Characteristic Basis Function 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 Within the CBFM, low-level basis functions have been replaced by high-level macro characteristic basis functions, resulting in a significant reduction in the number of degrees of freedom.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.

A Computationally Efficient Technique Using Characteristic Basis Functions and Large Block Sizes

A Computationally Efficient Technique Using Characteristic Basis Functions and Large Block Sizes

Fast Numerical Analysis of Metasurfaces by Characteristic Basis Functions in EFIE Framework

Fast Numerical Analysis of Metasurfaces by Characteristic Basis Functions in EFIE Framework

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.

Broadband RCS Acquisition by Finite Periodic Arrays Using the Characteristic Basis Function and Asymptotic Waveform Evaluation

Broadband RCS Acquisition by Finite Periodic Arrays Using the Characteristic Basis Function and Asymptotic Waveform Evaluation

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

Accelerated Method Of Generalized Transition Matrix Model Using Characteristic Basis Function For Large-Scale Open-Ended Cavities

Accelerated Method Of Generalized Transition Matrix Model Using Characteristic Basis Function For Large-Scale Open-Ended Cavities

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 dual compressive sensing method for solving the monostatic scattering problems of three-dimensional target

ABSTRACTAccording to the conventional dual compressive sensing method is limited to solving the electromagnetic scattering problems for two-dimensional targets, the Characteristic Basis Functions (CBFs) combined with the Compressive Sensing (CS) technique are proposed to solve the monostatic scattering problems for the three-dimensional (3D) target in this paper. The approach considered in this paper consists of successfully transforming the discrete surface-induced currents of Rao-Wilton-Glisson (RWG) basis functions using CBFs, which successfully enhance the sparsity of the induced currents. Then, the novel dual compressive sensing framework is obtained by applying the CBFs and discrete cosine transform matrices as sparse bases, respectively. The corresponding numerical calculations demonstrate that the proposed method can be used as an effective technical route to solve the monostatic scattering problem effectively.

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.

Accurate analysis of bistatic scattering problems using compressive sensing with a new sparse basis

Compressive sensing (CS) used as a sparse basis can enhance the characteristic basis functions (CBFs), which helps in analyzing the bistatic scattering problems of a three-dimensional (3D) object. However, a sparse basis constructed by the CBFs lacks current information under a single plane wave, leading to a low computation accuracy when analyzing complex objects. To resolve this issue, a new sparse basis construction method is presented in this work, which considers the current information under multilevel plane waves with different incident angles and different polarization modes. As this new sparse basis contains more comprehensive current information, the accuracy is considerably improved when analyzing the complex targets. Furthermore, the accuracy and efficiency of the proposed method are verified by extensive numerical simulations.

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.

Novel compressive sensing computing model used for analyzing electromagnetic scattering characteristics of three-dimensional electrically large objects

The method of moments is one of the most effective algorithms for solving electromagnetic scattering problems. However, the high computational complexity limits its application to electrically large problems. As an improved algorithm, the compressive sensing-based method of moments introduces the compressive sensing technique into the algorithmic structure, which avoids the inverse of the matrix equation and improves the computational efficiency. Using the underdetermined equation-based calculation model, this scheme is utilized to efficiently analyze the bistatic scattering of the objects. In this technique, the extracted few rows from the impedance matrix are used to construct the measurement matrix. Nevertheless, the results are unstable due to the random extraction utilized to build the measurement matrix. Furthermore, it is challenging task to provide an appropriate sparse basis for the induced currents of three-dimensional objects discretized by the Rao-Wilton-Glisson basis functions. To address the aforementioned issues, a novel compressive sensing calculation model that enhances measurement matrix building, sparse basis construction, and recovery is provided in this paper. First, several rows of the impedance matrix are uniformly extracted to produce consistent computation results, which is opposed to the randomly constructed measurement matrix in the conventional technique. The number of rows to be extracted is typically set to be 3–5 times the number of basis functions for high accuracy. Then, the characteristic basis functions based on the Foldy-Lax equation are employed to construct the sparse basis. Considering the prior knowledge that the lower order characteristic basis functions are dominant, the columns of the recovery matrix corresponding to some low-order characteristic functions are determined in advance as the columns that will be identified by the recovery algorithm, thus simplifying the recovery algorithm to a least-squares operation. Obviously, the matrix equation is reduced to an overdetermined equation instead of the underdetermined equation since only a few low-order basis functions are to be computed. Compared with the conventional compressive sensing-based method of moments with characteristic basis functions, the computation time is significantly reduced in terms of constructing the basis functions and recovering the current coefficients, while the accuracy is improved. Finally, both the suggested method and the conventional compressive sensing-based method of moments are used to simulate the bistatic radar cross sections of the perfect electrical conductor cube, cylinder, and missile model. The efficiency and accuracy of the proposed method are verified by the numerical results.

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.