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Skeletonization is an effective method to accelerate the solution of linear systems with multiple right-hand sides (RHSs) by exploiting the rank-deficiency property of the RHS matrix. However, when the size of the RHS matrix is very large, the memory requirement would become a bottleneck of the skeletonization technique. To reduce the memory cost, this letter presents the theoretical basis of how to find out the skeleton basis functions (SBFs) to construct the skeleton RHS matrix more efficiently from a purely algebraic point of view and proposes a multilevel algorithm to figure out the SBFs for solving the integral equations with multiple RHSs. The numerical results show that the proposed method accelerates the solution of the volume–surface integral equation with multiple RHSs and reduces the memory cost significantly.

During the solution of volume-surface integral equation (VSIE), to reduce the core memory requirement of the radiation patterns (RPs) of the basis functions, an improved spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) using the mixed-potential representation and the triangle-/tetrahedron-based grouping scheme is applied. Numerical results show that accompanying with a faster speed, the memory requirement of the RPs in the improved SE-MLFMA is several times less than that in the conventional MLFMA without compromising accuracy. A result employing the OpenMP parallelization and vector arithmetic logic unit (VALU) hardware acceleration technique is also shown to illustrate the robustness and scalability of the improved SE-MLFMA method.

An iterative-based hybrid method, which combines the volume-surface integral equation (VSIE) and the modified surface integration (MSI) method, is presented to analyze the radome-enclosed antennas in receiving mode. Compared with the previously published hybrid approaches, this method improves computational accuracy by including the effects of shaded wall of the radome and the mutual interactions between antennas and radome during the numerical solution of the VSIE in an iterative manner. By embedding different parts of the antenna-radome structure (ARS) into three distinct oct-trees, the multilevel fast multipole algorithm (MLFMA) is used to accelerate both the VSIE solution and the surface/volume integrations in the MSI stage. The new method obtains more accurate results than its original version within less CPU time, and keeps good accuracy with much less memory usage and computational time when compared with the MLFMA-accelerated full-wave VSIE solution for the entire ARS.

The validity of the use of continuity condition (CC) is studied when it is combined with the volume-surface integral equation (VSIE) to solve the electromagnetic scattering/radiation of composite conductor-dielectric objects. It is found that the explicit enforcement of CC in VSIE may be inaccurate if the involved conductor is infinitesimally thin, but it works well for the composite structures that only contain conductors with closed surfaces. A new combined field integral equation-volume integral equation with enforced CC (CC-CFIE-VIE) is then proposed, and a convenient way to embed it into the context of the multilevel fast multipole algorithm is also provided. Numerical results show that CC-CFIE-VIE not only reduces the overall memory usage and the CPU time of a single iteration, but also decreases the number of iterations to reach desired accuracy.

An efficient approach that combines the coupled volume surface integral equation (VSIE) accelerated by multilevel fast multipole algorithm (MLFMA) and the modified surface integration (MSI) method is proposed to analyze the antenna-radome structures (ARS) in receiving mode. The hybrid method not only reduces the computational time and memory requirement as compared to the purely full-wave solutions, but also more importantly overcomes the difficulties in conventional high-frequency approximate methods for analyzing the properties of the radome-enclosed receiving antennas or arrays. Numerical results are shown to illustrate the validity, efficiency, and accuracy of the proposed method.

An efficient method of moments (MoM) solution of the volume-surface integral equation (VSIE) is presented for the analysis of electromagnetic (EM) scattering and radiation of composite objects comprising arbitrarily contacted dielectrics and conductors. In contrast to the conventional Schaubert-Wilton-Glisson (SWG) and Rao-Wilton-Glisson (RWG) basis functions, which were widely used in the MoM solutions of the VSIE, a new hybrid pulse-rooftop basis function is proposed to explicitly enforce the boundary condition of vanishing tangential electric field at the dielectric-conductor interface. As a consequence, the displacement currents in the dielectrics can be efficiently modeled by a reduced number of volume bases on the same set of meshes, particularly when thin dielectric slabs are involved in the composite structures. The numerical results of EM scattering and radiation of several composite objects are shown to illustrate the accuracy and efficiency of the proposed scheme. Since the new hybrid basis function can be easily implemented into the existing fast algorithms, the VSIE solution presented in this paper is promising for EM problems of composite targets with large size.

The spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) is improved by using the mixed-potential representation of the combined field integral equation (CFIE) that is different from the most commonly used dyadic formulation in the existing MLFMA literature. The memory storage requirement and computation time for the spherical harmonics expansion of the radiation patterns of the basis functions are reduced effectively. Numerical results show that for the solution of CFIE, the memory cost by the radiation patterns is less than half of that in the conventional SE-MLFMA proposed by Eibert without any loss of accuracy.

In this paper, we present the space-domain integral- equation method for the analysis of frequency selective surfaces (FSS), consisting of an array of periodic metallic patches or a metal screens perforated periodically with arbitrarily shaped apertures. The computation of the spatial domain Green's function is accelerated by the Ewald transformation. The geometric model is simplifled by the lattice symmetry, so that the unknowns are greatly reduced. Time of fllling MOM matrix and solving linear system is dramatically reduced. Our technique shows much higher e-ciency when compared with the available commercial software and the existing methods published.

More accurate hybrid PO-MOM process combining physical optics (PO) with method of moment (MOM) is employed to analyze an electrically large antenna-radome structure. The mutual interactions among the antenna, the inner and outer surfaces of the radome are considered through a group of associated integral equations. In the analysis, the antenna surface and the sharp tip part on the radome surface are modeled accurately by using MOM while the rest smooth parts on the radome surfaces are approximated by using PO. Numerical results indicate that the hybrid process presented in this paper is much more accurate than the conventional PO-MOM ones.

A strip model is incorporated in the volume-surface integral equation (VSIE) to simplify the analysis of the probe-fed conformal microstrip antennas (CMSAs) with arbitrary shapes. The thin wire-surface junction of the feeding probe and the patch is transferred to the surface-surface junction that can be modeled by using Rao-Wilton-Glisson (RWG) basis functions easily. Thus, the use of complicated attachment mode basis function in the conventional VSIE is eliminated, which simplifies the calculation of the method-of-moments (MoM) matrix. The construction of RWG basis functions at the surface-surface junction is detailed as well. An effective remedy is also proposed to overcome the computation breakdown in the near-singularity treatment when the field point locates at the extension of one side of the source domain. Numerical results show the reliability and accuracy of the proposed method.

The effects of the superspheroidal radomes on the characteristics of Archimedean spiral antennas are investigated in detail, which may provide some useful insights in the design of the radome-antenna system in practical engineering. All interactions between the radome and antennas are rigorously included in the coupled surface integral equation (CSIE) model, which leads to more accurate results than those of the existing methods based on the high-frequency algorithm or the decoupled radome-antenna analysis procedure especially when the antennas are placed in the close proximity of the radome. Numerical results show that the performance of the spiral antenna is significantly changed due to the presence of the radome.

The main idea of Maxwellian circuits is that any wire structure, such as a thin wire antenna or a microstrip structure, can be represented by equivalent distributed circuits, the solution of which is identical to the solution of Maxwell's equations of that structure. Such circuits are said to be Maxwellian . In this paper, the Maxwellian circuits are implemented into a curved structure, i.e., spiral antennas. Since a spiral antenna has much stronger dispersion and mutual couplings than a straight antenna, the most challenging thing for the spiral antenna is how to realize the broadband equivalent circuits. Numerical results for the two-arm Archimedian spiral antenna show that the solutions of its Maxwellian circuits over a quite wide frequency band are the same as those obtained by the conventional integral equations, but solving the circuits represented by the differential equations is much more efficient than solving the integral equations.

An efficient and accurate closed-form solution, based on the spectral-domain method of moments (MoM), is presented to analyze the characteristics of cylindrically conformal microstrip antennas with arbitrary radii. First, an algorithm that combines the recursive and the uniform asymptotic expansion method in different regions is developed to calculate the spectral-domain Green's functions for arbitrary dielectric coated cylinders accurately. Next, the integrands of the spectral integrals involved in MoM equation are partitioned into two parts, i.e., the fast oscillatory, slowly convergent part and the well-behaved part. Consequently, all of the integrals in MoM analysis can be categorized into two types. Through the Sommerfeld identity and its extension, these integrals are cast into closed-forms by using the nonlinear approximation method (generalized pencil-of-function method). In this method, any time-consuming numerical integration procedure is eliminated, which improves the computational efficiency drastically. Compared with the results from published references, the validity and accuracy of the method are demonstrated.

In this letter, the performance of wire antennas enclosed by a small/moderate-size dielectric radome with arbitrary shape is investigated by using the coupled surface integral equation (CSIE). PMCHWT formula is applied on the surfaces of the radome, while the EFIE is employed to model the equivalent strip structure of wire antennas. The advantages of this approach over other methods are (1) all of the mutual interactions between antennas and radome are taken into account so that the performance of the composite antenna-radome system can be predicted rigorously and accurately; (2) one can use only one type of basis function (e.g. RWG functions) to represent the equivalent currents on both antenna and radome surfaces; (3) A simple delta-gap feed model can be conveniently incorporated in the method of moments (MoM) with good accuracy. Numerical results of wire antenna covered by radomes with both spherical shell and Von Karman shapes are presented to validate the proposed method.

In this letter, it is the first time to implement the theory of Maxwellian circuits (TMC) to the printed spiral antennas. First, the Maxwellian circuit models (MCM) for the printed spiral antennas are established through two independent sets of full-wave solutions of current and scalar potential distributions. In this stage, a relationship between the scalar potential and voltage is proposed to satisfy Ohm's law at the terminals of the antennas. Second, broadband MCM are developed to predict the characteristics of the antennas over a quite wide band by using the information at only three sampling frequencies. Numerical results indicate that solutions of the MCM (sparse matrix system) are much more efficient than those of the conventional integral equation solutions (full matrix system) without any accuracy sacrifice.

Numerical performance of Calderon Multiplicative Preconditioner (CMP) for the electrical field integral equation (EFIE) of 3-D open perfect electric conductors (PECs) is investigated in this paper. The iteration count for achieving convergence in iteratively solving MoM linear equations from CMP preconditioned EFIE of several PEC scatters or antennas are presented. Numerical experiments show that for the analysis of thin wire-like open PECs especially in certain electric field excitation condition where the induced surface current is mainly along the wire axis, the CMP may be unfortunately helpless to iterative solver in handling EFIE-MoM linear equations. Empirical analysis is addressed that the invalidation of CMP in these cases is due to the fact that the RWG functions have weak ability to simulate surface currents with rotational component.

A strip model is incorporated in the volume-surface integral equation (VSIE) to simplify the analysis of the probe-fed conformal antennas with arbitrary shapes. The thin wire-surface junction of the feeding probe and the patch is transferred to the surface-surface junction that can be modelled by using Rao-Wilton-Glisson (RWG) basis functions easily. Thus, the use of complicated attachment mode basis function in the conventional VSIE is eliminated, which simplifies the calculation of the method of moments (MoM) matrix. The construction of RWG basis functions at the surface-surface junction is detailed as well. An effective remedy is also proposed to overcome the computation breakdown in the near-singularity treatment when the field point locates at the extension of one side of the source domain. Numerical results show the reliability and accuracy of the proposed method.

In this paper, based upon the equivalent principle and surface integral equations, the exact model of an antenna and dielectric radome structure is established by using method of moments (MoM). The equivalent strip-model is used for the thin wire antenna, in order to alleviate the singularities in the meshing process. The ill-conditioned MoM matrix is improved by the preconditioning technique. The fast multipole method (FMM) is used to reduce the memory occupation and accelerate the iteration convergence of the conjugate gradient (CG) method.

The effects of the electrically large rotation ellipsoid radome on the radiation characteristics of two kinds of wire antennas are analyzed by an improved hybrid method, which combines the method of moments (MOM) and physical optics (PO). Based on a group of associated integral equations, the mutual interactions among the antenna, the inner and outer surfaces of the radome are all considered. In the analysis, the antenna surface and the sharp tip part on the radome surface are modeled accurately by using MOM, while the smooth parts on the radome surfaces approximated by using PO method. Numerical results indicate that the radome parameters can affect the antenna radiation characteristics seriously.