基于高阶M-HODLR算法的复合结构目标电磁响应高效求解

任仪; 张扬; 李琎

doi:10.12263/DZXB.20251179

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基于高阶M-HODLR算法的复合结构目标电磁响应高效求解

学术论文 | 更新时间：2026-05-28

- 基于高阶M-HODLR算法的复合结构目标电磁响应高效求解
- Efficient Solution of Electromagnetic Response for Composite Structures Based on High-Order M-HODLR Algorithm
- 电子学报 2026年54卷第2期页码：765-773
- 作者机构：
  
  1.西安电子科技大学电子工程学院，陕西西安 710071
  2.北京华大九天科技有限公司，北京100102
- 作者简介：
  
  [ "任仪男，1982年12月出生于安徽省巢湖市。现为西安电子科技大学电子工程学院教授、博士生导师。主要研究方向为计算电磁学、阵列天线设计与分析。E-mail: yren@xidian.edu.cn" ]
  [ "张扬男，1981年10月出生于四川省成都市。现为西安电子科技大学电子工程学院工程师。主要研究方向为计算流体力学、低速风洞试验、低速风洞设计等。在国内外期刊发表学术论文十多篇。E-mail: zhangy29v@126.com" ]
  [ "李琎男，1980年4月出生于陕西省西安市。现为北京华大九天科技有限公司高级产品经理。主要研究方向为射频技术、雷达系统、卫星通信及多物理场仿真工具研发。E-mail: lijin1@empyrean.com.cn" ]
- 基金信息：
  
  国家自然科学基金(62271365;U2241203)
- DOI：10.12263/DZXB.20251179
  中图分类号： TP391.4;
- 收稿：2025-01-27，
  
  录用：2026-02-12，
  
  纸质出版：2026-02-25
- 稿件说明：
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任仪, 张扬, 李琎. 基于高阶M-HODLR算法的复合结构目标电磁响应高效求解[J]. 电子学报, 2026, 54(02): 765-773.

REN Yi, ZHANG Yang, LI Jin. Efficient Solution of Electromagnetic Response for Composite Structures Based on High-Order M-HODLR Algorithm[J]. Acta Electronica Sinica, 2026, 54(02): 765-773.
任仪, 张扬, 李琎. 基于高阶M-HODLR算法的复合结构目标电磁响应高效求解[J]. 电子学报, 2026, 54(02): 765-773. DOI：10.12263/DZXB.20251179

REN Yi, ZHANG Yang, LI Jin. Efficient Solution of Electromagnetic Response for Composite Structures Based on High-Order M-HODLR Algorithm[J]. Acta Electronica Sinica, 2026, 54(02): 765-773. DOI：10.12263/DZXB.20251179

摘要

本文针对金属介质复合结构目标多右端项电磁响应求解效率低下的问题，提出一种高效稳定的直接求解器算法。首先，基于M-HODLR架构，研究适用于金属介质复合结构的基函数分组与M-HODLR算法构建策略。随后，将高阶电磁建模引入所提金属介质复合结构的M-HODLR算法中，在保证高精度求解的同时，显著减少未知量，有效提高算法效率。最后，针对高阶电磁建模中的基函数分组策略问题，研究了基于高阶基函数簇的分组策略，并将不同层间的基函数进行顺序重排，结合聚合操作，实现了M-HODLR中金属介质复合问题的向上聚合。所提高阶电磁建模的M-HODLR算法极大地加速了金属介质复合结构目标电磁响应的求解效率。理论分析与数值算例验证了本文所提方法的有效性。

Abstract

This paper addresses the issue of low computational efficiency in solving electromagnetic responses for multiple right-hand sides in metal-dielectric composite structures by proposing an efficient and stable direct solver algorithm. First

based on the M-HODLR framework

strategies for grouping basis functions and constructing the M-HODLR algorithm suitable for metal-dielectric composite structures are investigated. Subsequently

high-order electromagnetic modeling is integrated into the proposed M-HODLR algorithm for such structures

significantly reducing the number of unknowns while ensuring high solution accuracy

thereby effectively improving computational efficiency. Finally

to address the basis function grouping issue in high-order electromagnetic modeling

a grouping strategy based on clusters of high-order basis functions is developed. By reordering the basis functions across different layers and incorporating aggregation operations

upward aggregation for metal-dielectric composite problems within the M-HODLR framework is achieved. The proposed M-HODLR algorithm with high-order electromagnetic modeling significantly accelerates the solution of electromagnetic responses for metal-dielectric composite structures. Theoretical analysis and numerical examples validate the effectiveness of the proposed method.

关键词

Keywords

references

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