Characteristic Basis Function Method Research Articles

SOLUTION FOR WIDE BAND SCATTERING PROBLEMS BY USING THE IMPROVED ULTRA-WIDE BAND CHARACTERISTIC BASIS FUNCTION METHOD

The ultra-wide band characteristic basis function method (UCBFM) is an efficient approach for analyzing wide band scattering problems because ultra-wide characteristic basis functions (UCBFs) can be reused for any frequency sample in the range of interest. However, the errors of the radar cross section calculated by using the UCBFs are usually large at low frequency points. To mitigate this problem, an improved UCBFM is presented. Improved UCBFs (IUCBFs) are derived from primary characteristic basis functions and secondary level characteristic basis functions (SCBFs) by applying a singular value decomposition procedure at the highest frequency point. This method fully considers the mutual coupling effects among sub-blocks to obtain the SCBFs. Therefore, the accuracy is improved at lower frequency points because of the higher quantity of current information contained in the IUCBFs. Numerical results demonstrate that the proposed method is accurate and efficient.

Efficient Computation of Wideband RCS Using Singular Value Decomposition Enhanced Improved Ultrawideband Characteristic Basis Function Method

The singular value decomposition (SVD) enhanced improved ultrawideband characteristic basis function method (IUCBFM) is proposed to efficiently analyze the wideband scattering problems. In the conventional IUCBFM, the SVD is only applied to reduce the linear dependency among the characteristic basis functions (CBFs) due to the overestimation of incident plane waves. However, the increase in the size of the targets under analysis will require a large number of incident plane waves and it will become very time-consuming to solve such numbers of the matrix equation. In this paper, the excitation matrix is compressed by using the SVD in order to reduce both the number of matrix equation solutions and the number of CBFs compared with the traditional IUCBFM. Furthermore, the dimensions of the reduced matrix and the reduced matrix filling time are significantly reduced. Numerical results demonstrate that the proposed method is accurate and efficient.

Solving Scattering From Multiple Bodies of Revolution by Modal Characteristic Basis Function Method With Sparse Matrix Technique

Modal Characteristic Basis Function method for bodies of revolution (BoR-CBFM) is a fast solver for scattering from multiple BoRs. By using of BoR-CBFM, the modal characteristic basis functions (MCBFs) are constructed, and the size of impedance matrix is greatly reduced. However, the matrix filling, especially the filling of mutual-interaction matrix, is still a huge burden for numerical computation. To further enhance the efficiency of BoR-CBFM and reduce the cost of matrix filling, we present a sparse technique for BoR-CBFM. Through this technique, those weak elements in mutual-interaction matrix that contribute little to the linear system are neglected, and a sparse impedance matrix is achieved. As a result, this technique leads to a reduction on the cost of matrix filling. Numerical results are presented to prove the efficiency of this technique.

Numerical Analysis of Single Microstrip Antenna and Antennas Array in Spherically Layered Media

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.

Full wave analysis of the arbitrarily arranged spherical conformal microstrip antenna array

The surface integral equation is adopted to analyse the characteristics of the arbitrarily arranged spherical conformal microstrip antenna array based on the moment method. The Rao–Wilton–Glisson basis function and triangle function are used to simulate equivalent current on the patch and probe, respectively. A novel basis function at the junction of wire and surface is proposed to ensure continuity of the current from probe to patch. Then, the magnetic frill loop is used as excitation source in this study, and the field on the antenna surface generated by magnetic frill loop is deduced with the help of magnetic dyadic Green's functions on the surface of sphere. For the antenna array analysis, the characteristic basis function method combined with equivalent dipole method is employed to save the consumed memory and computation time. The characteristics of several pairs of conformal spherical microstrip antennas are presented and shown to be in good agreement with data from literatures and FEKO software. At last, a result comparison between the method in this study and FEKO software is drawn to show the efficiency of this method.

Multilevel Fast Adaptive Cross-Approximation Algorithm With Characteristic Basis Functions

This paper presents a multilevel fast adaptive cross-approximation (MLFACA) algorithm for accelerated iterative solution of the method of moments (MoM) matrix equation for electrically large targets. The MLFACA compresses the impedance submatrices between well-separated blocks into products of sparse matrices, constructed with the aid of the fast adaptive cross-sampling (FACS) scheme and the butterfly algorithm. As a result, the MLFACA can reduce both the computational time and the storage of the MoM to ${\mathbf{O}}({\mathbf{N}}\;{\mathbf{log}}^{\mathbf{2}}{\text{N}})$ , where ${\mathbf{N}}$ is the number of the Rao–Wilton–Glisson (RWG) basis functions in the analyzed target. Meanwhile, the MLFACA maintains the adaptive and kernel-independent properties. Furthermore, the characteristic basis function method (CBFM) is employed to decrease the size of the outer matrices of the MLFACA to further reduce the storage and iteration time. Numerical results are presented to demonstrate the advantages of the proposed method, including a successful solution of a scattering problem involving 10 861 668 RWG basis functions.

Efficient computation of macro-domain basis functions when applying the characteristic basis function method to the modeling of forest scattering

In this work, we discuss the use of diagonal representation (DR) of the macro-domain basis functions, in the context of the characteristic basis function method (CBFM) applied to forest scattering problem. We examine the suitability of this enhancement technique for heterogeneous natural forests. Results show that the use of the DR for the MBFs, according to certain criteria, enables us to significantly reduce the CPU time needed to generate the CBFs with little loss of accuracy, and without increasing memory costs. Consequently, the strategy of using the DR for the computing of the CBFs enables us to simulate larger forest scenes and to do so at higher frequencies.

Full‐wave analysis of electromagnetic wave propagation over terrain using the Improved Tabulated Interaction Method

AbstractThis paper proposes extending the forward scattering based Tabulated Interaction Method (TIM) for computing electromagnetic wave propagation over terrain profiles to one incorporating backscattering. The proposed method uses a common set of basis functions in conjunction with a “matching technique” to produce a linear system with much fewer unknowns than that created using pulse basis functions and therefore provides a very efficient and accurate method. The original TIM is shown to be a special case of the proposed method whereby the lower triangular portion of the reduced system is retained and solved. The proposed method is compared with the recently proposed Characteristic Basis Function Method with which it shares several features. The complexity and numerical analysis demonstrates that the proposed method has an extremely low computational complexity and storage.

Efficient iterative solution of electromagnetic scattering using adaptive cross approximation enhanced characteristic basis function method

A new hybrid adaptive cross approximation-characteristic basis function method (ACA-CBFM) is proposed to efficiently solve the electromagnetic scattering problems. In the conventional ACA-CBFM, the ACA is only applied to speed up the construction of the reduced matrix that is directly solved and stored. However, with the increase of the size of the targets under analysis, the reduced matrix will become so large that it is difficult to directly solve and store. In this study, the reduced matrix is further compressed by the adaptive cross approximation-singular value decomposition (ACA-SVD) and solved by an iterative method, which leads to reduced storage and accelerated matrix vector product. Furthermore, the ACA-SVD is adapted to efficiently generate the characteristic basis functions (CBFs), which reduces both the time of generating initial CBFs and the SVD time of initial CBFs. Numerical results about the electromagnetic scattering from perfect electric conducting targets are given to demonstrate the merits of the proposed methods.

Fast Frequency Sweep for Multiple PEC Objects RCS Computation Based on the Characteristic Basis Function Method

To obtain wideband radar cross-section (RCS) frequency response of multiple perfectly electric conducting (PEC) objects, the frequency sweeping by reusing the ultra-wide band characteristic basis functions (UCBFs) is applied. This method, based on the Characteristic Basis Function Method (CBFM), maintains all the benefit of CBFM, especially accelerating the solution of matrix equations generated by the method of moments (MoM) applied to the scatting problems in electromagnetics. Compared with conventional CBFM procedure, reusing the UCBFs without repeating the calculations of them at different frequency points leads to a significant reduction of computational time. Generating UCBFs for highest frequency, reusing UCBFs for lower frequencies and constructing reduced matrix for each frequency are the three keys of this method. Numerical results demonstrated the efficiency of this method.

Fast Analysis of Large 3-D Dielectric Scattering Problems Arising in Remote Sensing of Forest Areas Using the CBFM

We apply the characteristic basis function method (CBFM) to compute the electromagnetic fields scattered by three-dimensional dielectric objects in the context of forest scattering simulation. We study the effect of some CBFM parameters on the accuracy of the results, and on the performance of the CBFM when compared to the classical MoM. We show that once the CBFM parameters have been appropriately chosen, this new method realizes a significant reduction both in terms of CPU time and memory use, while maintaining a level of accuracy comparable to that of the conventional MoM. Consequently, the CBFM enables us to handle electrically larger forest simulation scenes than is possible with classical MoM for higher frequencies.

Equivalence principle algorithm using characteristic basis functions with application to finite periodic arrays including uniaxial dielectrics and conducting objects

In this paper, an equivalence principle algorithm combined with the characteristic basis function (CBF) method has been developed to efficiently analyze the finite periodic arrays composed of uniaxial dielectric materials and conducting objects. Three kinds of the CBFs for each equivalent surface and its surrounding object are simultaneously constructed using multiple plane wave illuminations and singular value decomposition technique, and thus memories related to the scattering and translation operators are significantly saved, while retaining good computational accuracy. Numerical results of a frequency selective conducting array, a uniaxial dielectric cube array, and a periodic array of the composite object including a uniaxial rod and a split ring resonator are given to illustrate good performance of proposed method.

Analysis of electromagnetic scattering from perfect electric conducting targets using improved characteristic basis function method and fast dipole method

The characteristic basis function method (CBFM) is an efficient approach to analyze electromagnetic problems through the size reduction of the original matrix in the method of moments equation. However, adequate plane waves (PWs) must be set in each sub-block to construct characteristic basis functions (CBFs), thus increasing the number of CBFs and causing higher time consumption in singular value decomposition. In addition, the reduced matrix calculation procedure is time-consuming because numerous vector–matrix–vector products (VMVPs) are contained. To mitigate these problems, an improved CBFM is presented. This method fully considers the mutual coupling effects among sub-blocks to obtain the secondary level characteristic basis function (SCBF). Therefore, the number of PWs, as well as the number of CBFs, is significantly reduced. The fast dipole method is also used to accelerate the matrix–vector products in the construction of SCBFs and VMVPs in the calculation of the reduced matrix. Numerical results demonstrate that the proposed method is accurate and efficient.

Analysis of Electromagnetic Scattering Characteristics from Conducting Targets Using Improved Fast Dipole Method and Characteristic Basis Function Method

Analysis of Electromagnetic Scattering Characteristics from Conducting Targets Using Improved Fast Dipole Method and Characteristic Basis Function Method

Modal Characteristic Basis Function Method for Solving Scattering From Multiple Conducting Bodies of Revolution

The analysis of scattering from multiple bodies of revolution (BoRs) has important applications in microwave remote sensing, radar imaging and other areas. For single BoR, three dimensional problem can be degenerated into 2.5 dimensional problem based on the modal Green functions (MGFs), reducing the solving time and storage remarkably. However, it is difficult to extend the MGF to multiple arbitrarily orientated BoRs. This paper presents a modal characteristic basis function method for solving the scattering from multiple BoRs. It combines the MGF of BoR with the characteristic basis function method, named as the BoR-CBF method. Here, the MGF of BoR is first applied to efficiently solve the current distribution on the surface of each BoR. The singular value decomposition is then used to construct the global modal characteristic basis functions (MCBFs) for each BoR. Finally, the MCBFs are transformed into the RWG basis functions using a basis function mapping technique so that the filling of the interaction matrix can be accelerated by the multilevel fast multipole algorithm. By using the BoR-CBF method, the scattering of multiple arbitrarily orientated BoRs can be solved efficiently. Numerical results are presented to demonstrate the accuracy and efficiency of the BoR-CBF method.

Analysis on spherical conformal microstrip antenna array by characteristic basis function method

Spherical conformal microstrip antenna array which is used widely in the field of aeronautics is analyzed by the full wave analysis in this paper. Using the surface integral equation with spherical dyadic Green's function can decrease the number of unknowns remarkably, and also reduce the demand of memory as compared with the method using volume-surface integral equation. The curvilinear triangle is proposed to mesh the surface of the microstrip antenna array, which can simulate the characteristic of spherical surface accurately. Firstly, the problem about probe feed model is solved successfully by introducing the half Rao-Wilton-Glisson function and boundary charge, and the image method is used to treat the line integral singularity problem. Then, the characteristic basis function method is employed to further save memory and computation time further by reducing the rank of impedance matrix. Finally, the input impedance and far-field spherical conformal microstrip antenna array of different sizes are analyzed. Results are in good agreement with those in the literature and simulation software, and thus the validity and effectiveness of the analysis method are demonstrated.

Broadband Adaptive RCS Computation through Characteristic Basis Function Method

A broadband radar cross section (RCS) calculation approach is proposed based on the characteristic basis function method (CBFM). In the proposed approach, the desired arbitrary frequency band is adaptively divided into multiple subband in consideration of the characteristic basis functions (CBFs) number, which can reduce the universal characteristic basis functions (UCBFs) numbers after singular value decomposition (SVD) procedure at lower subfrequency band. Then, the desired RCS data can be obtained by splicing the RCS data in each subfrequency band. Numerical results demonstrate that the proposed method achieve a high accuracy and efficiency over a wide frequency range.

Application of the Characteristic Basis Function Method Using CUDA

The characteristic basis function method (CBFM) is a popular technique for efficiently solving the method of moments (MoM) matrix equations. In this work, we address the adaptation of this method to a relatively new computing infrastructure provided by NVIDIA, the Compute Unified Device Architecture (CUDA), and take into account some of the limitations which appear when the geometry under analysis becomes too big to fit into the Graphics Processing Unit’s (GPU’s) memory.

The Numerical Analysis of an Antenna near a Dielectric Object Using the Higher-Order Characteristic Basis Function Method Combined with a Volume Integral Equation

SUMMARY The higher-order characteristic basis function method (HO-CBFM) is clearly formulated. HO-CBFM provides results accurately even if a block division is arbitrary. The HO-CBFM combined with a volume integral equation (VIE) is used in the analysis of various antennas in the vicinity of a dielectric object. The results of the numerical analysis show that the HO-CBFM can reduce the CPU time while still achieving the

Modeling large nonuniform optical antenna arrays for metasurface application

We analyze large non-uniform optical antenna arrays of nanorods, which form optical vortices, axicons and lenses, by using a numerically efficient technique, called the Characteristics Basis Function Method (CBFM). The efficiency is realized by deriving an accurate, efficient simplified representation of nanorod, and by using the CBFM, which not only reduces the number of unknowns significantly without sacrificing the computational accuracy, but also enables us to handle large, truncated and non-uniform arrays. The method is numerically rigorous and includes all of the mutual coupling effects to obtain accurate results. Furthermore, it is readily parallelizable and can be generalized to handle more complex shapes of nanoantennas, without any difficulty.