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A quasi-mixed-potential layered medium Green’s function (QMP-LMGF) is proposed for non-Galerkin surface integral equation (SIE) formulations in the modeling of homogeneous dielectric objects in layered medium. The formulation is derived based on the pilot vector potential approach. In this method, the field-type LMGF in the $L$ -operator is decomposed into two parts, a “vector potential” term in a dyadic form, and a “scalar potential” term in a vector form, to represent the field components from current and charge sources, respectively. Since the proposed two potential terms (vector potential and scalar potential) do not satisfy the Lorenz gauge, we term them as quasi-mixed-potentials. The property of the two potentials is investigated to reveal that the proposed QMP-LMGF is compatible with the vector and scalar potentials in free space. Moreover, due to the continuity of the integration kernels across the interfaces, undesired line integrals are absent in the proposed QMP-LMGF when the objects are straddling different layers. Three popular non-Galerkin SIEs for dielectric objects in layered medium are studied, and the corresponding numerical results are demonstrated to validate the proposed method. [ABSTRACT FROM AUTHOR]

A higher order current and charge integral equation (CCIE) approach is developed for accurate electromagnetic scattering analysis of dielectric objects for a wide frequency band, that is from extremely low frequency to microwave frequency. Compared to the conventional CCIE method, its accuracy has been considerably improved by expanding the currents and charges using high-order hierarchical vector basis functions and higher order orthogonal scalar polynomials, respectively. The proposed higher order approach retains whole-frequency-range stability as the traditional low-order counterpart, but characterized with enhanced accuracy and higher convergence rate. Moreover, the consistency of the basis functions’ expansion order in currents and charges is not mandatorily required, which further increase the flexibility in electromagnetic modeling. The scattered fields of penetrable objects are analyzed to validate the effectiveness of this new higher order CCIE, as well as investigate its accuracy, stability, and flexibility. [ABSTRACT FROM AUTHOR]

An efficient improved spectrum integral method (ISIM) is proposed to accelerate the scattering simulation of cuboid object by method of moment (MoM) in multiplanar layered medium (LM). The layered medium Green’s functions (LMGFs) are studied and decomposed into transmission and reflection terms, which hold the translational invariance and reverse translational invariance, respectively. By virtue of the (reverse) translational invariance of LMGF from the uniform square grids on the surface of the cuboid object, most of the coupling between the expanding basis functions and the testing basis functions can be represented by two kinds of submatrices, i.e., the Toeplitz matrix when transmission term is involved, and the conjugate Toeplitz matrix when reflection term is involved. Moreover, the submatrix coupling the expanding/testing basis functions defined on the edges with those defined on the parallel surfaces/edges is also extended to the (conjugate) Toeplitz matrixes. This will significantly alleviate the heavy computation and memory burden from the conventional SIM. With the improved operations on the basis functions associated with the edges of the cuboid object, the proposed ISIM in LM can reach the computational complexity as low as ${O}$ (${N} ^{1.5}$ log(N)) in the matrix vector production, while the computational complexity of matrix filling and the memory requirement are both ${O}$ (${N}^{1.5}$). Moreover, compared with conventional SIM, both theoretical analysis and numerical results demonstrate that the memory requirement and matrix filling time are dramatically decreased. [ABSTRACT FROM AUTHOR]

An approximation scheme that combines approximate solutions with error estimators to accelerate the adaptive h‐refinement of the RWG‐based method of moments (MoM) with the electric field integral equation (EFIE) is presented. The scheme is effectively implemented by using the near‐field matrix to solve the approximate solution. Several conventional error estimators incorporated with the scheme are investigated. Compared to using the full MoM system, it significantly reduces the computational cost while maintaining the refinement effect. Numerical results indicate that the scheme could accelerate the adaptive refinement, yielding significant reductions in computational time and memory requirements. [ABSTRACT FROM AUTHOR]

A set of coupled integral equations is presented based on Love’s and Schelkunoff’s field equivalence principles. According to Love’s equivalence principle and the boundary conditions, a general form of the Poggio–Miller–Chang–Harrington–Wu formulation is applied for modeling the waveguide cavities containing composite structures. The structures are discretized using the higher order polynomial basis functions, whose orders are adaptively adjusted for accurately modeling current distributions in this kind of strong near-field coupling and resonance problems. Moreover, the integral equations for the apertures involving the waveguide ports, each of which is terminated by a semi-infinite waveguide, are established according to Schelkunoff’s equivalence principle and the boundary conditions. Because the free-space Green’s function as well as the spatial discretization-based basis functions cannot be applied to semi-infinite waveguides, we employ waveguide eigenfunctions as the basis functions for the outer surface of an aperture. These coupled integral equations are then solved numerically using the method of moments accelerated by the parallel computing techniques. Comparisons with two well-developed software products demonstrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The higher order method of moments (HOMoM) with a direct solver is hybridized with the multilevel fast multipole algorithm given the multiscale nature of airborne antenna arrays. The Poggio–Miller–Chang–Harrington–Wu formulation and the combined filed integral equation are solved for modeling metallic/dielectric antennas on a conducting platform. To accelerate the outer iteration between the two algorithms, the lower/upper decomposed matrix in HOMoM is reused and the initial values of current coefficients are properly set. Furthermore, a computational scheme based on the high-performance computing technique is designed to improve the hybrid method. A large model of a 2132-element microstrip array mounted on a 1020-wavelength airplane is accurately simulated. [ABSTRACT FROM PUBLISHER]

The efficiency of a parallel higher-order method of moments is illustrated using up to 4096 CPU cores on a supercomputer. The scattering problems solved include the analysis from two full scale airplanes and the radiation problems include performance of a microstrip patch phased array antenna mounted on an airplane. Both the scattering and radiation problems are simulated to demonstrate the efficiency of the algorithm implementation. Numerical results show that one can achieve above 60% efficiency when the used memory to the total memory ratio is larger than 15%, and the time can reach a theoretical value between O (N ^2) and O (N ^3), where N is the number of unknowns. Due to its high efficiency, the algorithm is able to accurately solve large complex electromagnetic problems including composite and multiscale structures. [ABSTRACT FROM PUBLISHER]

In marching-on-in-degree time domain method of moment, the transient responses are often expanded by a finite number of associated Laguerre functions. There is an error associated in truncating the associated Laguerre function series beyond that what is necessary in the solution process. This error is related to the scaling factor used in the argument of the associated Laguerre functions that actually approximates the unknown temporal variations. A least upper bound of this error is deduced. Based on this bound, one can obtain an optimum scaling factor to minimize this error so that it is guaranteed to be below a certain bound. [ABSTRACT FROM PUBLISHER]

An integral equation‐based nonoverlapping domain decomposition method (IE‐NDDM) is proposed for efficient and accurate scattering analysis of electrically large PEC targets in a half‐space environment. Taking the condition that there are null fields as well as current inside PEC objects in the original problem, a novel explicit transmission condition is proposed to ensure continuity of electric currents between adjacent subdomains. Moreover, to deal with this situation that targets located in half‐space environment, the stratified‐medium dyadic Green's function is adopted. Numerical examples are provided to demonstrate the correctness and the performance of the proposed method. In detail, an analysis about electromagnetic scattering respect to the altitude of the target away from half‐space interface, the incident direction of plane wave, and the material parameters of the lower half‐space is presented; furthermore, the convergence behavior of the proposed method is studied. [ABSTRACT FROM AUTHOR]

A hybrid message passing interface and open multiprocessing (OpenMP) enabled many integrated core (MIC) coprocessor-accelerated implementation of the large-scale parallel method of moments (MoM) for solving electromagnetic problems is presented. The out-of-MIC memory strategy and asynchronous data transfer scheme are employed to address the problems of accelerating MoM on CPU/MIC computing platform, and a parallel framework is designed to achieve large-scale parallel algorithm on CPU/MIC clusters. The experimental results show that a high parallel efficiency of 45% is achieved when 1024 computing nodes or 80 000 cores are utilized. [ABSTRACT FROM AUTHOR]