Macro Basis Functions Research Articles

Macro Basis Function Methods With Multilevel DCA Acceleration for Antenna Array Analysis

Macro Basis Function Methods With Multilevel DCA Acceleration for Antenna Array Analysis

Macro Basis Functions for Efficient Analysis of Thick Wires in the MoM

Macro Basis Functions for Efficient Analysis of Thick Wires in the MoM

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.

An Inhomogeneous Plane-Wave Based Single-Level Fast Direct Solver for the Scattering Analysis of Extremely Large Antenna Arrays

A semianalytic single-level fast direct solver (FDS) is presented for the method-of-moments (MoM) analysis of large planar antenna arrays with up to few thousands of complex elements on current desktop computers. Assuming a partition of the impedance matrix, the proposed scheme factorizes the near-field blocks via a singular value decomposition (SVD)-based low-rank approximation and the intermediate-field blocks via an analytical inhomogeneous plane-wave (IPW) expansion. The near- and intermediate-field bases are then unified to leverage the Woodbury formula for the inversion. The solutions for the excitation of each array ports are obtained at once with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N^{15/7} \ln ^{3} N)$ </tex-math></inline-formula> computational cost and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N^{11/7} \ln N)$ </tex-math></inline-formula> memory for array problems with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> basis functions. The complexities are traced precisely and the error is controlled by means of analytical formulas for the required number of IPWs. The FDS is also combined with a macrobasis function (MBF) approach to deal with antenna geometries containing many subwavelength details. This article includes simulations of regular arrays of about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$169^{2}~3$ </tex-math></inline-formula> -D dipoles and an irregular array composed of seven stations of the low-frequency square kilometer array (SKA) telescope comprising each 256 log-periodic (LP) antennas. The proposed FDS allows the analysis of the coupling effect both within any one station but also between the stations of the telescope, a size and complexity of problem which has not been possible with existing published techniques.

Predicting Macro Basis Functions for Method of Moments Scattering Problems Using Deep Neural Networks

In this letter, we present research on the application of deep neural networks to predicting macro basis functions for complicated computational electromagnetics problems. We provide error statistics and representative examples for networks trained on simple and complicated datasets of method of moments scattering problems. Notably, we demonstrate that the networks learn generalizable knowledge applicable to problem types on which they were not trained. We conclude that the networks produce encouraging results, especially for cross validation, and larger training datasets will improve reliability for general scattering problems.

Efficient Iterative Analysis Technique of Complex Radome Antennas Based on the Characteristic Basis Function Method

We present a new approach for the analysis and design of radome structures. It makes use of extended domain macro-basis functions obtained from the characteristic basis function method in order to represent the current distribution over the radome. This involves computational advantages due to the reduction in the number of unknowns compared to conventional approaches. This approach involves dividing the scenario into two domains, antenna and radome, and calculating the influence between them using a technique that iteratively corrects the error of the currents on each domain. This technique can be used to analyze arbitrary-shaped radome antennas including several material layers with different thicknesses and dielectric properties that can embed frequency selective surfaces on any interface. Several test cases are presented for the validation of the proposed technique.

Diagnosis of Array Antennas Based on Phaseless Near-Field Data Using Artificial Neural Network

Diagnosis of array antennas based on phaseless near-field data is a practically important nonlinear inverse problem. One of the biggest challenges for the nonlinear inverse problem is to alleviate an ill-posedness resulting in poor accuracy. In this article, a novel source reconstruction method, which is based on an artificial neural network (ANN) enhanced by eigenmode currents, is proposed. Eigenmode currents, which work as macro basis functions, can be obtained numerically once precise geometry of the array antennas is found. The proposed source reconstruction method is named an ANN-EC (eigenmode currents) and is applied to diagnosis of array antennas based on phaseless near-field data. The ANN-EC has two advantages over conventional source reconstruction techniques purely based on the ANN. The first one is enhancement of accuracy and the second one is robustness to noise. Both of these advantages stem from reduction of the number of eigenmode currents using source reconstruction. Accuracy of the reconstructed currents is evaluated and these advantages of the ANN-EC over conventional ANN are demonstrated. To the best of the authors' knowledge, this is the first paper demonstrating the effectiveness of the eigenmode currents on the nonlinear inverse problem.

Full-Wave Computation of Monostatic RCS Using Ray-Tracing and Adaptive Macro-Basis Functions

This article presents a technique for the computation of the monostatic radar cross section of complex objects based on a combination of macro-basis functions (MBFs) and the multilevel fast multipole algorithm. An initial pool of excitation-independent MBFs is first obtained, generating the corresponding reduced coupling matrix as well as the multipole data. For each excitation, ray-tracing processing is performed, extracting a number of critical points that are used to obtain a mask that allows to dynamically select the basis functions to be considered in the analysis. This strategy allows a noticeable reduction in the size of the problems with minimal CPU-time preprocessing overhead.

Data-Enabled Advancement of Computation in Engineering: A Robust Machine Learning Approach to Accelerating Variational Methods in Electromagnetics and Other Disciplines

In this letter, we propose and demonstrate a data-driven machine learning-based approach to accelerate the finite element method (FEM), method of moments (MoM), finite difference (FD) method, and related variational methods, while maintaining the attractive properties that have allowed such methods to dominate computational science and engineering fields like computational electromagnetics. We use a neural network to predict a set of macro basis functions for a given problem, using only the solution to an extremely coarse description of the problem as input. We then solve the problem using the predicted macro basis. Unlike some existing methods, ours does not rely on the direct prediction of the solution. We show that our macro basis function approach corrects errors in the raw prediction of the network, achieving a far more accurate solution. Results are presented for a class of finite element scattering problems, with error statistics presented from 1000 validation examples and compared to standard and naive approaches. These results suggest the described macro basis function approach is superior to machine learning approaches that directly predict the solution. Meanwhile, our method achieves comparable accuracy to the full solution while requiring only a fraction of the degrees of freedom.

A novel CEM technique for modeling electromagnetic scattering from metasurfaces

AbstractThis paper presents a novel computational electromagnetics (CEM) technique, which hybridizes the periodic finite element method (FEM) with the method of moments (MoM), for efficient numerical modeling of electromagnetic scattering from metasurfaces consisting of truncated periodic or locally varying quasi‐periodic array of structures. Based on the quasi‐periodic nature of metasurfaces, the periodic FEM is employed to generate high‐level macro basis functions (MBFs). Following that, a reduced MoM matrix is formed by using the MBFs with unknown coefficients belonging to each cell of the periodic array. The proposed hybrid method reduces the computational load significantly when compared with conventional numerical methods, especially for electrically large truncated metasurfaces involving arbitrarily inhomogeneous unit cells. Various numerical results are presented, and the accuracy and performance of the proposed method are tested against commercial codes, as well as an in‐house FEM code.

Dynamic Threshold Selection Based on Radiation Pattern Characteristics for the Generation of Macro Basis Functions

An approach for the generation of macro basis functions considering the directivity of the sources and the ray-tracing characteristics of the scenario is described in this letter. The number of basis functions generated is highly optimized by dynamically generating the threshold to be applied for the retrieval of the macro basis functions after the application of the singular value decomposition of the currents induced by the plane wave spectrum surrounding each block. Significant performance gains are shown due to the reduction of the number of unknowns compared to the conventional generation of macro basis functions.

Efficient and Memory Saving Method Based on Pseudoskeleton Approximation for Analysis of Finite Periodic Structures

An efficient and memory saving method based on pseudoskeleton approximation (PSA) is presented for the effective and accurate analysis of finite periodic structures. Different from the macro basis function analysis model, our proposed method uses the formulations derived by the local Rao-Wilton-Glisson basis functions. PSA is not only used to accelerate the matrix-vector product (MVP) inside the single unit but also adopted to decrease the calculation burden of the coupling between the different cells. Moreover, the number of decomposed coupling matrices is minimized due to the displacement invariance of the periodic property. Consequently, even compared with the multilevel fast multipole algorithm (MLFMA), the new method saves much more memory resources and computation time, which is also demonstrated by the numerical examples.

Efficient Generation of Macro Basis Functions for Radiation Problems Using Ray-Tracing Derived Dynamic Thresholds

This communication presents a technique that allows an efficient selection of the number of macro basis functions for each block by assigning dynamic thresholds applied after the singular value decomposition of the currents induced by the plane wave spectrum. It makes use of a ray-tracing preprocessing of the scenario, where a number of critical points are identified. The threshold assigned for the selection of the high-level basis functions on each block is based on the distance of the center of the block to the nearest critical point. Representative examples are included in order to illustrate the efficiency and accuracy of the proposed approach.

Sparse Approximate Inverse Preconditioner With Parametric Sparsity Pattern Applied to the Macrobasis Function Methods

An efficient approach for the generation of sparse preconditioners, tailored for the application of macrobasis function methods, is described in this letter. The preconditioner is highly scalable and generated by the computing groups of rows that share a common sparsity pattern, calculated by using a distance threshold between geometrical blocks that controls the amount of data to be considered. This approach is suitable for the analysis of very large and realistic problems, as shown in some test cases included. Due to the clustering nature of this technique, the preconditioners can be generated in a substantially lower amount of time than that required by conventional approaches.

Fast and Accurate Simulation Technique for Large Irregular Arrays

A fast full-wave simulation technique is presented for the analysis of large irregular planar arrays of identical 3-D metallic antennas. The solution method relies on the Macro Basis Functions (MBF) approach and an interpolatory technique to compute the interactions between MBFs. The Harmonic-polynomial (HARP) model is established for the near-field interactions in a modified system of coordinates. For extremely large arrays made of complex antennas, two approaches assuming a limited radius of influence for mutual coupling are considered: one is based on a sparse-matrix LU decomposition and the other one on a tessellation of the array in the form of overlapping sub-arrays. The computation of all embedded element patterns is sped up with the help of the non-uniform FFT algorithm. Extensive validations are shown for arrays of log-periodic antennas envisaged for the low-frequency SKA (Square Kilometer Array) radio-telescope. The analysis of SKA stations with such a large number of elements has not been treated yet in the literature. Validations include comparison with results obtained with commercial software and with experiments. The proposed method is particularly well suited to array synthesis, in which several orders of magnitude can be saved in terms of computation time.

A Comparison of Macro Basis Function Methods for Interconnected Endfire Antenna Arrays

Two approaches to the macro basis function (MBF) method that target interconnected subdomains have been adapted to finite linear arrays, and benchmarked against each other in order to estimate their performance with respect to the strong near field coupling that occurs under the endfire mode operation. The methods, here referred to as methods A and B, are based on the synthetic function and characteristic basis function method, respectively, presented in the previous literature. The occurrence of very strong near-field coupling can be seen to affect the number of MBFs required for a certain level of accuracy, although both approaches perform well under the test scenario. However, method B provides a considerably more efficient compression with respect to a maximum acceptable error level.

The CBFM-Enhanced Jacobi Method for Efficient Finite Antenna Array Analysis

An enhancement to the iterative Jacobi technique with the characteristic basis function method is presented. The resulting method is intended for efficient method of moments (MoM)-based analysis of large, disjoint finite antenna arrays. The enhancement improves the convergence rate of the Jacobi method by better accounting for mutual coupling between array elements. This involves solving a small, global problem at each iterative step, using macrobasis functions that are iteratively generated. Results are presented, and it is found that the proposed method can recover fast convergence in cases where the Jacobi method diverges or converges slowly. The proposed method also converges significantly faster than a conventional, preconditioned, iterative solution of the MoM matrix equation.

Fast Full-Wave Synthesis of Printed Antenna Arrays Including Mutual Coupling

A fast full-wave scheme is presented for the analysis of large printed antenna arrays, making use of the macrobasis functions (MBFs) technique. The interaction between MBFs is computed efficiently through a combination of the contour-fast Fourier transform (C-FFT) and interpolatory MBF-based techniques, which effectively deal with different parts of the printed structure. Substantial improvement is introduced to C-FFT by adding up the FFT tables before interpolating, which dramatically reduces the memory required to store the tables and accelerates the method-of-moment matrix filling time. The current on the antenna array and embedded element patterns (EEPs) are then rapidly obtained. Furthermore, an optimization method relying on sequential convex optimization and the fast full-wave scheme is proposed for the array synthesis. At each optimization iteration, EEPs are precomputed and assumed to be locally constant, which enables the implementation of convex programming to rapidly optimize the antenna positions. The EEPs are then quickly updated for the new antenna positions. The scheme enables the efficient inclusion of mutual coupling in array synthesis problems. Numerical results are presented and discussed for the synthesis of linear and planar arrays made of printed bowtie antennas.

Antenna Calibration for Near-Field Material Characterization

A novel antenna calibration method is presented for near-field problems, such as material characterization or inverse scattering. The procedure accurately accounts for differences between simulations of objects close to antennas and the equivalent experimental measurements. It is based on the method of moments (MoM) solution to surface integral scattering equations. An efficient choice of macrobasis functions (MBFs) is applied to the antenna, which reduces the computational costs by several orders of magnitude. The calibration involves scanning a target of known constitution through the antenna near field, assigning a tuning parameter to each MBF and optimizing said parameters, so as to reduce the error between antenna simulations and measurements. This adjusts the antenna’s simulated surface currents, so as to more accurately represent the currents on the experimental apparatus. Thus, an efficient antenna model is obtained, which more accurately represents the real-world antenna. The calibration technique is verified by applying it to the characterization of dielectric objects of known but arbitrary shape.

An Efficient Numerical Solution Method for Reflectarrays of Varying Element Sizes

A novel method is developed for the efficient solution of reflectarrays of variable size elements. The method relies on using characteristic modes (CM) as macro basis functions and reusing the dominant CM of the resonant element for all elements in the reflectarray. This utilization leads to obtaining a reduced matrix system where the number of unknowns is drastically decreased. As far as the far field is concerned, accurate results are achieved even with a single CM. The accuracy is attained owing to preservation of mutual coupling information via the original method of moments (MoM) impedance matrix. The solution is further accelerated by tabulating the entries of the reduced matrix as a function of interacting patch sizes and their relative displacements. It is observed that for sufficiently separated patches, the reduced matrix entry is almost a separable function of the two-dimensional (2-D) displacement between patches and patch sizes associated with the matrix entry. Tabulation is efficiently performed by exploiting this fact. Achieved acceleration is sufficient to use this analysis method in the design of reflectarrays. For a 1000-element array, the tabulation process takes 28 min on a platform with 3.3 GHz CPU clock speed. With the lookup table at hand, the solution time is 0.38 s which is important for the design iterations.