) method appropriate for modeling conformal antennas on doubly curved surfaces is developed. The FE-BI method is extended to model doubly curved, convex surfaces by means of a specially formulated asymptotic dyadic Green's function. The FE-BI method will then be used to examine the effect of curvature variation on the resonant input impedance of a cavity-backed, conformal slot antenna and a conformal patch antenna recessed in a perfectly conducting, electrically large prolate spheroid surface. The prolate spheroid shape provides a canonical representation of a doubly curved mounting surface. The numerical results for conformal slot and patch antennas on the prolate spheroid are compared as a function of curvature and orientation.

A Flush-Mounted Multifunctional Slot Aperture (Combo-Antenna) for Automotive Applications

Two novel antennas: a variable growth, two-arm slot spiral and an annular slot are combined into a single, multicavity backed configuration. The spiral occupies the center/interior region and operates as a second mode circularly polarized (CP) antenna at 2.339 GHz. The annular slot occupies the outer region (at the periphery of the spiral) and is designed to operate as an omnidirectional vertically polarized antenna at 1.472 GHz. This combo antenna is intended for automotive applications and it was designed using the finite element-boundary integral method. Its performance was verified experimentally in a stand alone configuration and while mounted on a vehicle platform.

Electromagnetic Scattering from Three-Dimensional Bianisotropic Objects using Hybrid Finite Element-Boundary Integral Method

Electromagnetic scattering from arbitrarythree-dimensional bianisotropic objects is studied using hybrid finite element-boundary integral method. Analy tical expressions of finite element matrices for tetrahedrons are at first derived with the aid of Schur product of matrices. These expressions are valid for anylinear bianisotropic materials and are in consistent with those previously published for isotropic media. Numerical calculations are carried out so as to validate our developed algorithm. Further, the effects of different bianisotropic material parameters on the scattering characteristics of some typical three-dimensional objects are examined and compared.

Robust design of absorbers using genetic algorithms and the finite element-boundary integral method

A new method for the genetic algorithm (GA) based design of broadband, high-performance electromagnetic absorbers is discussed. The method gives rise to novel absorber designs with a geometrical complexity greater than that of absorbers typically in use today. The finite element-boundary integral method is applied to efficiently analyze the scattering from complex geometries occupied by given lossy material, and genetic algorithms are adopted to optimize the geometry parameters to minimize the overall reflection coefficients. In addition, a method is proposed for accelerating the convergence of the GA. Numerical results for absorbers are presented for wide-angle incidence over a broad frequency range considering both polarizations, and demonstrate the new technique's power and robustness.

Chiral cover effects on microstrip antennas

By exploiting a rigorous variational formulation, we point out the main effects of a chiral cover on a cavity backed microstrip patch antenna. A hybrid finite element-boundary integral method is employed to solve numerically the electromagnetic problem modeled by a variational functional. The dependence of the resonance frequency on the cover thickness and on the chirality admittance of the material is first investigated. In more detail, it is demonstrated that a chiral cover permits reducing the antenna dimensions, compared to an isotropic one, for a fixed working frequency. Then, through several numerical examples, we also investigate the variation of gain properties, cross-polarization levels, radiation resistance, radiation efficiency, and radar cross-section.

Mutual coupling between patch antennas recessed in an elliptic cylinder

Cavity-backed microstrip patch antennas are often used in aircraft applications because of their ability to conform to the vehicle surface. For arrays of patches, it is important to be able to predict the dependence on surface curvature of the coupling between patches. The mutual impedance between two rectangular patch antennas recessed in an elliptic cylinder is computed using a finite element-boundary integral method. Results show that the coupling between the antennas is dependent on the curvature of the cylinder surface. For H-plane coupling, the coupling decreases as the radius of curvature increases. For E-plane coupling, the strongest coupling occurs for a specific curvature.

Hybrid finite element-boundary integral method for cavities recessed in an elliptic cylinder

The highly versatile finite element-boundary integral method is presented for accurate modeling of fields within cavities recessed in a perfectly conducting, infinite, elliptic cylinder. Properties of flush-mounted cavities and antennas are explored and compared with prior developments. This formulation represents a significant advancement over prior techniques since surface curvature variation, either across a single element or across an array of elements, is now accurately included into the antenna model. An advantage of this approach is the ability to model cavities with curvature varying from planar to the constant curvature of a circular cylinder. Computed eigenvalues for planar-rectangular and cylindrical-rectangular closed cavities are compared with theoretical values. Eigenvalues are presented for elliptic-rectangular cavities. Furthermore, the input impedance of a conformal cavity-backed patch antenna mounted on an elliptic cylinder is presented and compared with a similar antenna on a circular cylinder.

Radiation and scattering features of patch antennas with bianisotropic substrates

The analysis of patch antennas residing in cavities filled by general inhomogeneous and lossy bianisotropic substrates is presented. The theoretical study is based on a variational formulation associated with the boundary value problem under analysis, and a hybrid finite element-boundary integral method is employed to solve the electromagnetic field inside and outside cavities numerically. Initially, the general formulation presented is applied to some particular cases known in the literature. Then, the main scattering and radiation features of cavity backed patch antennas with chiral, anisotropic, and bianisotropic materials are presented. Particularly, it is shown that complex media allow for frequency control and for a reduced antenna size at a given operating frequency.

Mutual coupling in conformal microstrip patch antenna arrays

A finite element–boundary integral method has been developed to investigate the impedance properties of patch elements in an array environment, when the array is embedded in a conformal surface. The effect of mutual coupling between elements in such an array is included in the analysis. In this paper, the method is tested on patch antennas mounted on planar and cylindrical surfaces. For the examples considered, it is shown that the simulated results are in good agreement with measurement.