Electromagnetic solution for composite metallic and material objects with FEBI method and multilevel complex source beam method

Summary form only given. Numerical analysis of electromagnetic scattering has been widely studied in the past. The method of moments (MoM) is suitable to simulate scattering from an object in an open region. In order to solve problems with complicated geometries and materials, the finite element method (FEM) is preferred. However, when solving unbounded problems with FEM, the use of absorbing boundary conditions or perfectly matched layers will result in truncation errors. To combine the advantages of both MoM and FEM, the finite element-boundary integral (FE-BI) method was developed and widely used (J. M. Jin, The Finite Element Method in Electromagnetics, Second Edition. New York: Wiley, 2002). This algorithm is not only able to deal with highly complicated geometry and material, but also able to eliminate the truncation error. However, since the MoM has O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2)</sup> computational and storage complexities, the computational cost of the BI-related algorithm is still prohibitively high when solving large-scale scattering problems. To alleviate this problem, the multilevel fast multipole algorithm (MLFMA) has been incorporated into the FE-BI method (J. Liu and J. M. Jin, IEEE Trans. Antennas Propag., vol. 51, pp.1157-1167, Jun. 2003). Another important technique to accelerate the computation is to resort to parallel computers. Recently, the graphics processing unit (GPU), as one of many-core computing systems, has received intensive attention from the scientific computing community due to its low price, a massive number of processors, and the resulting high computational efficiency. In this work, we discuss the GPU implementation of the FE-BI algorithm for solving electromagnetic scattering problems. First, the assembly of the BI-related matrix is parallelized on GPU by NVIDIA's compute unified device architecture (CUDA). A massive number of threads are assigned to carry out the assembly, and each thread computes one element in the BI-related matrix. Second, both the direct and iterative solvers are implemented on GPU. For the direct solver, the Intel's math kernel library (MKL) is used for LU decomposition, and the CUSPARSE (a set of basic linear algebra subroutines used for handling sparse matrices) is employed to speedup forward and backward substitutions. For the iterative solver, the high performance CUDA Basic Linear Algebra Subprograms (BLAS) is utilized for the matrix-vector multiplication and the vector-vector multiplication. Extensive numerical experiments are conducted to validate the implementation and demonstrate the achievable computational speedup.

Finite element-boundary integral (FE-BI) method is a powerful tool to model electromagnetic scattering from three-dimensional large, deep, and arbitrarily-shaped cavities. The FE-BI method with higher-order tetrahedral element has been implemented to evaluate the interior electromagnetic scattering from typical and unconventional cavity structure. Using this method, we can understand the underlying phenomena of scattering from various cavities, which will benefit the design of realistic cavity structure

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.

By virtue of their low operation count, the application of fast integral methods such as the fast multipole (FMM) and adaptive integral methods (AIM) result in a substantial quickening of the boundary integral portion of the hybrid finite element-boundary integral (FE-BI) method, independent of the shape of the BI contour. Recently, various versions of the FMM have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this Letter is to provide a comparison of the effect of these fast integral algorithms on the boundary integral when used in conjunction with the traditional FE-BI method.

Numerical computations of electromagnetic radiation and scattering problems for arbitrarily shaped and electrically large objects in the same environment are preferably performed by combining the method of moments (MoM) with the uniform geometrical theory of diffraction (UTD). Composite metallic/dielectric objects with arbitrary shape are handled efficiently with the finite element boundary integral (FEBI) method. For large scale problems, the MoM solution is accelerated by the multilevel level fast multipole method (MLFMM). On the other hand, electrically large objects with relatively simple shape are treated sufficiently with ray-based high-frequency methods, like geometrical optics (GO) and UTD. However, until now MoM-UTD hybrid approaches have been restricted to conventional MoM formulations with only the electric field integral equation (EFIE), resulting in limited modeling capabilities. The same restrictions also exist in the hybrid FEBI-UTD method. The paper presents MLFMM-UTD hybridization for the combined field integral equation (CFIE), in order to extend further the applicability of the FEBI-UTD method. The resulting modeling technique is referred to as the FEBI-MLFMM-UTD method. The MLFMM-UTD hybridization is performed in the translation procedure on the various MLFMM levels, by taking into account additional contributions received at the testing groups due to UTD objects. Due to different ray directions for outgoing and incoming waves, appropriate interpolation and anterpolation procedures must be applied to consider the UTD contributions.

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme.

A new iterative strategy combining analytical Kirchhoff Approximation (KA) with the powerful simulation tool finite elementboundary integral (FE-BI) method is presented in this paper to study the interactions between an object and the underlying rough surface. This hybrid FE-BI-KA scheme is an improved and generalized version of MOM-KA. Instead of using MOM, FE-BI is used to model scattering from the above object with the original incidence and scattered wave by the rough surface as the exciting source. Whereas scattering from rough surface is studied by the classical KA in order to reduce the computation resource and time required

Finite element - boundary integral (FE-BI) equations with domain decomposition method (DDM) provide a very powerful way of combining FE-BI method and DDM for modeling total electromagnetic scattering from cavities. But its resultant system of linear equations is usually ill-conditioned and has to be preconditioned for speeding up iterative solution process. This ill-conditioned matrix equation can be preconditioned using finite element-robin transmission condition-absorber boundary condition (FE-RTC-ABC) preconditioner. In this paper, we propose an efficient way to implement the FE-RTC-ABC preconditioner for large FE-BI-DDM system through applying the reverse Cuthill-McKee (RCM) algorithm in iterative solution process. Numerical results obtained show the effectiveness of the proposed implementation of the FE-RTC-ABC preconditioner for solving cavity problems.

We present a surface integral equation (SIE) solution for a special class of anisotropic media, whose permittivity and permeability are both symmetric full tensors with the same or multiple values. This kind of media is generated from the invisible cloaking or absorbing material of a perfectly matched layer (PML) design. A new derivation based on the potential functions is presented to obtain the closed-form Green’s function. Detailed and rigorous proofs of some vector identities are given for the first time. Special treatments are detailed to address the singularity of the anisotropic Green’s function for discretizing the SIE. Numerical experiments validate the accuracy, stability, and high efficiency of the proposed solution compared with the analytical solution or the finite element-boundary integral (FE-BI) method.

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.

The finite element-boundary integral (FE-BI) method has been used in the past to characterize conformal antennas recessed in plane and circular cylinder surfaces. This method has also been extended for use in elliptic cylinder and prolate spheroid surfaces. Typically, the input, or driving point, impedance and radiation pattern have been quantities of particular interest. However, the mutual coupling between conformal antennas is also of interest for the design community. In this paper, the mutual impedance formulation and example results for microstrip patch antennas recessed in an elliptic cylinder are presented. In particular, validations with planar results in the limit of an electrically large cylinder are provided.

A domain decomposition method based on the hybrid finite element–boundary integral method is presented for analyzing electromagnetic scattering problems involving multiple separable objects. In this method, the finite element formulation is applied inside each object to derive a linear system of equations associated with edge field values. The boundary integral equation is then applied on the surfaces of the objects to truncate the computational domain and to connect the matrix subsystem generated from each object. The coupling system of equations is solved by a hybrid domain decomposition algorithm. Numerical results are presented to demonstrate the accuracy, efficiency, and capability of the proposed method.

Conformal antennas are typically mounted on surfaces which possess some curvature. However, no rigorous design analysis techniques are available for printed antennas on curved surfaces. Hence, most often planar designs are used and thus the curvature is not considered until expensive prototypes are built. Often, it is desirable to enclose each radiating element within a metallic cavity in order to suppress spurious substrate coupling. In the present paper the authors give a rigorous finite element-boundary integral (FE-BI) formulation for the analysis of wrap-around and cylindrical-rectangular cavity-backed patch arrays on a cylindrical surface. The paper presents the first rigorous solution for cavity-backed antennas embedded in a circular cylinder. The analysis technique is validated for single cylindrical-rectangular patches and for an array of four such elements. Results are also presented which give an understanding of the radiation properties for both circumferentially and axially polarized elements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A combined field integral equation (CFIE)-based electromagnetic solver is presented for solving scattering from a composite object. The object is first decomposed into multiple bodies according to its material property. Then the finite element-boundary integral method is applied to model bodies with complicated materials, and the method of moments is employed to model bodies with homogeneous or conducting materials. To couple different bodies, the CFIE is used to formulate the interaction between the bodies. An example of a composite sphere is given to validate the proposed method.

The “conventional” finite element‐boundary integral (FE‐BI) method suffers from two major drawbacks, one is the huge computer resources required by the dense BI submatrix; the other is the slow convergence rate of the resulting linear system of equations. In this article, both the drawbacks are investigated. First, the integral equation fast Fourier transform (IE‐FFT) algorithm with a Gaussian interpolation scheme is employed to deal with the BI part. Second, an effective and simple preconditioner is developed for solving the matrix equation obtained from FE‐BI method. Numerical results show that the proposed preconditioner can dramatically speed up the convergence of the FE‐BI system, whatever the combined field integral equation (CFIE), the electric field integral equation (EFIE), and the magnetic field integral equation (MFIE) are employed on the truncation boundary. Some examples are given to demonstrate the accuracy and efficiency of the method. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2065–2071, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24538