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一种基于不连续伽辽金方法求解多区域目标散射问题的优化预处理器

张慧雯 黄晓伟 吴比翼 盛新庆

张慧雯,黄晓伟,吴比翼,等. 一种基于不连续伽辽金方法求解多区域目标散射问题的优化预处理器[J]. 电波科学学报,2022,37(3):1-8. DOI: 10.12265/j.cjors.2021065
引用本文: 张慧雯,黄晓伟,吴比翼,等. 一种基于不连续伽辽金方法求解多区域目标散射问题的优化预处理器[J]. 电波科学学报,2022,37(3):1-8. DOI: 10.12265/j.cjors.2021065
ZHANG H W, HUANG X W, WU B Y, et al. An optimal preconditioning scheme for the discontinuous Galerkin solution of multi-region target scattering problems[J]. Chinese journal of radio science,2022,37(3):1-8. (in Chinese). DOI: 10.12265/j.cjors.2021065
Citation: ZHANG H W, HUANG X W, WU B Y, et al. An optimal preconditioning scheme for the discontinuous Galerkin solution of multi-region target scattering problems[J]. Chinese journal of radio science,2022,37(3):1-8. (in Chinese). DOI: 10.12265/j.cjors.2021065

一种基于不连续伽辽金方法求解多区域目标散射问题的优化预处理器

doi: 10.12265/j.cjors.2021065
基金项目: 科技部重点研发计划(2017YFB0202500);国家自然科学基金(61901036);中国科协青年人才托举工程(2020QNRC001)
详细信息
    作者简介:

    张慧雯:(1998—),女,北京人,北京理工大学博士研究生,研究方向为计算电磁学

    黄晓伟:(1995—),男,江西人,北京理工大学博士研究生,主要研究方向为计算电磁学

    吴比翼:(1990—),男,安徽人,北京理工大学信息与电子学院预聘助理教授,硕士生导师,研究方向为计算电磁学

    盛新庆:(1968—),男,安徽人,北京理工大学讲席教授,博士生导师,2004年教育部长江学者特聘教授,主要从事计算电磁学、目标电磁特性与探测技术、隐身目标分析与设计、天线分析与设计、电磁环境预测技术等方面的研究

    通讯作者:

    吴比翼 E-mail: biyi.wu@bit.edu.cn

  • 中图分类号: O441

An optimal preconditioning scheme for the discontinuous Galerkin solution of multi-region target scattering problems

  • 摘要: 在电磁散射问题中,由均匀介质和金属组合而成的多区域结构目标在天线仿真、雷达成像等工程问题中有着广泛应用. 针对多区域目标的散射问题,研究了不连续伽辽金(discontinuous Galerkin, GD)方法在多区域面积分(surface integral equation, SIE)矩量法中的使用,同时提出了一种优化的距离稀疏预处理(optimized distance sparse preconditioner, O-DSP)方法。该方法根据阻抗矩阵中不同积分算子随距离变化的特性来个性化选择预处理矩阵,进一步增加了预处理矩阵的稀疏性. 数值计算表明,相比之前的距离稀疏预处理方法,优化的预处理矩阵非零元素仅为以前的一半,而且具有相同加速迭代效果.
  • 图  1  任意交界表面与其两侧体积区域示意图

    Fig.  1  An arbitrary surface with its internal and external regions

    图  2  多区域交界处示意图

    Fig.  2  The junction of multiple regions

    图  3  介质球体不同算子矩阵块内元素模值随距离约束的变化

    Fig.  3  The variation of modulus value with distance constraint of a dielectric sphere

    图  4  介质球的区域分解形式

    Fig.  4  Domain partitioning for the dielectric sphere

    图  5  介质球的双栈VV-RCS

    Fig.  5  The bistatic VV-RCS of the dielectric sphere

    图  6  K算子矩阵迭代次数和元素数量随距离约束的变化

    Fig.  6  The iteration numbers and element numbers of K operator matrix block, as a function of distance constraint

    图  7  介质球的不同区域分解

    Fig.  7  Domain partition schemes for a dielectric sphere

    图  8  介质球内嵌不同个数的导体块模型

    Fig.  8  Different numbers of conducting spheres embedded in one dielectric sphere

    图  9  介质球内嵌不同个数导体块模型的双栈VV-RCS

    Fig.  9  The bistatic VV-RCS for the model of multiple conducting spheres embedded in one dielectric sphere

    图  10  射频芯片模型的区域分解

    Fig.  10  Illustration of subdomain partition scheme of a radio frequency chip model

    图  11  射频芯片模型的双栈VV-RCS

    Fig.  11  The bistatic VV-RCS of the radio frequency chip model

    图  12  使用不同预处理器求解射频芯片模型的迭代收敛情况

    Fig.  12  Convergence histories for the radio frequency chip model under different preconditioners

    图  13  四旋翼无人机模型的区域分解示意图

    Fig.  13  Illustration of subdomain partition scheme of a four-rotor aircraft model

    图  14  四旋翼无人机模型的双栈VV-RCS

    Fig.  14  The bistatic VV-RCS of the four-rotor aircraft model

    图  15  使用不同预处理器求解四旋翼无人机模型的迭代收敛情况

    Fig.  15  Convergence histories for the four-rotor aircraft model under different preconditioners

    表  1  不同预处理器的DG方法计算数值效果对比

    Tab.  1  Comparison of the n umerical performance of the DG solution with different preconditioner

    预处理策略迭代次数矩阵元素数百分比/%
    $ \mathcal{L} $:ST4,$ \mathcal{K} $:ST4 (NP)542--
    $ \mathcal{L} $:ST4,$ \mathcal{K} $: ST4 (NFP)1519 541 312100.0
    $ \mathcal{L} $:ST2,$ \mathcal{K} $: ST2 (DSP)144 354 94422.3
    $ \mathcal{L} $:ST3,$ \mathcal{K} $:ST3142179 1360.9
    $ \mathcal{L} $:ST2,$ \mathcal{K} $: ST4(DS-2BDP)302 177 47211.1
    $ \mathcal{L} $:ST2,$ \mathcal{K} $: ST3(O-DSP)142 213 66411.3
    注:NP为无预处理器(No preconditioner);DS-2BDP为距离稀疏二对角块预处理器(distance sparse two-partition block-diagonal preconditioner)
    下载: 导出CSV

    表  2  不同分解区域数对DSP和O-DSP的迭代次数和元素比率的影响

    Tab.  2  Comparison of the iteration numbers and element ratios of the DG solution with DSP and O-DSP for different decomposed spheres

    MDSP 迭代次数O-DSP 迭代次数元素比/%
    4141450.831
    8171650.815
    16171750.807
    32444350.757
    下载: 导出CSV

    表  3  导体块数量不同情况下三种预处理器迭代次数和元素个数对比

    Tab.  3  Comparison of the iteration numbers and element numbers by 3 different preconditioners with different numbers of conducting spheres

    预处理器 导体块数量 矩阵元素数 迭代次数
    DSP 2 5 055 045 27
    4 5 779 960 23
    8 7 287 724 22
    DS-2BDP 2 2 615 816 266
    4 3 077 832 187
    8 4 065 434 221
    O-DSP 2 2 651 908 35
    4 3 114 024 29
    8 4 106 265 38
    下载: 导出CSV

    表  4  DSP和O-DSP预处理器计算四旋翼无人机迭代次数和矩阵元素数量对比

    Tab.  4  Comparison of the iteration numbers and element numbers of the DG solution with DSP and O-DSP for the four-rotor aircraft model

    预处理器迭代次数矩阵元素数百分比/%
    DSP140172 320 815100.0
    O-DSP16498 643 74357.2
    下载: 导出CSV
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  • 收稿日期:  2021-10-09
  • 录用日期:  2021-12-13
  • 网络出版日期:  2021-12-13

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