A Multi-Step Solution Algorithm for Maxwell Boundary Integral Equations Applied to Low-Frequency Electromagnetic Testing of Conductive Objects

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) ≤ (ωε
₀
/σ)
^1/2
<; O(1) and L(ωσ μ
₀
)
^1/2
= O(1), which includes in particular the case of eddy current (EC) testing and assuming Lω(ε
₀
μ
₀
)
^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.