New moment method tool combining FMLMP, CBF and MPI

The MLFMM (Multilevel Fast Multipole Method) is an alternative formulation of the technology behind the MoM (Method of Moment) and is applicable to much larger structures than the MoM, making full-wave current-based solutions of electrically large structures a possibility. This fact implies that it can be applied to most large models that were previously treated with the MoM without having to change the mesh. In this paper we discuss the development and implementation of volumetric integral equations for both dielectric and magnetically permeable materials using curvilinear hexahedral elements. Both piecewise constant and higher order basis functions will be examined in the context of volumetric multilevel fast multipole method implementation. Comparisons with corresponding finite element-boundary integral solutions will also be presented and compared in terms of accuracy and efficiency.

To study wave scattering from random lossy dielectric rough surfaces with large permittivities using the method of moments, a dense grid is needed for accurate results. A dense grid requires more CPU and memory. The physics‐based two‐grid (PBTG) method can reduce both CPU and memory requirements. In this paper, the PBTG is used in conjunction with the multilevel fast multipole method (FMM) to solve wave scattering from one‐dimensional random lossy dielectric rough surfaces. The proposed algorithm has the computational complexities of O(Ndg) for near‐field interactions and O(Ncg) for nonnear‐field interactions, where Ndg and Ncg are the number of sampling points on the dense and coarse grids, respectively. Using the proposed algorithm, wave scattering from Gaussian and non‐Gaussian rough surfaces is investigated and illustrated. Special emphasis is put on checking the accuracy of the algorithm and energy conservation.

Diagonalization of the fast multipole method (FMM) for the Helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves. The resulting k-space integral over the Ewald sphere is numerically evaluated. Storing the k-space quadrature samples of the method of moments (MoM) basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems. In this paper, it is proposed to expand the k-space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules. Aggregations, plane wave translations, and disaggregations in the realized multilevel fast multipole method (MLFMM) are carried out using the k-space samples of a numerical quadrature rule. However, the incoming plane waves on the finest MLFMM level are expanded in spherical harmonics again. Thus, due to the orthonormality of spherical harmonics, the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients. Overall, the resulting MLFMM can save a considerable amount of memory without compromising accuracy and numerical speed.

Complex scattering problems are solved with the multilevel fast multipole method (MLFMM). Geometries include metallic structures (wires and surfaces) as well as dielectric bodies (volume and surface equivalence principle). Validation and application examples show the large savings in memory and run-time of the MLFMM as compared to the standard method of moments (MoM). Limitations regarding dielectric bodies are addressed, which are encountered when attempting to model highly lossy dielectric bodies with a high permittivity.

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 combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

a Design Concept of Piecewise Variable Wall Thickness of Radome Is Proposed to Simulate the Radome which Has Variable Wall. the Paper Calculates the Far Field of a Medium-Size Radome in the Case of Piecewise Variable Thickness by Three Methods as Follows: Method of Moment (MOM), Multilevel Fast Multipole Method (MLFMM) and Physical Optics& the Method of Moments (PO/MOM) Respectively. after Comparing the Results, we Find that the PO/MOM Method Have the Superiority in Simulation of Radome’s Electromagnetic because it’s More Accuracy and Less Memory Consuming than the other Two Methods. Also it Proves the Feasibility of the Design Concept of Piecewise Variable Thickness for Radome.

The aim of this research work is to discuss the use of the diagonal representation (DR) for the construction of the macro-basis functions (MBFs) when applying the Characteristic Basis Function Method (CBFM) to the problem of modeling of scattering from forests. We have applied the CBFM to improve the performances of a previously studied 3D full-wave model in order to solve electrically large forest simulation scenes. This efficient domain decomposition method has shown good performance both in terms of CPU time and memory while achieving a satisfactory level of accuracy compared to that of a conventional Method of Moments (MoM). Therefore, it enables us to solve forest EM problems of upward of 2 million unknowns by consuming only a reasonable amount of CPU time and using just 48 GB of shared memory (Fenni I.; Roussel H.; Darces M.; Mittra R., AP IEEE Trans., 62–8, 4282–4291, 2014).

In this study, doubly periodic arrays with three-dimensional metallic inclusions in free space and multilayered media are studied. The random hill climbing (RHC) optimisation method is used to find optimal structures. Periodic method of moments (PMOMs) is applied to calculate the fitness functions of the resulted structures from RHC optimiser. The procedure which is proposed here for the optimisation of the structures may be used to design periodic sketches with arbitrary properties. The simulation results are compared with high-frequency structure simulator computer-aided design tool outcomes to verify the validity of the implemented PMOM code.

This paper numerically analyzes reflector antennas with complex mesh weave patterns by using extended physical optics (PO) combined with the periodic method of moments (MoM). Periodic MoM calculates the transmission coefficient matrix (T-matrix) of the realistic, complex weave pattern of the planar mesh, in order to calculate the modified PO current on the mesh reflector. The analysis of the mesh reflectors with two different complex weave patterns (single Satin and single Atlas at Ka band) is performed to exemplify the application of the extended PO/periodic MoM algorithm. The paper also verifies the equivalent strip width for a cylindrical wire for mesh reflector antennas with experimental and numerical analysis.

The development of vehicle-detection radar system has attracted much attention in recent years due to the increasing interest of smart car and traffic control applications [1, 2]. The success of such radar applications highly depend on reliable estimation of signal echo from the targets, which provide the information of target detection, vehicle identification, and the estimation of locations and speeds. In contrast to the conventional radar applications, where the targets are very far away from the antennas, the vehicles under detection are in the near zone. The detection highly depends on a proper use of antennas, in particular a proper radiation beamwidth for the target illumination. Since the radar detection is directly related to the electromagnetic (EM) backscattering, the estimation of various vehicles is apparently helpful to the radar system design. In this paper, we will present a full-wave numerical simulation over popular vehicle types including sedan and trucks, where the multi-level fast multipole method (MLFMM) of method of moment (MoM) is applied. The vehicles are assumed to be in the near zone of antennas, where the phased array antennas with various beamwidths are used to estimate the EM backscattering fields. To improve the detection accuracy, we also developed a moving signal average technique of signal estimation such that the influence of structure variation in a vehicle on the radar signals can be reduced. Thus in the presentation, the moving signal average method is also applied to the estimation of backscattering fields to exhibit their characteristics.

Reflector antennas with complex mesh weave patterns are numerically analyzed by using extended physical optics (PO) combined with the periodic method of moments (MoM). The method applies the periodic MoM with Rao-Wilton-Glisson (RWG) basis and testing functions. It calculates the transmission coefficient matrix (T-matrix) of the realistic, complex weave pattern of the planar mesh, in order to calculate the modified PO current on the mesh reflector. When analyzed, the planar grid mesh is found to be compatible with the commonly used wire-grid model. The modified PO current on the locally planar mesh is implemented on the curved reflector surface for the diffraction analysis of the mesh reflector antennas. The far-field pattern of the offset parabolic antenna with grid mesh, modelled using periodic MoM, agreed well with those obtained from the wire-grid model. T-matrix calculated from the tabulated T-matrix data using the interpolation method is sufficiently accurate and compares well with the one calculated using the direct method, allowing users to choose one of the T-matrix calculation methods depending on the problem. The analysis of the mesh reflectors with two different complex weave patterns (single Satin and single Atlas at Ka band) is performed to exemplify the application of the extended PO/periodic MoM algorithm. It is shown that differences were observed in cross-polarization discrimination (XPD) for circular polarization operations depending on the weave patterns. This result demonstrates the usefulness of the proposed technique in accurate performance prediction of mesh reflector antennas with complex weave patterns

Finite arrays of waveguides and horn antennas are widely used both as direct radiators as well as feed clusters for reflector antennas. Accurate and efficient numerical simulation techniques represent a powerful tool for the design of such antennas. Many approaches have been proposed in the literature that employ hybrid techniques to efficiently analyze both the interior waveguide problem and as well as their coupling to the outer free space [1]–[3]. The mode matching (MM) is used to compute the generalized scattering matrix (GSM) for the inner waveguide problem, whereas the Method of Moments (MoM) evaluates the GSM for the outer free space coupling. When the array is electrically large in terms of number of elements or radiating apertures dimensions, the applicability of this approach is limited because the associated MoM matrix is large. Some novel approaches have been proposed in the literature to reduce the matrix size [4]. Recently the Characteristic Basis Function method (CBFM) [5] has been proposed to solve electrically large problems by using a set of high-level basis functions, called CBFs, that are physics-based and tailored to the problem.

The iterative solution of linear equation systems resulting from Method of Moments (MoM) discretizations of integral equations is of particular attractiveness because of the possibility to employ fast integral methods such as the Multilevel Fast Multipole Method (MLFMM). However, the robustness of the iterative solvers is often still not satisfying and the search for improved preconditioners is an ongoing process. In this paper, we concentrate on two classical near-zone preconditioning techniques: Gauss-Seidel smoothing and a special form of incomplete LU factorization. It is found that Gauss-Seidel smoothing is a relatively cheap preconditioner working well for fine meshes. Our special form of incomplete LU factorization gives reliable convergence for complex problems with very bad convergence behavior, regardless of mesh density but for the cost of increased memory requirements.

This communication presents a comprehensive numerical analysis of single microstrip antenna and antennas array in spherically layered media, using the method of moments (MoM). The curvilinear Rao–Wilton–Glisson (CRWG) triangular basis functions are employed to simulate the equivalent current on the antenna surface. First, the dyadic Green’s functions using Debye potential are deduced. Then, their efficient computation procedures are carried out to improve calculation efficiency. Finally, the characteristic basis function method is employed to save memory and calculation time by reducing dimension of the impedance matrix. The results of this study are in good agreement with those of the FEKO software, and they show that the method proposed in this communication is more efficient than FEKO in the analysis process.