基于层次矩阵算法的低频曲面积分方程快速求解器

IF 6.7 1区计算机科学 Q1 Physics and Astronomy

Progress in Electromagnetics Research-Pier Pub Date : 2018-01-01 DOI:10.2528/PIER17111701

Ting Wan, Q. Dai, W. Chew

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引用次数: 6

摘要

提出了一种基于层次矩阵算法的低频曲面积分方程快速求解器。首先，引入增广电场积分方程(A-EFIE)公式，消除了传统增广电场积分方程的低频击穿;为了处理大规模问题，采用低频多电平快速多极算法(LF-MLFMA)构造a - efie系统矩阵的层次(H-)矩阵表示。此外，提出了一种再压缩方法，对LF-MLFMA生成的h矩阵进行进一步压缩。基于h矩阵的三角分解算法可以在几乎线性的计算复杂度和内存需求下执行，从而产生了一个快速的多个右边(RHS)问题的直接求解器，并为加快迭代求解器的收敛速度提供了一个很好的预条件。数值算例验证了该方法对各种低频问题分析的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fast Low-Frequency Surface Integral Equation Solver Based on Hierarchical Matrix Algorithm

A fast low-frequency surface integral equation solver based on hierarchical matrix algorithm is proposed. First, the augmented electric field integral equation (A-EFIE) formulation is introduced to eliminate the low-frequency breakdown of traditional EFIE. To deal with large-scale problems, the lowfrequency multilevel fast multipole algorithm (LF-MLFMA) is employed to construct a hierarchical (H-) matrix representation of the A-EFIE system matrix. Moreover, a recompression method is developed to further compress the H-matrix generated by LF-MLFMA. The H-matrix-based triangular factorization algorithm can be performed with almost linear computational complexity and memory requirement, which produces a fast direct solver for multiple right-hand-side (RHS) problems, and a good preconditioner to accelerate the convergence rate of an iterative solver. Numerical examples demonstrate the effectiveness of the proposed method for the analysis of various low-frequency problems.

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来源期刊

Progress in Electromagnetics Research-Pier 物理-电信学

CiteScore

7.20

自引率

3.00%

发文量

审稿时长

1.3 months

期刊介绍： Progress In Electromagnetics Research (PIER) publishes peer-reviewed original and comprehensive articles on all aspects of electromagnetic theory and applications. This is an open access, on-line journal PIER (E-ISSN 1559-8985). It has been first published as a monograph series on Electromagnetic Waves (ISSN 1070-4698) in 1989. It is freely available to all readers via the Internet.