求解三维准静态矢量磁位的快速多极方法

王晓丽; 罗先觉; 盛剑霓

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求解三维准静态矢量磁位的快速多极方法

专题研究 | 更新时间：2025-12-08

- 求解三维准静态矢量磁位的快速多极方法
- Calculating Magnetic Vector Potential in 3-D Electromagnetoquasistatic Field with Fast Multipole Method
- 西安交通大学学报 2007年41卷第4期页码：489-492
- 作者机构：
  
  西安交通大学电气工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  中图分类号： TM153.1
- 网络首发：2007-04-10，
  
  纸质出版：2007
- 稿件说明：
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王晓丽, 罗先觉, 盛剑霓. 求解三维准静态矢量磁位的快速多极方法[J]. 西安交通大学学报, 2007,41(4):489-492.

王晓丽, 罗先觉, 盛剑霓. Calculating Magnetic Vector Potential in 3-D Electromagnetoquasistatic Field with Fast Multipole Method[J]. 2007, 41(4): 489-492.
王晓丽, 罗先觉, 盛剑霓. 求解三维准静态矢量磁位的快速多极方法[J]. 西安交通大学学报, 2007,41(4):489-492. DOI：

王晓丽, 罗先觉, 盛剑霓. Calculating Magnetic Vector Potential in 3-D Electromagnetoquasistatic Field with Fast Multipole Method[J]. 2007, 41(4): 489-492. DOI：

摘要

将快速多极算法(FMM)应用于三维准静态电磁场矢量磁位的求解

首先根据计算精度的要求把连续分布的场源进行离散化处理

然后通过静电类比分析

将求解三维准静态矢量磁位的问题转化为多体问题

进而利用快速多极方法来计算三维空间中载流导体产生的矢量磁位

可以将计算量由O(N

)降低为O(N)次运算

大大提高了计算速度.算例的计算结果表明

当取剖分体积单元的边长等于0.25倍透入深度时

采用FMM方法计算的电流密度不均匀分布载流导体在其自身所在空间的磁矢位与精确解的相对误差小于0.005

而其在自身所在空间以外的磁矢位的FMM计算结果

具有更高的精度.经过积分方程离散和静电模拟分析

应用FMM算法可正确地计算三维空间载流导体的矢量磁位

计算误差可通过剖分密度进行控制.提出的方法扩展了FMM算法在准静态矢量磁位数值计算领域中的应用

为芯片上互连电感参数的计算奠定了基础.

Abstract

The fast multipole method(FMM)is introduced to solve the magnetic vector potential in 3-D electromagnetoquasistatic field. The continually distributed source is discretized according to the required accuracy

the electromagnetoquasistatic integral function is discretized by electrostatic analogy analysis

and then the magnetic vector potential created by current-carry conductors in 3-D space is transformed into N-body problem which can be calculated by FMM.Thus the computation is reduced from O(N

) to O(N) and the error can be flexibly controlled by division density. The numeral results demonstrate that with division length of volume cell density as a quarter o

f skin depth

the relative error of the FMM result of the magnetic vector potential of the redistributed current-carry conductor in its own space gets less than 0.005

and the result of magnetic vector potential outside the conductor is more accurate. The fast multipole method for calculating the magnetic vector potential in 3-D electromagnetoquasistatic field can be extended to evaluate the on-chip interconnect inductance parameters.

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references

Belenguer A, Elsteban H,Boria V E,et al. Computation of the scattering of electrically large 2-D objects using FMM with TE/sup z/incidence [C]∥Antennas and Propagation Society International Symposium.Los Angeles: IEEE, 2005: 455-458.

Wei X C,Li E P,Zhang Y J. Efficient solution to the large scattering and radiation problem using the improved finite-element fast multipole method [J].IEEE Transactions on Magnetics,2005, 41(5):1684-1687.

Zhao Zhiqin, Li Ling, Smith J. Analysis of scattering from very large three-dimensional rough surfaces using MLFMM and ray-based analyses [J].IEEE Antennas and Propagation Magazine, 2005, 47(3):20-30.

Takahashi Y, Fujishima Y, Wakao S. Large-scale analysis of surface charge in eddy-current problems by the fast multipole method [J]. IEEE Transactions on Magnetics, 2005, 41(5): 1700-1703.

Takahashi Y, Wakao S. Large-scale analysis of eddy-current problems by the hybrid finite element-boundary element method combined with the fast multipole method [J]. IEEE Transactions on Magnetics, 2006,42(4):671-674.

Rubinacci G,Tamburrino A,Ventre S,et al. A fast 3-D multipole method for eddy-current computation [J]. IEEE Transactions on Magnetics, 2004,40(2):1290-1293.

Wu Fang,Zhang Yaojiang. Parallel multilevel fast multipole method for solving large-scale problems [J]. IEEE Antennas and Propagation Magazine,2005,47(4): 110-118.

Greengard L. The rapid evaluation of potential fields in particle systems [M]. Cambridge:MIT Press, 1988: 45-90.

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