低频薄集肤非理想导体电磁场的边界元解
Boundary Element Solution of Electromagnetic Fields for Non-Perfect Conductors at Low Frequencies and Thin Skin Depths
摘要：
本文提出了一种新的边界元法，用于求解薄趋肤深度近似中的涡流问题。假设散射体外的时谐磁场可以用准静态近似来描述。一个两项渐近展开相对于一个小参数表征趋肤深度推导出的磁场和电场的外部和内部的散射体，如果需要，可以扩展到高阶项。引入特殊的表面运算符（逆表面梯度）可以降低问题的复杂性。开发了一种计算该算子的方法。所得到的配方操作仅与标量，并需要计算的表面运营商是常见的边界元（矩量法）的拉普拉斯方程的解决方案。使用快速多极子方法可以加速该制剂。该方法比求解矢量麦克斯韦方程组要快得多。将所得解与Mie球散射解进行了比较，并对解的误差进行了研究。计算更复杂的形状不同的拓扑结构，包括用于测试中使用的磁场和电场笼也进行和讨论。
英文摘要：
A novel boundary element formulation for solving problems involving eddy currents in the thin skin depth approximation is developed. It is assumed that the time-harmonic magnetic field outside the scatterers can be described using the quasistatic approximation. A two-term asymptotic expansion with respect to a small parameter characterizing the skin depth is derived for the magnetic and electric fields outside and inside the scatterer, which can be extended to higher order terms if needed. The introduction of a special surface operator (the inverse surface gradient) allows the reduction of the problem complexity. A method to compute this operator is developed. The obtained formulation operates only with scalar quantities and requires computation of surface operators that are usual for boundary element (method of moments) solutions to the Laplace equation. The formulation can be accelerated using the fast multipole method. The method is much faster than solving the vector Maxwell equations. The obtained solutions are compared with the Mie solution for scattering from a sphere and the error of the solution is studied. Computations for much more complex shapes of different topologies, including for magnetic and electric field cages used in testing are also performed and discussed.
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