Element-boundary Integral-multilevel Fast Multipole Algorithm Research Articles

A Novel Hybrid Approach for Computing Electromagnetic Scattering from Objects with Honeycomb Structures

We propose in this paper a novel hybrid numerical modeling method for computing electromagnetic scattering from inhomogeneous targets containing honeycomb structures. In the proposed approach, the whole honeycomb structure is divided into the inner and outer two subregions. Each thin wall of a unit cell in the outer subregion is replaced by a zero-thickness surface, with the aid of a resistive sheet boundary condition (RSBC) to describe the electric and magnetic field discontinuities across the surface. Each unit cell in the inner subregion is homogenized by using the Hashin–Shtrikman and the Mori–Tanaka formulae. The two subregions are further divided into smaller subdomains by introducing the Robin-type transmission condition to couple subregion interfaces, as well as subdomain interfaces. The whole solution region is then discretized and solved using the nonconformal domain decomposition-based hybrid finite element–boundary integral–multilevel fast multipole algorithm (FE-BI-MLFMA). The numerical results demonstrate that the proposed approach exhibits a high accuracy, efficiency, and flexibility. Solutions of scattering by a wing-like object and a practical unmanned aerial vehicle (UAV) model with honeycomb radar-absorbing structures are presented, showing the superior performance of the proposed algorithm.

Resistive Sheet Boundary Condition-Based Nonconformal Domain Decomposition FE-BI-MLFMA for Electromagnetic Scattering From Inhomogeneous Objects With Honeycomb Structures

A flexible and efficient resistive sheet boundary condition (RSBC)-based hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is presented for computing electromagnetic scattering from inhomogeneous objects with microwave-absorbing honeycomb structures. In the proposed algorithm, each nonmagnetic and high lossy material coated unit cell wall of the honeycomb is first approximated by the multilayered RSBC as a zero-thickness resistive sheet to eliminate the computational burden due to the extremely thin and multilayered characteristics of the coated unit cell wall. Then, the RSBC is incorporated into the FE-part of the FE-BI-MLFMA formulation. To further reduce the burden of meshing complicated objects involving cellular structures after RSBC approximation, the hybrid conformal and nonconformal domain decomposition method (DDM) of the FE-BI-MLFMA, which integrates the nonconformal Schwarz DDM-FE and the simplified discontinuous Galerkin (S-DG), is employed to bring significant flexibility and versatility in geometry modeling and mesh generating. An effective block low-rank multifrontal solver-based domain decomposition finite-element method (FEM)-absorbing boundary condition (ABC) preconditioner is constructed to speed up the solution of the FE-BI equations using locally approximated integral operators for the BI part. Numerical examples are given to demonstrate the accuracy, capability, and performance of the proposed algorithm, including a high-definition complicated fighter model with antenna array, multilayer dielectric radome, and microwave-absorbing honeycomb structures.

A Flexible and Efficient Method for the Analysis of Electromagnetic Scattering by Inhomogeneous Objects With Honeycomb Structures

We present in this letter an efficient numerical method for the analysis of electromagnetic scattering by inhomogeneous objects with arbitrarily oriented honeycomb radar absorbing structures. In this method, each cellular honeycomb structure is first homogenized as a diagonal anisotropic medium in local coordinate system by using a new hybrid Hashin–Shtrikman and Mori–Tanaka formula. Then, a Euler rotation matrix is employed for describing a honeycomb structure with arbitrary orientation in a global coordinate system by transforming a diagonal tensor into a general 3 × 3 tensor. Finally, the object with homogenized honeycomb structures are simulated by using the nonconformal domain decomposition finite element-boundary integral-multilevel fast multipole algorithm. Numerical examples are presented to demonstrate the accuracy, efficiency and capability of the proposed algorithm, including the scattering by a typical sandwich panel with honeycomb core, and a complicated fighter model which includes antenna array, dielectric radome and radar-absorbing honeycomb structure.

Nonconformal FETI-DP Domain Decomposition Methods for FE-BI-MLFMA

The nonconformal domain decomposition methods (DDMs) of the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) are presented for computing large electromagnetic scattering/radiation problems. The numerical performance of different transmission conditions between finite element method (FEM) subdomains, and FEM and BI domains is studied in this paper. The Dirichlet transmission condition (DTC) employed at the interface between FEM and BI domains has faster convergence than the Robin-type transmission condition, and this finding is different from the conclusions for the FEM DDMs published in the literature. Furthermore, the cement-element (CE)-based dual-primal finite element tearing and interconnecting (FETI-DP) DDM has faster convergence than the Lagrange-multiplier-based FETI-DP method under the FE-BI system, and is also different from that under the system of the FEM with the absorbing boundary condition (FEM-ABC). It shows that the DDMs of FE-BI-MLFMA have some essential differences from those of FEM-ABC. The analysis of these numerical phenomena is presented in this paper. Further comparison between the DDMs of FE-BI-MLFMA and FEM-ABC demonstrates that the DDMs of FE-BI-MLMFA have essential advantages over those of FEM-ABC. Various numerical experiments confirm the accuracy, efficiency, and flexibility of the nonconformal DDM of FE-BI-MLFMA, which is the CE-based FETI-DP DDM with DTC connecting FEM and BI.

A non‐conformal FETI‐like domain decomposition approach of FE‐BI‐MLFMA for 3‐D electromagnetic scattering/radiation problems

SummaryA non‐conformal finite element tearing and interconnecting‐like (FETI‐like) domain decomposition approach (DDA) of the hybrid finite element–boundary integral–multilevel fast multipole algorithm (FE‐BI‐MLFMA) is presented by integrating a series efficient techniques for computing electromagnetic scattering/radiation problems. The Robin transmission condition is employed to cement the non‐conformal meshes on the interconnected surfaces between the interior and exterior regions and between sub‐domains in the interior region. The FETI‐like technique is applied to reduce the FE‐BI matrix equation. Furthermore, a preconditioner is constructed to accelerate the convergent speed of this non‐conformal FETI‐like DDA. The numerical performance of the presented non‐conformal FETI‐like DDA‐FE‐BI‐MLFMA is studied for scattering/radiation problems. Copyright © 2015 John Wiley & Sons, Ltd.

An Accurate Bistatic Scattering Center Model for Extended Cone-shaped Targets

An accurate bistatic scattering center model for cone-shaped targets is proposed in this paper. The model describes the overall attributes of dominant bistatic scattering centers. It includes not only the sliding scattering centers on the smooth surface and bottom edge, but also the scattering centers induced by creeping waves and traveling waves which are not considered in the previous models. To validate the proposed model, the results based on this model are compared with precise scattered fields computed by the full-wave numerical method, namely the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). Excellent agreement has been achieved. In contrast to the traditional assumption, it is concluded in this paper that the scattering centers of creeping waves and traveling waves are important, and can not be ignored particularly under bistatic mode.

An Effective Domain-Decomposition-Based Preconditioner for the FE-BI-MLFMA Method for 3D Scattering Problems

A domain-decomposition-based preconditioner (DDP) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). The formulation of FE-BI is first approximated by the finite element method (FEM) with absorbing boundary condition (ABC). Then this approximate FEM-ABC formulation is solved by using the finite element tearing and interconnecting method (FETI). Finally, an inner-outer iterative algorithm with variable convergence threshold is designed for FE-BI-MLFMA. Because of good numerical scalability of FETI and good approximation of FEM-ABC, this DDP-FE-BI-MLFMA performs well even for large lossless objects.

Application of Interpolative Decomposition to FE-BI-MLFMA for Fast Computation of Monostatic Scattering from 3-D Complex Composite Objects

Interpolative decomposition (ID) algorithm is applied to the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for fast computation of monostatic scattering from 3-D complex composite objects in this letter. The sparse skeleton directions are first selected from dense incident directions by employing ID. Then, the scattering fields from these skeleton directions are computed by FE-BI-MLFMA. Finally, scattering fields from any other interested directions can be constructed by the scattering fields from the skeleton directions. The numerical performance of ID for FE-BI-MLFMA has been investigated in detail through computing monostatic scattering by typical complex composite objects. It is observed that the skeleton directions by using ID are nonuniform and far less than directions uniformly selected. Furthermore, the result of skeleton directions by using ID is very robust and almost independent of procedures of using ID. Based on it, a two-level approach of using ID is first presented to reduce memory requirement in using ID in this letter.

Parallel Domain-Decomposition-Based Algorithm of Hybrid FE-BI-MLFMA Method for 3-D Scattering by Large Inhomogeneous Objects

The hybrid method of the finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) has been recognized as one of the most powerful numerical methods for analyzing large inhomogeneous radiation/scattering problems. A domain decomposition algorithm (DDA) of FE-BI-MLFMA is presented in this paper by using the finite element tearing and interconnecting method (FETI). The formulation of DDA-FE-BI-MLFMA is presented and analyzed in detail. The numerical performance of DDA-FE-BI-MLFMA is investigated by numerical experiments from many aspects. It includes the convergence speed versus types of domain decomposition, number of subdomains, types and inhomogeneity of dielectrics involving in solved problems, and the scalability of DDA-FE-BI-MLFMA. The comparison of DDA and previous algorithms of FE-BI-MLMFMA is also carried out. Finally, the capability of DDA-FE-BI-MLFMA is shown for large inhomogeneous problems.

Influence of migratory scattering phenomenon on micro‐motion characteristics contained in radar signals

The micro-motion characteristics of radar target are useful features for target recognition. Extended targets (as opposed to point target) have various scattering centres, such as the familiar point, localised and distributed scattering centres, as well as the rarely discussed but often encountered migratory scattering centres. The migratory scattering phenomenon of smooth surface is particularly concerned in this study. The motion information recoded in radar signals are actually that of migratory scattering centres rather than the real motions of the rigid target. Therefore the misleading motion information will bring unpredictable error to the radar application of target discrimination or recognition. To tackle this problem, the influence of migratory scattering phenomena of extended targets on micro-motion characteristics contained in radar signal is analysed in detail. Some meaningful conclusions are reached. The backscattered signals of extended targets are computed by the well-validated full-wave numerical method, hybrid finite element-boundary integral-multilevel fast multipole algorithm. The numerical results agree well with the analytical conclusions given in this study.

Application of Asymptotic Waveform Evaluation to Hybrid FE-BI-MLFMA for Fast RCS Computation Over a Frequency Band

The asymptotic waveform evaluation (AWE) technique has been widely used in the method of moment (MoM), the finite element method (FEM), and the hybrid finite element-boundary integral method (FE-BI) for fast computation over a wide frequency band. However, how to apply AWE to the multilevel fast multipole algorithm (MLFMA) still remains challenge. This paper proposes an efficient and robust approach to apply AWE to the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). The validity of the proposed approach is verified by numerical examples for scattering problems. Numerical experiments show that the application of AWE to FE-BI-MLFMA can greatly improve the efficiency of FE-BI-MLFMA for computation of scattering over a wide frequency band.

DOMAIN DECOMPOSITION FE-BI-MLFMA METHOD FOR SCATTERING BY 3D INHOMOGENEOUS OBJECTS

The hybrid flnite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is a powerful method for calculating scattering by inhomogeneous objects. However, the conventional FE-BI-MLFMA often sufiers from iterative convergence problems. A non-overlapping domain decomposition method (DDM) is applied to FE-BI-MLFMA to speed up the iterative convergence. Furthermore, a preconditioner based on absorbing boundary condition and symmetric successive over relaxation (ABC-SSOR) is constructed to further accelerate convergence of the DDM-FE-BI-MLFMA. Numerical experiments demonstrate the e-ciency of the proposed preconditioned DDM-FE-BI-MLFMA.

Hybrid h- and p-Type Multiplicative Schwarz (h-p-MUS) Preconditioned Algorithm of Higher-Order FE-BI-MLFMA for 3D Scattering

A hybrid h- and p-Type multiplicative Schwarz (h-p-MUS) preconditioned algorithm is proposed to improve efficiency of higher-order finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for 3D scattering in this paper. An h-p-MUS precondtioner is first constructed for the FEM matrix obtained by using vector higher-order hierarchical basis functions. Numerical experiments show that this preconditioner can offer a better efficiency both in CPU time and memory requirement than the h-MUS and the p-MUS preconditioners. Then this h-p-MUS preconditioner for the FEM matrix is applied to different algorithms of FE-BI-MLMFA. Analysis and Numerical results show that the h-p-MUS preconditioned conventional algorithm (h-p-MUS-CA) has a better efficiency over other h-p-MUS preconditioned algorithms. A variety of numerical experiments are performed for large objects in this paper, demonstrating that this h-p-MUS-CA exhibits superior efficiency in the CPU time and memory, and greatly improves the capability of the higher-order FE-BI-MLFMA.

A Concave FE-BI-MLFMA for Scattering by a Large Body With Nonuniform Deep Cavities

A concave finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is presented for scattering by a large body with nonuniform deep cavities. Different from the conventional FE-BI-MLFMA, the boundary integral equation in this concave FE-BI-MLFMA is established on a concave surface to reduce the region of the finite element method (FEM), which can significantly reduce the dispersion error from the FEM and improve the efficiency of FE-BI-MLFMA especially for nonuniform cavities. To eliminate the problem of slow convergence caused by concave surface, an efficient preconditioner based on the sparse approximate inverse (SAI) is constructed in this paper. Numerical performance of the constructed preconditioner based on the SAI is investigated in detail. Numerical experiments demonstrate the accuracy and efficiency of this SAI preconditioned concave FE-BI-MLFMA for nonuniform deep and large cavites. This SAI preconditioned concave FE-BI-MLFMA is parallelized to further improve its capability in this paper. An extremely big and deep nonuniform cavity has been calculated, demonstrating the great capability of this parallel concave FE-BI-MLFMA.

Scattering of a Plane Wave by an Anisotropic Plasma-Coated Conducting Sphere

The electromagnetic field in homogeneous plasma anisotropic medium can be expressed as the addition of the first and second spherical vector wave functions in plasma anisotropic medium. The tangential electromagnetic fields are continued in the boundary between the homogeneous plasma anisotropic medium and free space, and the tangential electrical field is zero in the surface of conducting sphere. The coefficients of electromagnetic fields in plasma anisotropic medium expanded in terms of spherical vector wave functions in plasma anisotropic medium are derived, and then the coefficients of scattering fields in terms of spherical vector functions in free space can be obtained. Numerical results between this paper and hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) are given, and they are in agreement very well. Some new numerical results of a plane wave scattering by an anisotropic plasma-coated conducting sphere are obtained.

How to Predict Scattering and Range Profiles using Complex Targets with Cavities

How to predict the scattering and range profiles using complex targets with cavities is investigated by using the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). A double-check criterion is presented for validating the reliability of FE-BI-MLFMA. The accuracy of both amplitude and phase of the scattering field using the complex target is emphatically validated based on the criterion. The range profiles of a typical target-cylinder with cavity-are investigated with the validated FE-BI-MLFMA.

Analysis of scattering by large objects with off-diagonally anisotropic material using finite element-boundary integral-multilevel fast multipole algorithm

The scattering by large anisotropic objects is computed using the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA). The validity of FE-BI-MLFMA for objects with off-diagonally anisotropic material is convincingly verified by comparing numerical results with analytical values. The numerical performance of the FE-BI-MLFMA is in detail investigated for anisotropic objects. It is shown that the numerical performance of the FE-BI-MLFMA is much worse for off-diagonally anisotropic objects than that for isotropic and uniaxially anisotropic objects. A node-edge element is employed for improving the efficiency of the FE-BI-MLFMA for anisotropic objects. The scattering characteristics by different large anisotropic objects are analysed by the FE-BI-MLFMA. Numerical results demonstrate that the anisotropic materials, especially off-diagonally anisotropic materials, can significantly change the radar cross section (RCS) pattern by complicated mechanisms, which depend on the structure of objects.

Parallel High-Order FE-BI-MLFMA for Scattering by Large and Deep Coated Cavities Loaded with Obstacles

A parallelization approach of the finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is presented and implemented for scattering by large and deep coated cavities loaded with obstacles. Numerical experiments demonstrate the parallel efficiency of this parallelization approach. The capability of the parallel FE-BI-MLFMA is demonstrated by computing scattering by a big and deep brick cavity with 15λ×15λ×100λ. A three-layer meshing approach with the aid of commercial software 'ANSYS' is presented to facilitate the FE-BI-MLFMA to efficiently analyze cavities loaded with complex obstacles. Numerical examples of complex cavities are performed to validate the meshing approach. Comparisons of numerical results and measured data verify the accuracy of the FE-BI-MLFMA for complex cavities.

AN EFFICIENT TWOFOLD ITERATIVE ALGORITHM OF FE-BI-MLFMA USING MULTILEVEL INVERSE-BASED ILU PRECONDITIONING

It is known that the conventional algorithm (CA) of hybrid flnite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) usually sufiers the problem of slow convergence, and the decomposition algorithm (DA) is limited by large memory requirement. An e-cient twofold iterative algorithm (TIA) of FE-BI- MLFMA is presented using the multilevel inverse-based incomplete LU (MIB-ILU) preconditioning in this paper. It is shown that this TIA can ofier a good balance of e-ciency between CPU time and memory requirement. The tree-cotree splitting technique is then employed in the TIA to further improve its e-ciency and robustness. A variety of numerical experiments are performed in this paper, demonstrating that the TIA exhibits superior e-ciency in memory and CPU time to DA and CA, and greatly improves the computing capability of FE-BI- MLFMA.

A Flexible and Efficient Higher Order FE-BI-MLFMA for Scattering by a Large Body With Deep Cavities

The hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is applied to solve the challenge problem of scattering by a large body with deep cavities in this paper. The hierarchical higher order curvilinear vector finite element (HCVFE) is employed to reduce the numerical dispersion error in the FEM and to efficiently model the geometry of the cavity. The coupling approaches are investigated at the interface between the FE region and the BI region for handling the problem of the different order basis functions and meshes used in the FE and BI region. The problems encountered with the previous decomposition algorithm of FE-BI-MLFMA are pointed out and analyzed in this paper. A special algorithm of FE-BI-MLFMA is designed based on the distinct geometry characteristics of deep cavity. Numerical results are presented to demonstrate the accuracy, efficiency and flexibility of the higher order FE-BI-MLFMA for scattering by a large body with big and deep cavities.