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A parallelizable direct solution of integral equation methods for electromagnetic analysis

机译：电磁分析积分方程方法的可并行直接解

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摘要

A parallelizable direct solution of integral equation methods is proposed for electromagnetic scattering analysis in low to intermediate frequency regime. There are mainly two parts of the proposed direct solution: forward decomposition and backward substitution. For the forward decomposition, the dense impedance matrix is decomposed of the product of several block diagonal matrices implicitly, which is shown to be O(Nlog~2N) for both memory and CPU time cost. The final solutions are obtained with several matrix vector products (MVPs) in the part of backward substitution with O(Nlog~2N) complexity as well. Both forward decomposition and backward substitution can be parallelized because of the group independence. Furthermore, an effective preconditioner with a reasonable selection criterion of the diagonal blocks region is proposed to accelerate the convergence of the iterative solver. The proposed solution is independent of the Green's function, and it is suitable for all the integral equation methods. Without loss of generality, the solution is proposed to solve the electric field integral equation (EFIE) in this work. Numerical tests demonstrate the effectiveness of the proposed solution for the electromagnetic analysis, especially for multiscale structures.
机译：提出了一种积分方程方法的可并行直接解，用于低频到中频范围的电磁散射分析。提议的直接解决方案主要有两个部分：正向分解和反向替换。对于正向分解，密集阻抗矩阵隐式分解为多个块对角矩阵的乘积，对于内存和CPU时间成本，该矩阵均显示为O（Nlog〜2N）。最终的解决方案是使用几种矩阵向量乘积（MVP）获得的，同时具有O（Nlog〜2N）复杂度的向后替换部分。由于组独立性，前向分解和后向取代都可以并行化。此外，提出了一种有效的预处理器，其对角线块区域具有合理的选择准则，以加快迭代求解器的收敛速度。所提出的解决方案与格林函数无关，并且适用于所有积分方程方法。在不失一般性的前提下，本文提出了一种解决方案，以解决电场积分方程（EFIE）。数值测试证明了所提出的解决方案对电磁分析的有效性，尤其是对于多尺度结构。

著录项

  • 来源
    《Engineering analysis with boundary elements》 |2017年第12期|158-164|共7页
  • 作者

    Kechen Wang; Mengmeng Li; Dazhi Ding; Rushan Chen;

  • 作者单位

    Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, China;

    Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, China;

    Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, China;

    Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Hierarchical fast direct solver; Integral equation; Multiscale problems;

    机译：分层快速直接求解器;积分方程多尺度问题;

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