Parallelized multilevel Characteristic Basis Function method applied to scattering model for forest remote sensing

The multilevel characteristic basis function method (MLCBFM) with the adaptive cross approximation (ACA) algorithm for accelerated solution of electrically large scattering problems is studied in this paper. In the conventional MLCBFM based on Foldy-Lax multiple scattering equations, the improvement is only made in the generation of characteristic basis functions (CBFs). However, it does not provide a change in impedance matrix filling and reducing matrix calculation procedure, which is time-consuming. In reality, all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently. Therefore, ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study. Numerical results are given to demonstrate the accuracy and efficiency of the method.

This work investigates numerically two different methods of moments applied to Hermite derived probability distribution model and variations of Weibull distribution fitted to the short-term time series peaks sample of stochastic response parameters of a simplified jack-up platform model which represents a source of high non-Gaussian responses. The main focus of the work is to compare the results of short-term extreme response statistics obtained by the so-called linear method of moments (L-moments) and the conventional method of moments using either Hermite or Weibull models as the distribution model for the peaks. A simplified mass-spring system representing a three-legged jack-up platform is initially employed in order to observe directly impacts of the linear method of moments (L-moments) in extreme analysis results. Afterward, the stochastic response of the three-legged jack-up platform is analyzed by means of 3D finite element model. Bias and statistical uncertainty in the estimated extreme statistics parameters are computed considering as the “theoretical” estimates those evaluated by fitting a Gumbel to a sample of episodical extreme values obtained from distinct short-term realizations (or simulations). Results show that the variability of the extreme results, as a function of the simulation length, determined by the linear method of moments (L-moments) is smaller than their corresponding ones derived from the conventional method of moments and the biases are more or less the same.

Novel Construction of Characteristic Basis Functions Accelerated Multilevel Characteristic Basis Function Method for Fast Solution of Electrically Large Scattering Problems

In this paper, the semi-orthogonal compactly supported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computationally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze electromagnetic transients in a lightning protection systems schematized as a thin-wire structure. The study is carried out in frequency domain; a discrete fast Fourier transform algorithm can be used to compute time profiles of the electromagnetic interesting quantities. The unknown longitudinal currents are expressed by using multiscale wavelet expansions. Thus, the thin-wire EFIE is converted into a matrix equation by the Galerkin method. Results for linear spline wavelets along with their comparison with conventional MoM that uses triangular basis functions and the point matching procedure are presented, for two case studies. Good agreement has been reached with a strong reduction of the computational complexity.

Electromagnetic (EM) fields in a three-dimensional, arbitrarily shaped, heterogeneous dielectric or biological body illuminated by a plane wave are computed by an iterative conjugate gradient method. The method is a generalized method of moments applied to the volume integral equation. Because no matrix is explicitly involved or stored, the method is capable of computing EM fields in objects an order of magnitude larger than those that can be handled by the conventional method of moments. Excellent numerical convergence is achieved. Perfect convergence to the result of the conventional moment method using the same basis and weighted with delta functions is consistently achieved in all the cases computed, indicating that these two algorithms (direct and iterative) are equivalent.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, a novel formulation for scattering from one-dimensional (1D) rough surface problem has been presented. The formulation is based on the representation of the scattering field in spectral domain with an unknown spectral coefficient which is solved by applying Taylor series and Fourier Transforms techniques. It is also shown that forward–backward (FB) acceleration technique can be adapted to the spectral formulation to improve the effectiveness in a limited region of convergence. The obtained results are compared with the conventional method of moments (MoM) and the limitations of the formulation are analyzed in detail.

The utilization of physics-informed deep learning (PI-DL) methodologies provides an approach to augment the predictive capabilities of deep learning (DL) models by constraining them with known physical principles. We utilize a PI-DL model called the deep operator network (DeepONet) to solve two-dimensional (2D) electromagnetic (EM) scattering problems. Numerical results demonstrate that the discrepancy between the DeepONet and conventional method of moments (MoM) is small, while maintaining computational efficiency.

In the conventional modal method of moments (MoM) method, when shielding effectiveness (SE) of a rectangular enclosure is the goal, it is assumed that the incident wave is reflected from an infinite wall. This assumption makes the results inaccurate specifically at low frequencies where the wall size is not large compared to the illumination wavelength. In this study, the mentioned reflected wave is corrected by considering the reflection from a box without any aperture. To obtain the reflected wave from the box, an induced electric current on the metallic surface is assumed. Using Rao Wilton Glisson basis functions along with free space Green's function, the unknown electric currents and consequently the reflected wave are calculated. The results are compared with full wave numerical methods. A very good agreement is observed between the results and it is shown that for lower frequencies the proposed method has more accuracy rather than the modal MoM itself specifically for an enclosure with a very large aperture.

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.

In this paper, it is attempted to approach a fast efficient algorithm for solving the famous Hallen's and Pocklington's integral equations, regarding the current distribution on a finite-length linear thin wire antenna. Here, the conventional moment method in conjunction with wavelet basis functions was used to obtain the current distribution of the antenna. The aim of this work is first to introduce the application of wavelet in electromagnetic scattering, secondly a comparison of the two method of analysis the thin wire antenna. By using the wavelet expansion, wavelets as basis and testing functions, a sparse matrix is generated from the previous moment method dense matrix. A sparsely filled matrix is easier to store and invert. The result extracted from Pocklington's integral equation gives better convergence at the feeding point, though it takes more time to be computed because of the complexity in Pocklington's equation. Results are compared to the previous work done and published, excellent results are obtained.

A novel implementation of the characteristic basis function method (CBFM) is given, in which the high-level basis functions, called characteristic basis functions (CBFs), are represented in terms of curved rooftops generated from nonuniform rational B-splines (NURBS) in the parametric (u,v) domain. The associated macro-testing functions are defined by using curved razor-blade functions corresponding to each rooftop. The underlying objective of the CBFM is the reduction of the number of unknowns that arise from the discretization process when applying the conventional method of moments (MoM). The result is, therefore, an approach which can handle many complex cases via direct solvers, without suffering from convergence problems as many of the iterative techniques are known to do when dealing with ill-conditioned matrices. As a result of the combination of the CBFM with the special class of low-level basis and testing functions directly located over NURBS surfaces, complex and realistic geometries can be efficiently analyzed to yield accurate results while reducing the CPU time as well as required memory resources.

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).

The conventional hybrid method of moments (MoM)-physical optics (PO) technique provides a possible way to handle electrically large objects with affordable computer memory. However, its efficiency is not very good because the evaluation of the PO contribution to the MoM impedance matrix is very time-consuming. An efficient implementation of the iterative MoM-PO hybrid technique is presented in this paper to avoid the calculation of the PO contribution in matrix form. For electrically large objects, the proposed efficient iterative MoM-PO (EI-MoM-PO) method can greatly reduce the computational time and maintain the same or better accuracy with the same number of unknowns compared with the conventional MoM-PO method. Several examples of large-scale structures are analyzed by the EI-MoM-PO method, the conventional MoM-PO method, and the multilevel fast multipole algorithm. The excellent efficiency and accuracy are achieved by the proposed EI-MoM-PO technique.

This paper proposes a novel numerical technique for simulating electric fields in relatively far regions. For layered structures, the Method of Moments (MoM) using multilayer Green's functions significantly improves electromagnetic simulation efficiency. However, calculating electric field in relatively distant regions with multilayer Green's functions remains computationally expensive. To address this, we first compute the field distribution in dielectric media via layered electromagnetic analysis. These fields are then treated as equivalent sources, combined with metallic components, and used with free-space Green's functions to obtain electric fields. The computational results agree with conventional non-layered MoM requiring full dielectric discretization, validating the algorithm's precision. The results of near-field calculated by this method are compared with the non-layered MoM, and this paper gives the electric field results at relatively distant locations.

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.