Electromagnetic Analysis of Eddy Current Testing With Kelvin Transformation

The idea of the Kelvin transformation is extended to analyze the eddy current testing (ECT). The Kelvin transformation was originally proposed to solve the Poisson equation on the entire unbounded domain. When it was first applied to electromagnetic quasi-static problems, it was assumed that the analysis domain is surrounded only by air and nothing is inside the exterior domain. The analysis domain is truncated by a circular boundary in two dimensions and spherical in three dimensions, and another circular/spherical domain for emulating the exterior domain is connected through unknown equivalent boundary conditions. In this article, the Kelvin transformation is reformulated to derive the conductivity and permeability in the exterior domain, which conserves the conformal symmetry of Maxwell’s equations. Utilizing the derived conductivity and permeability, the materials can be both in the interior and exterior domains or even across the truncated boundaries. Some numerical examples are demonstrated to validate the proposed method. As an application of the proposed method, the electromagnetic analysis of the ECT model is performed.