Unified Regularization of 2D Singular Integrals for Axisymmetric Galerkin BEM in Eddy-Current Evaluation

TL;DR

This paper introduces a unified regularization approach for 2D singular integrals in an axisymmetric Galerkin BEM, improving accuracy and efficiency in eddy-current nondestructive evaluation of axisymmetric objects.

Contribution

It develops a unified regularization framework for 2D singular integrals in Galerkin BEM, simplifying numerical implementation and enhancing robustness for axisymmetric eddy-current modeling.

Findings

High accuracy across broad frequency ranges

Efficient computation for various geometries

Stable regularization of singular integrals

Abstract

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 across broad frequency ranges 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.