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首页> 外文期刊>IEEE Transactions on Magnetics >A Multi-Step Solution Algorithm for Maxwell Boundary Integral Equations Applied to Low-Frequency Electromagnetic Testing of Conductive Objects
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A Multi-Step Solution Algorithm for Maxwell Boundary Integral Equations Applied to Low-Frequency Electromagnetic Testing of Conductive Objects

机译：麦克斯韦边界积分方程的多步求解算法在导电物体低频电磁测试中的应用

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摘要

We consider the solution, using boundary elements (BEs), of the surface integral equation (SIE) system arising in electromagnetic testing of conducting bodies, with an emphasis on situations, such that o(1) ≤ (ωε0/σ)1/2 <; O(1) and L(ωσ μ0)1/2 = O(1), which includes in particular the case of eddy current (EC) testing and assuming Lω(ε0μ0)1/2 ≤ 2π, i.e., low-frequency conditions (L: diameter of conducting body). Earlier approaches for dielectric objects at low frequencies are not applicable in the present context. After showing that a simple normalization of the BE system significantly improves its conditioning, we propose a multi-step solution method based on block-successive over-relaxation iterations, which facilitates the use of direct solvers and converges within a few iterations for the considered range of physical parameters. This new treatment, albeit simple, allows to perform EC-type analyses using standard Maxwell SIE formulations, avoiding the adverse consequences of ill-conditioning for low frequencies and high conductivities. Its performance and limitations are studied on three numerical examples involving low frequencies and high conductivities.
机译：我们考虑使用边界元素（BEs），对导体进行电磁测试时产生的表面积分方程（SIE）系统的解决方案，重点是使o（1）≤（ωε0/σ）1/2 <; O（1）和L（ωσμ0）1/2 = O（1），其中特别包括涡流（EC）测试的情况并假设Lω（ε0μ0）1/2≤2π，即低频条件（L：导体的直径）。用于低频介电物体的较早方法在当前上下文中不适用。在证明BE系统的简单规范化可以显着改善其条件之后，我们提出了一种基于块成功的超松弛迭代的多步求解方法，该方法便于使用直接求解器并在考虑范围内的几次迭代中收敛物理参数。这种新方法尽管简单，却可以使用标准的Maxwell SIE配方进行EC型分析，从而避免了因低频和高电导率引起的不适情况的不利后果。在涉及低频和高电导率的三个数值示例上研究了其性能和局限性。

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