Unified Regularization of 2D Singular Integrals for Axisymmetric Galerkin BEM in Eddy-Current Evaluation
For researchers in computational electromagnetics, this work provides a robust and efficient BEM framework for axisymmetric eddy-current nondestructive evaluation, though it is an incremental improvement over existing regularization techniques.
The paper presents a unified regularization framework for 2D singular integrals in axisymmetric Galerkin BEM, enabling straightforward numerical quadrature without case-by-case analytical extraction. The method achieves high accuracy and efficiency for eddy-current evaluation on cylindrical, conical, and spherical shells.
This paper presents an axisymmetric Galerkin boundary element method (BEM) for modeling eddy-current interactions between excitation coils and conductive objects. The formulation derives boundary integral equations from the Stratton-Chu representation for the azimuthal component of the vector potential in both air and conductive regions. The central contribution is a unified regularization framework for the two-dimensional (2D) singular integrals arising in Galerkin BEM. This framework handles both logarithmic and Cauchy singularities through a common set of integral transformations, eliminating the need for case-by-case analytical singularity extraction and enabling straightforward numerical quadrature. The regularization and quadrature stability are proved and verified numerically. The method is validated on several representative axisymmetric geometries, including cylindrical, conical, and spherical shells. Numerical experiments demonstrate consistently high accuracy and computational efficiency over the tested frequency interval and coil lift-off distances. The results confirm that the proposed axisymmetric Galerkin BEM, combined with the integral transformation technique, provides a robust and efficient framework for axisymmetric eddy-current nondestructive evaluation.