Characteristic Basis Function Method Research Articles

Efficiently solving large-scale electrostatic lightning problems by integrating characteristic basis functions into boundary element method

The evaluation of the electric field near objects of complex geometries is critical in the pre-bridging regime of lightning strikes in high-voltage transmission systems, which is subject to an open domain problem and can be computationally expensive. In this paper, the characteristic basis function method (CBFM) is incorporated into the conventional boundary element method (BEM) to efficiently handle large-scale electrostatic problems. Within the CBFM, low-level basis functions have been replaced by high-level macro characteristic basis functions, resulting in a significant reduction in the number of degrees of freedom. This reduction in unknowns allows iteration-free direct solvers to approximate the matrices, further reducing the computational complexity of the problem. Numerical examples of the surface charge distribution of an actual 500 kV tower-transmission-line system and a three MW wind turbine in the lightning environment demonstrate the accuracy of the proposed CBFM, while requiring considerably much fewer computational resources compared with conventional BEM. Furthermore, CBFM is highly parallelizable, implying the feasibility of handling large electrostatic lightning problems with complex geometries.

Use of the Adaptive Cross Approximation for the Efficient Computation of the Reduced Matrix with the Characteristic Basis Function Method

A technique for the reduction in the CPU-time in the analysis of electromagnetic problems using the Characteristic Basis Function Method (CBFM) is presented here, allowing for analysis of electrically large cases where an iterative solution process cannot be avoided. This technique is based on the use of the Adaptive Cross Approximation (ACA) for the fast computation of the coupling matrix between CBFs belonging to adjacent blocks, as well as the Multilevel Fast Multipole Method (MLFMM) for the computation of matrix−vector products in the solution of the full system. This combination allows for a noticeable reduction in the computational resources during the analysis of electrically large and complex scenarios while maintaining a very good degree of accuracy. A number of test cases serve to validate the presented approach in terms of accuracy, memory and CPU-time compared with conventional techniques.

Characteristic Basis Function Method Combined With Krylov-Calderón Preconditioner for PMCHWT Formulation

Characteristic Basis Function Method Combined With Krylov-Calderón Preconditioner for PMCHWT Formulation

Flexible Approach for the Generation of Macro-Basis Functions Using the Characteristic Basis Function Method

This document presents a method for reducing the memory and CPU time required for the electromagnetic analysis of complex scenarios employing the Characteristic Basis Function Method. This technique introduces a novel procedure to accelerate the calculation of basis functions and the reduced matrix. The accuracy and computational cost associated with this approach are studied and validated through a number of test cases, making use of about five times less memory than with the conventional approach.

High-precision Solution of Monostatic Radar Cross Section based on Compressive Sensing and QR Decomposition Techniques

In solving the monostatic electromagnetic scattering problem, the traditional improved primary characteristic basis function method (IPCBFM) often encounters difficulties in constructing the reduced matrix due to the long computation time and low accuracy. Therefore, a new method combining the compressed sensing (CS) technique with IPCBFM is proposed and applied to solve the monostatic electromagnetic scattering problem. The proposed method utilizes the characteristic basis functions (CBFs) generated by the IPCBFM to achieve a sparse transformation of the surface-induced currents. Several rows in the impedance matrix and excitation vector are selected as the observation matrix and observation vector. The QR decomposition is adopted as the recovery algorithm to realize the recovery of surface-induced currents. Numerical simulations are performed for cylinder, cube, and almond models, and the results show that the new method has higher solution accuracy, shorter computation time, and stronger solution stability than the traditional IPCBFM. It is worth mentioning that the new method reduces the recovery matrix size and the number of CBFs quantitatively, and provides a novel solution for solving monostatic RCS of complex targets.

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Efficient Iterative Solution of Combined Source Integral Equation Using Characteristic Basis Function Method With Initial Guess

Efficient Iterative Solution of Combined Source Integral Equation Using Characteristic Basis Function Method With Initial Guess

Novel construction of measurement matrix and sparse basis to accelerate compressive sensing for solving wideband RCS of PEC objects

AbstractThis paper proposes a novel approach to enhance the computational efficiency and precision of the ultra‐wideband characteristic basis function method based on compressive sensing for calculating the wideband radar cross section (RCS) of objects, which involves the development of a new method for filling measurement matrix and constructing sparse basis. While randomly selecting rows from the original impedance matrix as the measurement matrix, the proposed method also avoids the double‐filling of equal elements in the measurement matrix. Furthermore, the Foldy–Lax equation is utilized to construct the merged ultra‐wideband characteristic basis functions (MUCBFs) at the highest frequency, and the sparse transform of the induced currents is performed using MUCBFs as the sparse basis. The numerical simulation results show that this method not only reduces the calculation effort of impedance matrix filling, but also effectively improves the calculation precision of the target wideband RCS.

Improved hybrid discretisation of volume integral equation with the characteristic basis function method for analysing scattering from complex dielectric objects

AbstractThe improved hybrid discretisation of volume integral equation (VIE) combined with the characteristic basis function method is proposed to analyse the scattering from complex dielectric objects in this study. To mitigate the excessive number of discrete elements which arise from the conformal discretisation on the complex dielectric objects, the hybrid discretisation is developed. For the conventional hybrid discretisation, the conformal Schaubert–Wilton–Glisson (SWG) basis functions are used to discretise the homogeneous regions, meanwhile, the non‐conformal half‐SWG basis functions are employed to discretise the boundary regions which separate different materials or multiscale structures. The hybrid discretisation takes advantage of the merits of both conformal and non‐conformal basis functions and improves the computational efficiency for solving the VIE. In our study, a kind of edge basis function defined within boundary tetrahedral elements substitutes for the SWG basis functions to model the boundary regions, leading to the further reduction on the number of basis functions. Moreover, the characteristic basis functions extracted from the low‐level basis functions are employed to construct the reduced matrix of which the size is considerably smaller than that of the system matrix derived from the VIE. Several numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

Enhancing CBFM With Adaptive Frequency Sampling for Wideband Scattering From Objects Buried in Layered Media

An adaptive frequency sampling (AFS) strategy is proposed in conjunction with characteristic basis function method (CBFM) to investigate the problem of wide-band scattering from objects buried in layered media. Conventionally, the CBFM is implemented to reduce the solution time at a single frequency. However, wide-band analysis of the above problem is still time consuming when a large number of frequency samples (FSs) are employed with uniform sampling. To mitigate this issue and improve efficiency, the AFS algorithm is proposed to select FSs with a reduced number via an iterative process based on error-estimators. The vector fitting (VF) algorithm is used to derive the rational model, which allows to generate the scattered fields in the band efficiently. The key feature of the proposed AFS is it minimizes the number of the FSs and guarantees the convergence of the solution simultaneously. Numerical results demonstrate that the number of required samples is significantly reduced without compromising the accuracy of the solution.

Range profile analysis of buried objects in layered media based on efficient full-wave simulation

The high-resolution range profiles (RPs) of 3-D objects buried in layered media are investigated. In order to simulate the RPs efficiently, wideband scattered fields are calculated by a method of moments (MoM) based fast algorithm, i.e. characteristic basis function method (CBFM). To achieve fast frequency sweep, an adaptive frequency sampling strategy (AFS) is implemented to accelerate the broadband simulation. Then by using the inverse discrete Fourier transform (IDFT), RPs of the object are obtained. To validate the proposed approach, range locations are predicted qualitatively based on the ray theory. Moreover, the ray approach also enables the physical interpretation of the scattering mechanisms corresponding to the peaks, for example, the specular reflection, the edge diffraction, and the higher-order effects. Since different scattering centers (SCs) dominate in different directions, the RPs are aspect dependent. Furthermore, the RPs are also dependent on the lossy and dispersive effects of the layered medium. Numerical results demonstrate that the peaks are significantly reduced when the layered medium is lossy, especially those due to the higher-order interactions between the object and the interfaces.

Scattering Analysis of Finite Periodic Array in the Vicinity of Arbitrary Object Using Hybrid Macro Basis Function Method

A hybrid macro basis function (MBF) method is proposed to analyze the finite periodic array in the vicinity of an arbitrary object. The array cells and object are modeled using the low order basis functions firstly. Afterwards, the MBFs defined on the cells are constructed using the modified accurate subentire domain basis function method. The MBFs on the object can be obtained using the characteristic basis function method. The total number of MBFs defined on the array cells and object is far less than that of the low order bases. Another advantage of the proposed method is that multiple excitations can be efficiently computed. Simulation results show that good agreement between the proposed method and other techniques is reached. In addition, computational efficiency is validated.

Hierarchical Pattern Exploitation for Efficient Electromagnetic Analysis of Finite Periodic Array

The hierarchical pattern exploitation (HPE) method is proposed for the efficient electromagnetic analysis of finite periodic arrays. Instead of taking advantage of the Toeplitz symmetry by discretizing integral equations (IEs), HPE partitions the array hierarchically to form considerably larger geometrical repetitions, which result in identical interaction blocks inside the system matrix. These interaction blocks representing patterns are characterized and hashed to generate a directory, which maps the patterns to the references of the submatrices. Due to the large proportion of repetitions in hierarchical matrix ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -matrix), HPE accelerates the matrix assembly and reduces the required storage drastically. Numerical examples show that the HPE outperforms the classical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -matrix by a large margin with much less storage and CPU time cost for the analysis of finite periodic arrays. Compared with the multilevel fast multipole algorithm (MLFMA) and the characteristic basis functions method (CBFM), HPE also demonstrates competitive performance, which validates the effectiveness and efficiency of the proposed method.

Optimization of block size for volume integral equation‐based characteristic basis function method

AbstractThe block size of the characteristic basis function method (CBFM) based on volume integral equation (VIE) is optimized to improve the efficiency on analyzing the scattering from dielectric objects in this study. Several literatures have discussed the optimum block size of surface integral equation (SIE)‐based CBFM, which achieved the minimum CPU time for analyzing conductor objects. However, due to the differences of basis functions, the conclusions derived from SIE‐based CBFM are not applicable for VIE‐based CBFM. This study presents the relationship between the Schaubert–Wilton–Glisson (SWG) basis functions and characteristic basis functions (CBFs), which paves the way for evaluating the computational complexity of VIE‐based CBFM. In addition, the Sherman–Morrison–Woodbury formula‐based algorithm (SMWA) and adaptive cross approximation (ACA) algorithm are combined to accelerate the CBFs generation and reduced matrix construction. Based on the computational complexity of the VIE‐based CBFM combined with SMWA and ACA, the optimal number of blocks for VIE‐based CBFM is derived theoretically. Numerical results of homogeneous and inhomogeneous dielectric objects scattering problems are presented to validate the feasibility and accuracy of the proposed optimization method.

Fast analysis of wideband scattering problems using universal characteristic mode basis functions

Fast analysis of wideband scattering problems using universal characteristic mode basis functions

Fast Computation of Electromagnetic Scattering From Dielectric Objects Using Quadrilateral Piecewise Sinusoidal Basis and Characteristic Basis Function Method

A method of moments (MoM)-based procedure is developed to calculate the scattering from homogeneous dielectric bodies. The technique uses quadrilaterals for the approximation of geometry and piecewise sinusoidal (PS) basis functions for the approximation of surface currents. The notable advantage of the PS basis is its radiated fields can be expressed in closed-form. The proposed approach therefore circumvents the need to use Green’s function in formulating the integral equations. Combined with a simple testing procedure, the matrix filling time is reduced and the concern of singularity is removed. To further reduce the computational complexity and enhance the performance, a characteristic basis function method (CBFM) is implemented and embellished with a new characteristic basis function (CBF) generation strategy. Specifically, a cubical surface bounding the entire target is first specified and discretized. A set of auxiliary sources are then defined in a manner similar to that done for a scattering body. These auxiliary sources are defined once and shared by different blocks. In comparison to the traditional plane wave spectrum (PWS) method, the CBFs generated by the new approach are valid not only for plane wave excitations but also for localized excitations. Numerical results are provided to validate the efficacy of the proposed algorithm.

A characteristic mode basis function method for solving wide-angle electromagnetic scattering problems

In the characteristic basis function method (CBFM) for the wide-angle electromagnetic scattering problems of electrically large objects, the low generation efficiency, and many characteristic basis functions exist due to the dependence on external excitation. This paper proposes a characteristic mode basis function method (CMBFM) with novel basis function construction to address this issue. In CMBFM, characteristic modes of each extended block obtained by dividing objects are calculated separately, and then the effective modes are selected as basis functions according to the modal significance. Compared with CBFM, the time performance of constructing basis functions is improved significantly. Furthermore, fewer basis functions are generated without a loss of accuracy. The corresponding numerical results demonstrate that significant efficiency and accuracy can be achieved by the proposed approach.

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Rough layer scattering filled by elliptical cylinders from the method of moments combined with the characteristic basis function method and the Kirchoff approximation.

In this paper, the electromagnetic field scattered by several 2D scatterers of any shape is calculated rigorously from the boundary integral equations discretized by the method of moments with the point matching method and pulse basis functions. In addition, the resulting linear system is efficiently solved from the domain decomposition method named the characteristic basis function method. To accelerate the computation of the primary basis functions, which requires solving sublinear systems, the Kirchoff approximation is applied for metallic and dielectric objects. The efficiency of the method is tested on several applications met in practice: stack of rough interfaces separating homogeneous media, collection of metallic and dielectric elliptical cylinders, collection of coated elliptical cylinders, and a combination of the previous scenarios.

Fast Hybrid Computational Technique for the Analysis of Radome Structures Using Dual Domain Decomposition

This work details a technique tailored to the analysis of complex radome structures based on the non-overlapping separation of two different domains: antenna and radome. Both domains are analyzed isolated using the method of moments with the multilevel fast multipole algorithm (MoM-MLFMA) for the antenna domain and a modified characteristic basis function method with the multilevel fast multipole algorithm approach for the radome domain. An iterative procedure is then applied to compute the effect of each domain over the complementary domain. This approach usually converges into a few iterations, yielding very good results and significant efficiency improvements with respect to other efficient approaches such as a full-wave MoM-MLFMA analysis of the full problem. A realistic test case is included, considering a radome with an embedded frequency selective structure on one of its interfaces. The results show a very good agreement considering only three iterations between domains, requiring only one-third of the CPU-time needed by the conventional approach.