Fast Multipole Algorithm Research Articles

Design of Wide Scanning Sparse Planar Array Using Both Matrix-Pencil and Space-Mapping Methods

A hybrid efficient optimizing method of wide scanning sparse planar array involving mutual coupling is investigated in this letter. The former work of matrix enhancement and matrix pencil (MEMP)-based synthesis method is extended to the design of pattern reconfigurable sparse arrays in wide-angle scanning. The genetic algorithm was utilized to further optimize the reconstructed sparse array including the actual antenna element, which differs from the only array factor synthesis of MEMP. To improve the optimization efficiency and design accuracy, the space mapping technique was exploited to accomplish the optimizing design, which also involves the interactions among elements during the optimizing process. A wide-scanning sparse array can be realized by the new relationship of parameter mapping courses between low-cost coarse model optimizations and high-accuracy fine model validations based on the characteristic mode and multilevel fast multipole algorithm. Numerical examples show the efficiency of the proposed method.

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.

Acceleration of the Multi-Level Fast Multipole Algorithm Using K-Means Clustering

The multilevel fast multipole algorithm (MLFMA) using K-means clustering to accelerate electromagnetic scattering analysis for large complex targets is presented. By replacing the regular cube grouping with the K-means clustering, the addition theorem is more accurately approximated. The convergence rate of an iterative solver is thus improved significantly. However, irregular centroid locations as a result of the K-means clustering increase the amount of explicit transfer function calculations, compared with the regular cubes. In the MLFMA, a multilevel hierarchical structure is applied to the finite multipole method (FMM) to reduce transfer function calculations. Therefore, the MLFMA is suitable for applying K-means clustering. Simulation results with both canonical and realistic targets show an improvement in the computation time of the proposed algorithm.

Fast solver for uncertainty EM scattering problems by the perturbed-based MLFMA

A novel fast algorithm is proposed to analyze the EM scattering from electrically large conducting targets with varying geometrical shapes. Firstly, the target surface can be constructed with several control points by using the non-uniform rational B-spline surface modeling method. More specifically, the surface integral equation can be rewritten in terms of these control points, which contains the geometrical coordinate information. Moreover, it should be noted that the derivatives of both the L and K operates are needed to describe the perturbation of electric currents. Therefore, a perturbed multilevel fast multipole algorithm (P-MLFMA) is proposed to accelerate the matrix vector multiplication. At last, numerical results are given to verify the accuracy and efficiency of the proposed P-MLFMA. It can be seen that higher computational efficiency can be obtained when compared with both the traditional Monte Carlo method and the Perturbation Approach for MoM.

Multilevel Fast Multipole Algorithm Enhanced Characteristic Mode Analysis for Half-Space Platform

The increasingly popular characteristic mode analysis (CMA) techniques in the free-space have been well-established, while the half-space counterpart is less concerned. In this communication, we consider the CMA for half-space platforms such as vehicles on the ground and ships on the sea surface, which is also commonly mounted with antennas. To overcome the difficulty of CMA’s application on electrically large targets, the half-space multilevel fast multipole algorithm is integrated into the eigensolver. Numerical results of half-space CMA for realistic platforms from FM-band to ${L}$ -band are presented to validate the accuracy and the robustness of the proposed method. It has been shown that this communication can be used as a legitimate CMA tool for the antenna design and integration on half-space platforms.

Scattering Prediction of Target Above Layered Rough Surface Based on Time-Domain Ray Tracing Modeling

In the past, most of the transient electromagnetic (EM) analyses focused on the scattering from the target. The transient scattering from rough surface was rarely studied, especially for the layered rough surface. When the target is above the rough surface, it needs to solve the composite transient scattering from the rough surface and the target above it. In this article, we mainly focus on the time-domain (TD) analysis for transient scattering from the target and layered rough surface based on time-domain ray tracing (TDRT) modeling. Applying geometrical optics (GO), the multiple bounces of the transient EM waves between layered rough surfaces and target are traced to obtain the incident field of the irradiated surfaces. Then considering the particularity of the layered rough surface, we modify TD Gordon integral and reduce the TD physical optics (TDPO) integral to closed-form expressions to improve the computing efficiency. To demonstrate the efficiency and accuracy of the proposed algorithm, the transient scattering simulations of the composite model involving target and layered rough surface are compared with frequency-domain ray tracing (FDRT) with inverse fast Fourier transform (IFFT), as well as the results obtained by the multilevel fast multipole algorithm (MLFMA) of FEKO in conjunction with IFFT (IFFT-MLFMA). The characteristics of transient scattering from the composite model are further studied to show the physical phenomenon of scattering mechanisms. Specifically, the transient scattering from the composite model for different parameters is simulated for sensitivity investigation of the transient scattering to the variations in the related parameters.

An Adaptive Segmented Reduced Basis Method for Fast Interpolating the Wideband Scattering of the Dielectric–Metallic Targets

In this letter, an interpolation method, i.e., the volume surface-integral equation-based adaptive segmented reduced basis method (VSIE-ASRBM), is proposed to fast analyze the wideband electromagnetic (EM) scattering of dielectric–metallic targets. First, by integrating with the hybrid multilevel accelerated Cartesian expansion multilevel fast multipole algorithm (MLACE-MLFMA), the broadband EM scattering of electrically large dielectric–metallic targets can be calculated without repeated meshes. Second, replicative calculations of the near-region impedance element are avoided by the empirical interpolation method. Moreover, different from the iteration process of the VSIE enhanced by MLACE-MLFMA, the current distribution can be obtained mainly by calculating the far-region impedance matrix and the sampling current vector multiplications. Meanwhile, an adaptive segmented strategy is adopted to further improve the interpolation efficiency. The proposed VSIE-ASRBM has three advantages: adaptive segmented interpolation, lower interpolation memory cost, and higher interpolation efficiency. The accuracy and efficiency will be demonstrated in two numerical examples.

Machine-Learning-Based Hybrid Method for the Multilevel Fast Multipole Algorithm

In this letter, a hybrid translation computation method for the multilevel fast multipole algorithm (MLFMA) is proposed based on machine learning. The hybrid method combines both generalized regression neural network (GRNN) and artificial neural network (ANN) to replace the traditional translation procedure during the solving process of the MLFMA. Based on the data corresponding to every one of the interaction list boxes at each level, the hybrid neural network is trained. Comparing with the previous machine learning method in this field, the proposed model is more general, and with lower complexity since it inherits the accuracy of the GRNN as well as the efficiency of the ANN. To the best of our knowledge, it is for the first time that the ANN is integrated into the MLFMA. Numerical examples are benchmarked to illustrate the reliability and capability, thus making it possible to solve similar problems during the fast inhomogeneous plane wave algorithm solving process in the multilayered medium.

Antenna In-Situ Performance Analysis for the Hypersonic Flight Vehicle HEXAFLY: Employing measurement data in a simulation model

An antenna in-situ performance analysis for the hypersonic flight vehicle HEXAFLY is presented. Two simulation tools and a compact antenna test range (CATR) measurement facility are employed to obtain the embedded radiation characteristics of two different antenna systems. In a first step, both antenna types are simulated and measured without the impact of the flight vehicle, but in an environment supporting correct functioning, e.g., on a finite conducting ground plane or on top of a vertical conducting stabilizer. A finite-element method (FEM) solver is used for this detailed full-wave analysis of antenna structures with fine geometrical and material details. Next, the FEM solver and a method of moments (MoM) solver with multilevel fast multipole algorithm (MLFMA) acceleration are used to obtain the in-situ radiation characteristic of both antennas mounted on the flight vehicle. The FEM solver is now utilized to simulate the complete setup, whereas the MoM solver works with an equivalent radiation source, which is obtained from CATR measurements of isolated antennas. The results confirm the effectiveness of the measurement data-based two-stepapproach, which helps to overcome the limitations of pure simulations that are often not feasible for off-the-shelf antennas and allows the overall validation process to be viewed with added confidence.

Acceleration of MLFMA Simulations Using Trimmed Tree Structures

We present a novel approach to accelerate the electromagnetic simulations by the multilevel fast multipole algorithm (MLFMA). The strategy is based on a progressive elimination of the electromagnetic interactions, resulting in trimmed tree structures, during iterative solutions. To perform such eliminations systematically, artificial neural network (ANN) models are constructed and trained to estimate the errors in the updated surface current coefficients. These column eliminations are supported by straightforward row eliminations, leading to increasingly sparse tree structures and matrix equations as iterations continue. We show that the proposed implementation, namely, trimmed MLFMA (T-MLFMA), leads to significantly accelerated electromagnetic simulations of the large-scale objects, while the accuracy is still much better than the high-frequency techniques. T-MLFMA can be seen as an exemplar of the implementations, where machine learning is successfully integrated into an electromagnetic solver for enhanced simulations.

Efficient parallelization of multilevel fast multipole algorithm for electromagnetic simulation on many-core SW26010 processor

A many-core parallel approach of the multilevel fast multipole algorithm (MLFMA) based on the Athread parallel programming model is presented on the homegrown many-core SW26010 CPU of China. In the proposed many-core implementation of MLFMA, the data access efficiency is improved by using data structures based on the structure of array. The adaptive workload distribution strategies are adopted on different MLFMA tree levels to ensure full utilization of computing capability and the scratchpad memory. A double buffering scheme is specially designed to make communication overlapped computation. The resulting Athread-based many-core implementation of the MLFMA is capable of solving real-life problems with over one million unknowns with a remarkable speedup. The capability and efficiency of the proposed method are analyzed through the examples of computing scattering by spheres and a practical aerocraft. Numerical results show that with the proposed parallel scheme, the total speedup ratios from 6.4 to 8.0 can be achieved, compared with the CPU master core.

Efficient computation of the reduced matrix of MLFMA–CBFM for electrically large blocks

In recent years, the characteristic basis function method has been developed as an efficient approach for the solution of large electromagnetic radiation or scattering problems. According to this technique, the currents over the scenario under analysis are defined using a set of pre-computed characteristic basis functions, associated with a number of blocks into which the geometry is partitioned. This involves some computational advantages due to the reduction of the number of unknowns compared to conventional approaches. However, additional pre-processing time is introduced due to the computation of the CBFs and the reduced coupling matrix. A novel strategy is presented in this study in order to accelerate the generation of the reduced matrix, based on the application of the multilevel fast multipole algorithm.

Efficient Technique for the Analysis of Electromagnetic Problems Involving Antenna Trajectories in Complex Scenarios

This letter presents an efficient approach for the electromagnetic analysis of complex scenarios involving transmitting antennas moving along predetermined trajectories. In order to efficiently reduce the size of the problem for each position of the antenna, we propose a technique based on macro basis functions that are dynamically generated using a ray-tracing analysis. The multilevel fast multipole algorithm is also included in order to reduce the memory consumption and speed up the solution process. Some representative test cases serve to validate the efficiency and performance of the proposed approach.

Research on Electromagnetic Scattering Characteristics of Combined Conducting and Dielectric Target Above Coastal Environment

The electromagnetic (EM) scattering characteristics of target above coastal environment are complicated due to the simultaneous existence of ground region and sea region. Nevertheless, the actual target possesses both conducting part and dielectric part. Such a composite scattering problem involves multiple media parameters and large amount of unknowns. Hence, aiming at accurately and efficiently calculating the EM scattering from combined conducting and dielectric target above coastal environment, the hybrid SIE-KA method is introduced in which single integral equation (SIE) method is utilized to reduce the number of combined target's unknowns and Kirchhoff approximation (KA) is applied to obtain induced electric and magnetic current on the surface of coastal environment. Moreover, multilevel fast multipole algorithm (MLFMA) is adopted to significantly reduce the computational cost and memory requirement. Several numerical examples demonstrate the accuracy and efficiency of the hybrid method. Finally, the EM scattering characteristics of combined conducting and dielectric target above coastal environment have been studied. The radar cross section (RCS) curves with different category of environment, polarization mode, working frequency, statistic parameters of coastal environment, permittivity of target's dielectric part, target's height and target category have been analyzed in detail to provide some useful conclusions. The approach and results can be broadly applied in remote sensing simulation of coastal environment with combined target.

A Concise and Efficient MLFMA Scheme for Electromagnetic Surface Integral Equations From Dielectric Objects

In the surface field integral equations (SIEs) from three-dimensional homogeneous dielectric objects, the equivalence electric and magnetic currents on the discontinuous interfaces between different homogeneous media are two independent sources. When the SIEs are iteratively solved, as indicated by the published literatures, the multilevel fast multipole algorithm (MLFMA) needs to be implemented respectively for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) with these two currents, and hence a few MLFMA implementations are necessary for each homogeneous medium. In this paper, a concise and efficient scheme is proposed for reducing the implementations of the SIEs-MLFMA. First, the summation of the EFIE and MFIE-MLFMA implementations with the two currents can be simplified into one EFIE or MFIE-MLFMA implementation with integrating electric and magnetic currents at the lowest-level aggregation stage. Secondly, the common matrix frameworks consisting of the EFIE and MFIE-MLFMA implementations used in the SIEs can be simplified into one MLFMA implementation with two lowest-level diaggregations. The enhanced MLFMA scheme has excellent applicability to eight kinds of SIEs in wide use. In this way, the resulted SIE-MLFMA scheme performs only once for each homogeneous medium when transforming outgoing wave expansions of the two currents into incoming wave expansions for bottom cubes. Compared with the widely-used implementation approach of the MLFMA one by one for the two currents, it reduces the computation complexity by one half without sacrificing accuracy and adding a little memory requirement. Some examples are presented to validate the enhanced MLFMA scheme.

A fast solver for the narrow capture and narrow escape problems in the sphere

We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective, except for a collection of small absorbing patches. The narrow escape problem is the dual problem: it models the behavior of a Brownian particle confined to the interior of a sphere whose surface is reflective, except for a collection of small patches through which it can escape.Mathematically, these give rise to mixed Dirichlet/Neumann boundary value problems of the Poisson equation. They are numerically challenging for two main reasons: (1) the solutions are non-smooth at Dirichlet-Neumann interfaces, and (2) they involve adaptive mesh refinement and the solution of large, ill-conditioned linear systems when the number of small patches is large.By using the Neumann Green's functions for the sphere, we recast each boundary value problem as a system of first-kind integral equations on the collection of patches. A block-diagonal preconditioner together with a multiple scattering formalism leads to a well-conditioned system of second-kind integral equations and a very efficient approach to discretization. This system is solved iteratively using GMRES. We develop a hierarchical, fast multipole method-like algorithm to accelerate each matrix-vector product. Our method is insensitive to the patch size, and the total cost scales with the number N of patches as O(Nlog⁡N), after a precomputation whose cost depends only on the patch size and not on the number or arrangement of patches. We demonstrate the method with several numerical examples, and are able to achieve highly accurate solutions with 100000 patches in one hour on a 60-core workstation. For that case, adaptive discretization of each patch would lead to a dense linear system with about 360 million degrees of freedom. Our preconditioned system uses only 13.6 million “compressed” degrees of freedom and a few dozen GMRES iterations.

Influence of CAD modeling accuracy on target scattering characteristics

In this paper, precision model, rough model and accurate model with YF-23 as original reference are established. The precision model is obtained by fine modeling based on pictures; the rough model is obtained by rough modeling based on pictures; the accurate model is obtained by fine modeling based on point cloud model. Three models correspond to three modeling methods in engineering practice. Based on the multilevel fast multipole algorithm (MLFMA), the vertical polarization transmitting/vertical polarization receiving (VV) and horizontal polarization transmitting/horizontal polarization receiving (HH) radar cross section (RCS) characteristics of three models were simulated at low and high frequencies. The relationship between aircraft surface details and radar stealth performance were investigated and analyzed according to the simulation results.

An Effective $\mathcal{H}$-LU-Based Preconditioner for the FE-BI-MLFMA for 3-D Scattering Problems

A flexible and efficient Hierarchical LU ( $\mathcal{H}$ -LU)-based preconditioner ( $\mathcal{H}$ -LU-P) is presented for the hybrid finite element-boundary integral (FE-BI) multilevel fast multipole algorithm for solving three-dimensional scattering by inhomogeneous objects. The formulation of FE-BI is first approximated by using locally approximated integral operators for the BI part to construct a finite element method-absorbing boundary condition (FEM-ABC) based preconditioning matrix. Then, the preconditioning matrix equation is solved by the nested dissection accelerated $\mathcal{H}$ -LU-based fast direct solver. A semi-geometric clustering strategy is proposed to simplify the cluster tree-building procedure in representing the preconditioning matrix in the $\mathcal{H}$ -matrix form. Numerical results demonstrate that the $\mathcal{H}$ -LU-P outperforms other alternative preconditioners, based on multifrontal approach. The scattering by a large and complex aircraft model with a radome on its nose section is calculated, showing the capability and efficiency of the preconditioner.

Ray-Tracing-Based Dual-Domain Analysis Technique Using the Method of Moments and the Multilevel Fast Multipole Algorithm

This paper presents a technique for the full-wave analysis of large problems using the method of moments, in combination with the multilevel fast multipole algorithm, based on a decomposition of the scenario into two domains using a ray-tracing analysis. These domains are computed considering the proximity to the critical points. The currents over the main scenario are obtained first and used to modify the excitation of the secondary domain, which in turn can be analyzed using a relaxed iteration error that very noticeably reduces the iteration time without a significant impact on the accuracy. The procedure used for the separation of both domains minimizes the amount of information exchanged between them.

Fast Solution of Volume–Surface Integral Equations for Multiscale Structures

Electromagnetic (EM) problems with conducting and penetrable media are formulated by volume–surface integral equations (VSIEs). Traditionally, the VSIEs are solved by the method of moments (MoM) with Rao–Wilton–Glisson (RWG) and Schaubert–Wilton–Glisson (SWG) basis functions. We develop a hybrid method to discretize the VSIEs where the surface integral equation (SIE) for the conducting part is discretized by the standard MoM, while the volume integral equations (VIEs) for the penetrable part are discretized by a point-matching scheme (PMS). The PMS can use unstructured or nonconforming meshes and make the integral kernels of VIEs be free of material parameters. Also, the VIEs can result in well-conditioned system matrices because they are the second kind of integral equations. For electrically large or complex problems with multiscale structures, we unite the hybrid method with the multilevel fast multipole algorithm (MLFMA) to accelerate the solutions. Since the MLFMA is sensitive to the conditioning of system matrices which the multiscale feature will deteriorate and is tedious to implement, using the VIEs can ameliorate the conditioning of system matrices and using the PMS can facilitate the implementation of MLFMA. The approach is demonstrated by several numerical examples and its good performance has been observed.