Efficient 3D Eddy Current NDE Model Based on Finite Element Boundary Integral Method

Abstract

In this paper, the finite element boundary integral (FEBI) method, for the first time, is applied to solve the 3-D arbitrary shaped eddy current nondestructive testing (ECNDT) problems. FEBI alleviates the extra computational costs of truncation region in finite element method (FEM) and the difficulty in derivation of the Green’s function in boundary element method (BEM). The boundary integral equation (BIE) selected is the combined field integral equation (CFIE) in the TENH (tangential testing of electric field and normal testing of magnetic field) form, which shows better convergence compared with other forms. In BEM, the equivalent electric and magnetic surface currents are expanded by Rao-Wilton-Glisson (RWG) vector basis functions. While in FEM, the electric field and electric surface current are expanded by tetrahedron-based edge elements and RWG vector basis functions, respectively. The discretized matrix achieved by BEM and FEM is coupled by the field continuity conditions. For ECNDT problems, inhomogeneous meshes are required due to the small size of cracks or slots than the whole solution domain. It makes the convergence for solving the coupled matrix formed by the sparse matrix generated by FEM and the dense matrix produced by BEM worse, thus, precondition is required for FEBI solution in iterative method, which complicates the solving procedure. To alleviate the cumbersome solving process, the inward-looking formulation method is studied to work as precondition by solving the inverse of FEM matrix directly, and then the coupled discretized matrix is solved iteratively. By evaluating several ECNDT benchmark cases involving the cylindrical flaws and surface slots, the predicted impedance changes achieved by FEBI method are compared with those by semi-analytical method, FEM, and experiment which demonstrates that the proposed FEBI method based forward solver can simulate the ECNDT problems both accurately and efficiently.