基于改进的体面积分方程区域分解方法高效求解有限大频率选择表面结构的电磁散射特性
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摘要
针对复杂的有限大频率选择表面(frequency selective surface, FSS)结构阐述了一种改进的非重叠和非共型的体面积分方程区域分解方法(volume-surface integral equation domain decomposition method, VSIE-DDM).为了对其进行高效的电磁分析,我们在最近发展的VSIE-DDM的基础上开发了不同的分区方式,每个子区域不必相同大小,可以任意形状,使该VSIE-DDM分区更加灵活.并且由于FSS的精细单元和薄介质基底,导致网格比较稠密,因此得到维度比较大的矩阵.为了更高效计算更大维度的子区自耦合矩阵的逆,使用了内外迭代技术使得该方法可以采用电尺寸更大的子区,获得更好的收敛性,进一步提高了仿真效率.通过几个数值算例验证了本文所提算法的计算性能.
This paper describes an improved non-overlapping and non-conformal volume-surface integral equation domain decomposition method(VSIE-DDM) for the complex finite frequency selection surface(FSS) structures. To efficient electromagnetic analysis of this complex FSS structure, based on the recently developed domain decomposition method(DDM), we first developed different partitioning methods, each subdomain must not be identical and can be arbitrarily shaped. It makes the VSIE-DDM more flexible. Then, due to the fine cells of the FSS and the thin dielectric substrate, the mesh is denser, so a matrix with a larger dimension is obtained. In order to calculate the inverse of the self-coupling matrix of the subdomains of larger dimensions more efficiently, an inner-outer iterative technique is used. Subdomains with larger electric size can be employed, which makes the DDM obtain better convergence and further
This paper describes an improved non-overlapping and non-conformal volume-surface integral equation domain decomposition method(VSIE-DDM) for the complex finite frequency selection surface(FSS) structures. To efficient electromagnetic analysis of this complex FSS structure, based on the recently developed domain decomposition method(DDM), we first developed different partitioning methods, each subdomain must not be identical and can be arbitrarily shaped. It makes the VSIE-DDM more flexible. Then, due to the fine cells of the FSS and the thin dielectric substrate, the mesh is denser, so a matrix with a larger dimension is obtained. In order to calculate the inverse of the self-coupling matrix of the subdomains of larger dimensions more efficiently, an inner-outer iterative technique is used. Subdomains with larger electric size can be employed, which makes the DDM obtain better convergence and further
引文
[1] MUNK B. Frequency selective surfaces: theory and design[M]. Hoboken: John Wiley & Sons, 2005.
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[4] LI X J, LEI L, ZHAO H, et al. Efficient solution of scattering from composite planar thin dielectric-conductor objects by volume-surface integral equation and simplified prism vector basis functions[J]. IEEE transactions on antennas and propagation, 2018, 66(5): 2686-2690.
[5] LI X, HU J, NIE Z P, et al. An efficient solution of scattering from thin dielectric structures by volume-surface integral equation and simplified prism vector basis functions[C]//IEEE International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017: 661-664.
[6] PENG Z, LIM K H, LEE J F. Computations of electromagnetic wave scattering from penetrable composite targets using a surface integral equation method with multiple traces[J]. IEEE transactions on antennas and propagation, 2013, 61(1): 256-270.
[7] PENG Z, LIM K H, LEE J F. A discontinuous Galerkin surface integral equation method for electromagnetic wave scattering from nonpenetrable targets[J]. IEEE transactions on antennas and propagation, 2013, 61(7): 3617-3628.
[8] ZHAO R, HU J, ZHAO H, et al. EFIE-PMCHWT-Based domain decomposition method for solving electromagnetic scattering from complex dielectric/metallic composite objects[J]. IEEE antennas wireless propagation letters, 2017, 16: 1293-1296.
[9] JIANG M, HU J, et al. Solving scattering by multilayer dielectric objects using JMCFIE-DDM-MLFMA[J]. IEEE antennas and wireless propagation letters, 2014, 13(1): 1132-1135.
[10] BAUTISTA M A E, VIPIANA F, FRANCAYILLA M A, et al. A nonconformal domain decomposition scheme for the analysis of multiscale structures[J]. IEEE transactions on antennas and propagation, 2015, 63(8): 3548-3560.
[11] ZHANG L M, SHENG X Q. Discontinuous Galerkin volume integral equation solution of scattering from inhomogeneous dielectric objects by using the SWG basis function[J]. IEEE transactions on antennas and propagation, 2017, 65(3): 500-1504.
[12] CHEN S W, ZHOU H X, ZHENG K L, et al., VIE-ODDM-FFT method using nested uniform cartesian grid for the analysis of electrically large inhomogeneous dielectric objects[J]. IEEE transactions on antennas and propagation, 2018, 66(1): 293-303.
[13] LI X, LEI L, CHENG Y P, et al. VSIE-based domain decomposition method with simplified prism vector basis functions for planar thin dielectric-conductor composite objects[J/OL]. IEEE antennas wireless propagation letters, [2018-08-30].https://ieeexplore.ieee.org/document/8413151/
[14] RAO S M, WILTON D R, GLISSON A W. Electromagnetic scattering by surface of arbitrary shape[J]. IEEE transactions on antennas and propagation, 1982, AP-30: 409-418.
[2] COLTON D, KRESS R. Integral equation methods in scattering theory[M]. Philadelphia: SIAM, 2013.
[3] PETERSON A F, RAY S L, MITTRA R. Computational methods for electromagnetics[M]. Piscataway: IEEE Press, 1998.
[4] LI X J, LEI L, ZHAO H, et al. Efficient solution of scattering from composite planar thin dielectric-conductor objects by volume-surface integral equation and simplified prism vector basis functions[J]. IEEE transactions on antennas and propagation, 2018, 66(5): 2686-2690.
[5] LI X, HU J, NIE Z P, et al. An efficient solution of scattering from thin dielectric structures by volume-surface integral equation and simplified prism vector basis functions[C]//IEEE International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017: 661-664.
[6] PENG Z, LIM K H, LEE J F. Computations of electromagnetic wave scattering from penetrable composite targets using a surface integral equation method with multiple traces[J]. IEEE transactions on antennas and propagation, 2013, 61(1): 256-270.
[7] PENG Z, LIM K H, LEE J F. A discontinuous Galerkin surface integral equation method for electromagnetic wave scattering from nonpenetrable targets[J]. IEEE transactions on antennas and propagation, 2013, 61(7): 3617-3628.
[8] ZHAO R, HU J, ZHAO H, et al. EFIE-PMCHWT-Based domain decomposition method for solving electromagnetic scattering from complex dielectric/metallic composite objects[J]. IEEE antennas wireless propagation letters, 2017, 16: 1293-1296.
[9] JIANG M, HU J, et al. Solving scattering by multilayer dielectric objects using JMCFIE-DDM-MLFMA[J]. IEEE antennas and wireless propagation letters, 2014, 13(1): 1132-1135.
[10] BAUTISTA M A E, VIPIANA F, FRANCAYILLA M A, et al. A nonconformal domain decomposition scheme for the analysis of multiscale structures[J]. IEEE transactions on antennas and propagation, 2015, 63(8): 3548-3560.
[11] ZHANG L M, SHENG X Q. Discontinuous Galerkin volume integral equation solution of scattering from inhomogeneous dielectric objects by using the SWG basis function[J]. IEEE transactions on antennas and propagation, 2017, 65(3): 500-1504.
[12] CHEN S W, ZHOU H X, ZHENG K L, et al., VIE-ODDM-FFT method using nested uniform cartesian grid for the analysis of electrically large inhomogeneous dielectric objects[J]. IEEE transactions on antennas and propagation, 2018, 66(1): 293-303.
[13] LI X, LEI L, CHENG Y P, et al. VSIE-based domain decomposition method with simplified prism vector basis functions for planar thin dielectric-conductor composite objects[J/OL]. IEEE antennas wireless propagation letters, [2018-08-30].https://ieeexplore.ieee.org/document/8413151/
[14] RAO S M, WILTON D R, GLISSON A W. Electromagnetic scattering by surface of arbitrary shape[J]. IEEE transactions on antennas and propagation, 1982, AP-30: 409-418.