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

作　　者：王晓丽[1] 罗先觉[1] 盛剑霓[1] 

机构地区：[1]西安交通大学电气工程学院,西安710049

出　　处：《西安交通大学学报》2007年第4期489-492,共4页Journal of Xi'an Jiaotong University

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(N2)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.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^2） 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 of 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.

关 键 词：快速多极算法 电磁场 数值计算 矢量磁位 载流导体 

分 类 号：TM153.1[电气工程—电工理论与新技术]