A curvature-profile-driven semi-analytical boundary integral method for magnetic flux leakage analysis of Euler-spiral defect boundaries

Magnetic flux leakage (MFL) analysis of defects with complex boundaries is often constrained by the geometric assumptions of analytical and semi-analytical forward models, which mainly describe straight, polygonal, or circular-arc boundaries. This study proposes a curvature-profile-driven semi-analytical boundary integral method for MFL fields generated by Euler-spiral defect boundaries. The boundary is specified by a linearly varying curvature profile and reconstructed through Fresnel integrals, yielding continuous coordinates and outward normal vectors. The equivalent line magnetic charge is obtained from the projection of uniform magnetization onto the local boundary normal, and the external leakage field is evaluated by a one-dimensional boundary integral. The model therefore links curvature profile, boundary geometry, source distribution, observation-line response, and response descriptors in a direct computational chain. Equivalent circular-arc comparisons quantify the error introduced by constant-curvature approximation, while FEM verification is organized through total-field inspection, Euler-minus-reference difference fields, and regularized semi-analytical/FEM comparison. Convergence, repeated-run timing, accuracy-cost trade-off, and parameter-sweep analyses are further used to assess numerical applicability. The boundary integral reaches descriptor-level errors on the order of 10 −7 at N s = 801 and a median scan-line calculation time of 2.240 ms. The proposed method provides an interpretable, mesh-reduced framework for curvature-sensitive MFL forward calculation, rapid parameter sweeping, and defect-boundary response descriptor generation.