Volume Integral Equation With Higher Order Hierarchical Basis Functions for Analysis of Dielectric Electromagnetic Scattering

Cai, Qiang‐Ming; Zhao, Yanwen; Zheng, Yu-Teng; Jia, Miao-miao; Zhao, Zhiqin; Nie, Zaiping

doi:10.1109/tap.2015.2481925

Cited by 20 publications

(23 citation statements)

References 34 publications

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“…Figure 7 shows the normalized far-field radiation pattern with or without a radome. It is observed that the proposed method agrees well with the result calculated by the commercial software FEKO, which is also consistent with the result of [11] (in Figure 8). This indicates the accuracy and reliability of the nonconformal VIE solver in this paper.…”

Section: Examples Of Scattering and Radiationsupporting

confidence: 89%

“…Consider an inhomogeneous dielectric object with a permittivity of ε r r and a permeability of μ 0 residing in free space with EM parameters ε 0 and μ 0 . The object is excited by an incident electric field E inc r , and the volume electric field integral equation (VEFIE) associated with the vector potential A r and scalar potential Φ r can be expressed by [11] D r ε r + jωA r + ∇Φ r = E inc r , 1…”

Section: Volume Electric Field Integral Equationmentioning

confidence: 99%

“…It should be noted that the larger l (denotes the lower level) corresponds to the smaller box size. By (11), the far field interactions of MVM are divided into ACA acceleration from k + 1 to L in the lower levels without LF breakdown and MLFMA acceleration from 2 to k 2 ≤ k ≤ L in higher levels to maintain high efficiency. If k = L, it means that only MLFMA is used.…”

Section: Constructing Swg Pairsmentioning

confidence: 99%

“…To further demonstrate the accuracy and flexibility of the proposed solver, a radiation pattern of an eightdipole array in a three-layer hemispherical dielectric radome is analyzed. The geometric model is shown in Figure 6 which is the same as the Figure 4(c) in [11]. The base radius R of the radome is 50 mm, the thicknesses and the relative permittivities of both the innermost and the outermost layers are 3 mm and 2.0-0 005j, and those of the middle layer are 4 mm and 1.5-0 035j, respectively.…”

Section: Examples Of Scattering and Radiationmentioning

confidence: 99%

See 3 more Smart Citations

Versatile Solver of Nonconformal Volume Integral Equation Based on SWG Basis Function

Luo

Pang

Lin

2018

International Journal of Antennas and Propagation

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In this paper, a versatile solver of a nonconformal volume integral equation based on the Schaubert-Wilton-Glisson (SWG) basis function is presented. Instead of using a piecewise constant function, the robust conventional SWG basis function is chosen and used directly for discontinuous boundaries. A new map method technique is proposed for constructing SWG pairs, which reduces the complexity from O N 2 to O N log N compared with a brute-force method. The integral equation is solved by the method of moments (MoM) and further accelerated by the multilevel fast multipole algorithm (MLFMA). What's more, the hybrid scheme of MLFMA and adaptive cross approximation (ACA) is developed to resolve the low-frequency (LF) breakdown when dealing with over-dense mesh objects. Numerical results show that when in analysis of radiation or scattering problems from inhomogeneous dielectric objects or in LF conditions, the proposed solver shows high efficiency without loss of accuracy, which demonstrates the versatile performance of the proposed method.

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Section: Examples Of Scattering and Radiationsupporting

confidence: 89%

Section: Volume Electric Field Integral Equationmentioning

confidence: 99%

Section: Constructing Swg Pairsmentioning

confidence: 99%

Section: Examples Of Scattering and Radiationmentioning

confidence: 99%

See 2 more Smart Citations

Versatile Solver of Nonconformal Volume Integral Equation Based on SWG Basis Function

Luo

Pang

Lin

2018

International Journal of Antennas and Propagation

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“…In 2012, R. D. Graglia and A. F. Peterson [14] proposed a new family of higher order hierarchical vector (HOHV) basis functions defined inside curved tetrahedrons. Then, Cai et al [15] used these HOHV bases to discretise the volume electric field integral equation (VEFIE) for the scattering analysis from isotropic medias, where its accuracy, flexibility, and efficiency were well-demonstrated. However, as reported by [15], high computational cost still has been yielded, especially when the scatters involve in multi-scale structure or high contrast media.…”

Section: Introductionmentioning

confidence: 99%

Higher order VIE method based on non‐conformal discretisation for EM scattering from anisotropic objects

Zhang

Cai

Zhao

et al. 2019

IET Microwaves, Antennas & Propagation

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This article presents a higher order method of moments (MoM) solution of the volume electric field integral equation (VEFIE) to model the electromagnetic (EM) scattering from anisotropic dielectric objects with arbitrary shape and inhomogeneity. This higher order solution is based on the higher order current modelling and higher order geometric modelling. Namely, the unknown electric flux density vector is discretised by the higher order hierarchical vector (HOHV) basis functions, and the geometric structure is discretised by the curved tetrahedral elements. Both kinds of higher order discretisation can reduce the number of mesh elements and the associated unknowns significantly. When the solution accuracy is on a comparable level, authors’ higher order VIE demands much less memory and CPU time than the conventional low‐order volume integral (VIE). Moreover, authors’ scheme accommodates the non‐conformal discretisation, because no divergence operator is imposed on the vectorial unknown. Numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of the proposed approach.

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Optimization of block size for volume integral equation‐based characteristic basis function method

Huang

Sun

2022

Micro & Optical Tech Letters

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The block size of the characteristic basis function method (CBFM) based on volume integral equation (VIE) is optimized to improve the efficiency on analyzing the scattering from dielectric objects in this study. Several literatures have discussed the optimum block size of surface integral equation (SIE)based CBFM, which achieved the minimum CPU time for analyzing conductor objects. However, due to the differences of basis functions, the conclusions derived from SIE-based CBFM are not applicable for VIE-based CBFM. This study presents the relationship between the Schaubert-Wilton-Glisson (SWG) basis functions and characteristic basis functions (CBFs), which paves the way for evaluating the computational complexity of VIE-based CBFM. In addition, the Sherman-Morrison-Woodbury formula-based algorithm (SMWA) and adaptive cross approximation (ACA) algorithm are combined to accelerate the CBFs generation and reduced matrix construction. Based on the computational complexity of the VIE-based CBFM combined with SMWA and ACA, the optimal number of blocks for VIE-based CBFM is derived theoretically.Numerical results of homogeneous and inhomogeneous dielectric objects scattering problems are presented to validate the feasibility and accuracy of the proposed optimization method.

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Volume Integral Equation With Higher Order Hierarchical Basis Functions for Analysis of Dielectric Electromagnetic Scattering

Cited by 20 publications

References 34 publications

Versatile Solver of Nonconformal Volume Integral Equation Based on SWG Basis Function

Versatile Solver of Nonconformal Volume Integral Equation Based on SWG Basis Function

Higher order VIE method based on non‐conformal discretisation for EM scattering from anisotropic objects

Optimization of block size for volume integral equation‐based characteristic basis function method

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