Multilevel Fast Multipole Method Research Articles

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.

Effect of Baffle Board on Aerodynamic and Stealth Performance of Double S-Duct Caret Intake

Intake is not only the main air supply component of an aircraft, but also one of the forward radar scattering sources. The aerodynamic and stealth performance of intake is critical to the serviceability of advanced fighter aircrafts. The effects of baffle boards with different configurations on the performance of the caret intake with a double S-duct diffuser are presented in this article. The multi-level fast multipole method (MLFMM) and the SST k-ω turbulence model were respectively used to calculate the surface current and the flow field. It was found that the average RCS value of intake can be effectively reduced by installing the baffle board with vertical orientation in the front diffuser, with the DC60 value and the loss of outlet total pressure both increased slightly. The boundary layer separation and the RCS characteristics of intake were closely related to the configuration of the corrugated baffle board. Compared with the traditional curved board, by installing the corrugated board with optimized corrugation number and shape, the stealth performance of intake can be further improved, and the loss of aerodynamic performance can be also reduced.

An efficient derivation of spatial Green's function of open-radiating rectangular cavity using CGF-CI technique

ABSTRACT A new technique for efficient calculation of spatial Green's function of open-radiating rectangular cavity is presented. The method is based on separability assumption of the original structure and characteristic Green's function method. Using complex image (CI) technique in spectral domain and well-known Weyl's identity, a closed-form relation for spatial Green's function can be derived. To obtain more accurate closed-form Green's function, before applying CI, discrete spectrum contribution part of the derived relation is modified by replacing more accurate reflection coefficients of surface wave modes from walls of the open-radiating cavity. Verification of the derivations of the proposed method is shown for dielectric loaded metallic box which is a separable structure. Method of moment + multilevel fast multipole method solution and also exact numerical integration approach for open-radiating rectangular cavity are considered to search the accuracy as well as speed of the proposed method. It is shown that the main advantage of the proposed method lies in its speed as well as its simple implementation while the accuracy is preserved.

Numerical Investigation of Aerodynamic and Electromagnetic Performances for S-Duct Caret Intake with Boundary-Layer Bleed System

This study presents the numerical results for the aerodynamic and electromagnetic performances of an S-duct caret intake. Using the multilevel fast multipole method (MLFMM) to solve Maxwell equations, the current on the intake surface is calculated, and the radar cross-section (RCS) is analyzed. Moreover, the intake flow field is numerically investigated using the SST k–ω turbulence model to solve the Reynolds-averaged Navier–Stokes equations. Compared to a straight intake, for an S-duct caret intake, the average RCS is lower by 7.65 dB, and the maximum RCS difference value caused by the blade rotation is lower by 6.75 dB. However, the flow capacity deteriorates when the total pressure recovery coefficient decreases by 0.004. Based on the analysis of the aerodynamic and electromagnetic characteristics of different intakes, a double S-duct intake is designed. Compared to a traditional S-duct intake, for the novel intake after model parameter modification, the average RCS is lower by 0.05 dB, and the total pressure distortion (TPD) is lower by 0.18. The analysis of the effects of different boundary-layer bleed systems shows that the symmetrical layout adversely affects the aerodynamic and electromagnetic performances of the S-duct intake, but the unilateral partial layout is beneficial, whose TPD is lower by 0.04 and average RCS is higher by −2.17 dB compared to a straight intake.

Near-Field IPO for Analysis of EM Scattering from Multiple Hybrid Dielectric and Conductor Target and High Resolution Range Profiles

Aiming at improving the accuracy and efficiency of scattering information from multiple targets in near-field regions, this paper proposes a near-field iterative physical optics (IPO) method based on a modified near-field Green’s function for the composite electromagnetic scattering analysis of multiple hybrid dielectric and conductor targets. According to the electric field and magnetic field integral equation, the electric and magnetic current were updated utilizing the Jacobi iteration method. Then, by introducing an expansion center lying in the neighborhood of the source point, Green’s function was modified for near-field scattering between multiple hybrid dielectric and conductor targets. To accelerate the implementation of the procedure, the multilevel fast multipole method, the fast far-field approximation, and parallel multicore programming were introduced. Numerical results indicate that there is good agreement between the results calculated by the near-field IPO method and MLFMM solver in commercial software FEKO while significantly reducing the computational burden. To fully exploit the scattering information, the high resolution range profiles (HRRP) of different targets under different conditions were analyzed, which can be further applied for automatic target detection and recognition.

Comparison of Linear Iteration Schemes to Improve the Convergence of Iterative Physical Optics for an Impedance Scatterer

The conventional iterative physical optics (IPO) method updates the surface current based on the Jacobi iteration scheme, which typically diverges for large objects. To control the convergence property of the IPO method, other iteration schemes, such as Gauss–Seidel and successive over-relaxation, can be used. In this study, we compare the convergence properties of three iteration schemes for scatterings by five scatterers comprising electrically perfect or imperfect conductors modeled with an impedance material. The accuracy of the IPO method is compared with that of the multi-level fast multipole method.

An efficient method for analysis of electromagnetic scattering from a 3-D coated object half-buried in PEC rough surface

ABSTRACT To accurately simulate the electromagnetic scattering from a three-dimensional (3-D) coated object half-buried in perfectly electrically conductor (PEC) rough surface, an efficient method combining the 3-D vector finite element method-boundary integral method (FEM-BIM) with fast multipole method (FMM) is proposed in this paper. FEM is used to model the coated object and the multiple interactions between the half-buried object and rough surface are handled by FMM-enhanced BIM. According to the characteristics of the FEM-BIM matrix equations, a hybrid solver is adopted to solve the matrix equations. In addition, OpenMP parallel acceleration technique is used in the numerical code to accelerate the intensive computations of the prediction process. The accuracy and efficiency of our numerical code are validated by multilevel fast multipole method (MLFMM) in FEKO for both TE and TM polarizations.

Design and Analysis of a Non-Uniform Antenna Array for IoT Applications

This letter proposes a mathematical model that allow to analyze the total field irradiated by a non-uniform antenna array, in which the elements consist of different types, with different radiation pattern, positioned and oriented randomly in space. The results obtained are compared with the Multilevel Fast Multipole Method. In the analysis performed, it was observed that both for azimuth and elevation variation the results obtained were significant. Furthermore, the analyzed scenarios are related antennas for internet of things applications, bringing the analysis of the proposed model to practical applications. This analysis can lead to a huge range of applications, depending on interest and necessity, given the possibility of obtaining the radiation pattern formed by a non-uniform antenna array with accurately and with reduced computational resources.

Simulation of realistic speckle fields by using surface integral equation and multi-level fast multipole method

This report presents a speckle simulator which calculates rigorously speckle fields with full randomization from rough surfaces. To achieve this, surface integral equation (SIE) method accelerated via multilevel fast multipole method (MLFMM) is implemented. Among several linear formulations to combine the electric and magnetic field integral equations, we demonstrate that one is most suitable for dielectric rough surfaces and one for metallic rough surfaces. As examples, silver and silicon rough surfaces are simulated at a wavelength of 500 nm. To investigate speckles from extended areas, silicon rough surfaces with a size of 30×30 µm2 and two million unknowns are calculated. Based on the resultant speckle fields, speckle contrast, angular speckle-correlation and transverse autocorrelation function of intensity in the van Cittert-Zernike zone are further calculated and known relations versus surface roughness are manifested, indicating that sufficient statistic surface information is encoded in the speckle fields. The SIE-MLFMM method with the suitable formulation proves to be an efficient rigorous simulation tool for relatively large rough surface problems and would enable more profound numerical studies for speckle involved optical metrologies.

An Accelerated Hybrid Method for Electromagnetic Scattering of a Composite Target–Ground Model and Its Spotlight SAR Image

In this paper, an accelerated hybrid method of physical optics (PO) shooting and bouncing ray (SBR)–physical theory of diffraction (PTD) is proposed to deal with the electromagnetic scattering of a complex target on rough ground. To accelerate the ray tracing progress, the ray marching technique based on octree structure is employed. In this technique, only the nodes passed by the ray are detected successively until the first facet intersected by ray is found or the ray passes through the bounding box, which greatly decreases the intersection test. Then, based on the accelerated PO-SBR-PTD method, the spotlight synthetic aperture radar (SAR) echo data of the composite target–ground model is obtained by the vector superposition of the echo on each meshed patch. Furthermore, the spotlight SAR image of the composite model is simulated by the polar format algorithm (PFA). In numerical simulations, both the EM scattering of the target and composite model are calculated and evaluated by comparing with the multilevel fast multipole method (MLFMM) in FEKO software. Meanwhile the spotlight SAR image of the composite target–ground model is also compared with the real image in MSTAR data, and a satisfactory similarity between them is obtained. In addition, the SAR images of two targets on rough ground for different pose angles are also presented and analyzed.

Efficient Scattering Center Prediction Method for Targets With Coating Defects Through Deep Learning

The dielectric coating defects existing on the surface of low detectable targets have nonnegligible impacts on their electromagnetic (EM) scattering characteristics. Due to the large electrical dimension of the target, traditional EM analysis methods are inefficient and cannot meet the requirement of real-time analysis. To address this issue, this article proposed a U-net-based deep neural network (DNN) to perform efficient scattering center (SC) prediction for targets with coating defects from the input 2-D geometric image of it. Furthermore, facing the difficulty of limited training dataset due to the high cost of full-wave numerical simulations, this article proposed a transfer learning method by pretraining the network on a large dataset obtained by the shooting and bouncing ray (SBR) and then fine-tuning it on the target small dataset obtained by the multilevel fast multipole method (MLFMM), which greatly reduced the training difficulty and improved the accuracy and generalization ability of the model. Numerical results are presented to evaluate the performance of the proposed method. It is proven that the proposed method is promising in providing efficient SC prediction in real-time EM analysis scenarios.

Numerical Optimization of Electromagnetic Performance and Aerodynamic Performance for Subsonic S-Duct Intake

In order to improve the performance of subsonic unmanned aerial vehicle (UAV), a knapsack S-duct intake has been designed. The influences of an S-bend diffuser on aerodynamic performance and electromagnetic performance were analyzed firstly. The viscous flow field has been simulated by solving Favre averaged Navier–Stokes equations using a shear stress transport (SST) k-ω turbulence model. The surface current has been simulated by solving Maxwell equations using a multi-level fast multipole method (MLFMM). The multi-objective optimization of the S-duct intake was studied by using the diffuser as the optimized object. The parametric expression of the diffuser model was realized using the fourth order function geometric representation technique. The efficient model based on the Kriging model and non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ) were used to accelerate the optimization progress. By analyzing the results of an optimal intake chosen from the Pareto front, the total pressure distortion (TPD) index DC60 has decreased by 0.24 at the designed Mach number of 0.9, and the average Radar Cross Section (RCS) has decreased by 2db at the frequency of 3GHz. The optimized S-duct intake could have both excellent aerodynamic performance and electromagnetic performance at various complex conditions.

An Accelerated SBR Method for RCS Prediction of Electrically Large Target

This letter proposes an improved shooting and bouncing ray (SBR) method to efficiently predict the radar cross (RCS) of electrically large targets. First, the scan line algorithm is used to convert three-dimensional (3-D) processing to the 2-D graphic display, which expedites the elimination of shadows. Then, the ray tracing process is accelerated by the ray-marching technique which greatly decreases the intersection test. The validity of the proposed method is verified by comparing the simulation results with those of the multilevel fast multipole method. The runtime performance contrast of the traditional Octree-SBR method and ours indicates that the accelerated algorithm is more computationally efficient. Therefore, the presented algorithm has an excellent performance in the RCS prediction of electrically large targets.

LBVH 순회를 이용한 거대 도체 구조의 레이다 단면적 분석

In this study, the radar cross-section (RCS) of a large structure is analyzed using the linear bounding volume hierarchy (LBVH), which is a representative acceleration algorithm of the ray-tracing technique. A ray-tracing technique, which is a high-frequency method, is used to analyze the electromagnetic properties of large structures, and bounding volume hierarchy (BVH), a binary tree structure, is applied to reduce the intersection search time. The improvement in the calculation speed is quantitatively analyzed by dividing an arbitrary scatterer into several triangles. The calculation results are compared with those of multilevel fast multipole method (MLFMM) and ray-launching geometrical optics (RL-GO) using the Feko commercial software to verify the accuracy. The proposed technique can be utilized for the efficient RCS calculations of large structures.

A Fully Polarimetric Multilevel Fast Spectral Domain Algorithm for 3-D Imaging With Irregular Sample Locations

A fully polarimetric frequency-wavenumber domain algorithm for 3-D imaging using the synthetic aperture radar technique with irregular sample locations is introduced. At its core, the algorithm works with a multilevel plane-wave representation and relies on some of the concepts of the multilevel fast multipole method (MLFMM). By utilizing a recursive segmentation scheme, the presented algorithm efficiently handles irregular observation locations, which can vary along all three dimensions in space. The basic idea is to divide the observation region into subdomains of decreasing size, until the calculation of the spectral domain representation of the observation data in the individual subdomains by a discrete Fourier transform (DFT) without further acceleration is feasible. The overall uniformly sampled spectral representation of the observation data is then obtained by hierarchical aggregation of the subdomain spectra. The probe influence is fully compensated by the combined processing of several polarizations and solving small linear systems of equations related to the frequency-wavenumber samples on the coarsest level. The focused image is finally computed by fast Fourier transforms (FFTs). This approach, as opposed to conventional coherent back-projection algorithms (BPAs), allows for a fully polarimetric description of the scattering object and achieves good efficiency without loss of accuracy. To show the effectiveness of the algorithm, imaging results obtained from numerical simulations as well as from the evaluation of measured field data are presented and discussed.

Strip SAR image simulation of a composite vehicle-ground model.

In this paper, the strip synthetic aperture radar (SAR) image of a composite vehicle-ground model is simulated by combining the electromagnetic scattering algorithm and radar imaging algorithm. A linear frequency modulated wave is incident on the composite model, which is partitioned into a mass of triangular patches. In the "stop-and-go" radar mode, for each patch, the amplitude of scattered echo in the frequency domain is solved by a hybrid method of physical optics (PO)-shooting and bouncing ray (SBR)-physical theory of diffraction (PTD). For the composite model, the total scattered echo in terms of range frequency and azimuth time is obtained by the vector superposition of echo on patches. Then the SAR image of the composite model is generated by the range-Doppler algorithm. In numerical simulations, both the electromagnetic scattering of a target by the SBR-PTD method and composite scattering by the PO-SBR-PTD method are validated and evaluated by comparing with the multilevel fast multipole method (MLFMM) in FEKO software. Moreover, the SAR image of the composite vehicle-ground model is also compared with the real image in Moving and Stationary Target Acquisition and Recognition database, which verifies the feasibility of the proposed method. SAR images of the composite model for different incident angles are also presented and analyzed.

Radar Cross Section Prediction Using Iterative Physical Optics With Physical Theory of Diffraction

A new approach is presented to predict radar cross section (RCS) of electrically large conducting geometries using iterative physical optics (IPO) in conjunction with physical theory of diffraction (PTD). IPO is based on iterative refinement of physical optics (PO) currents to include multiple reflections. However, IPO does not yield sufficient accuracy in diffraction dominant regions since it does not properly include effects of edge diffractions. Hence, the proposed approach includes diffraction effects using PTD, which introduces edge currents. Diffracted fields due to these edge currents are radiated on triangular facets to modify the PO currents before IPO iterations. Scattered fields are computed from converged IPO surface currents and PTD edge currents. A new set of PTD edge currents excited by the fields due to the IPO currents are also found and the fields radiated by these PTD edge currents are added to the scattered fields. Therefore, interactions between the surface and edge currents are included. Computations are accelerated by parallel processing using message passing interface (MPI). Monostatic and bistatic RCS are predicted using the proposed approach for tail-wing and trihedral corner reflector geometries. The IPO-PTD results are compared with method of moments (MoM) and multilevel fast multipole method results obtained using field calculations involving bodies of arbitrary shape (FEKO) commercial electromagnetic simulation software for validation.

Particle Layer Effects on Flowfield and Infrared Characteristics of Aircraft Exhaust Plume

Most existing plume infrared (IR) suppression techniques are difficult to apply to an already established aircraft system and cannot be applied in an active way. As an alternative solution, the present study explores an active technique for shielding IR signals by injecting particles into the engine exhaust plume. A Eulerian–Lagrangian-based discrete phase method was used to calculate a multiphase flow composed of exhaust gas and injected particles. To analyze the characteristics of thermal flow and particle distribution under flight conditions, a cruise condition of Mach number 0.7 at an altitude of 20,000 ft was considered. Water droplets and carbon particles with diameters of 5 and were considered, and placed randomly within the particle layer. To analyze the shielding effect according to particle size, material type, and distribution pattern, the transmittance of IR electromagnetic waves of wavelength was analyzed using a Maxwell multilevel fast multipole method. When the total mass was kept the same, water droplets in wavelength bands below , and water droplets or carbon particles in wavelength bands above were more effective for shielding. If the single-layer transmittance information obtained in the present study is extended to actual particle layers of several tens of centimeters, it is expected that the shielding effect will be significantly higher.

ISAR Imaging for Target Above Rough Surface Based on Time-Domain Scattering Echo

The inverse synthetic aperture radar (ISAR) imaging of the target above the rough surface based on the time-domain (TD) electromagnetic (EM) scattering algorithms is focused on in this paper. It effectively combines TD ray tracing (TDRT) method for the composite scene and radar imaging model. The scattering echoes for ISAR imaging are solved by TDRT that the TD mutual coupling between the target and rough surface can be considered by the ray bounce strategy. Compared with the frequency domain ray tracing (FDRT) and multilevel fast multi-pole method (MFMM), TDRT algorithm not only ensures the calculation accuracy, but also greatly reduces the calculation cost. Then, we generate the ISAR image of the target above the rough surface according to the echo matrix based on TDRT. In order to improve the imaging quality of the target, the non-linear mapping theory is presented to suppress the virtual image points and noisy points and it is beneficial to the future research of target recognition in the composite scene.

Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

This paper presents a new fast power series solution method to solve the Hierarchal Method of Moment (MoM) matrix for a large complex, perfectly electric conducting (PEC) 3D structures. The proposed power series solution converges in just two (2) iterations which is faster than the conventional fast solver–based iterative solution. The method is purely algebraic in nature and, as such applicable to existing conventional methods. The method uses regular fast solver Hierarchal Matrix (H-Matrix) and can also be applied to Multilevel Fast Multipole Method Algorithm (MLFMA). In the proposed method, we use the scaling of the symmetric near-field matrix to develop a diagonally dominant overall matrix to enable a power series solution. Left and right block scaling coefficients are required for scaling near-field blocks to diagonal blocks using Schur’s complement method. However, only the right-hand scaling coefficients are computed for symmetric near-field matrix leading to saving of computation time and memory. Due to symmetric property, the left side-block scaling coefficients are just the transpose of the right-scaling blocks. Next, the near-field blocks are replaced by scaled near-field diagonal blocks. Now the scaled near-field blocks in combination with far-field and scaling coefficients are subjected to power series solution terminating after only two terms. As all the operations are performed on the near-field blocks, the complexity of scaling coefficient computation is retained as O(N)O⁢(N). The power series solution only involves the matrix-vector product of the far-field, scaling coefficients blocks, and inverse of scaled near-field blocks. Hence, the solution cost remains O(NlogN)O⁢(N⁢l⁢o⁢g⁢N). Several numerical results are presented to validate the efficiency and robustness of the proposed numerical method.