A custom edge-element FEM solver for eddy current NDT

In this paper, a custom finite element solver is included, which separates the solution into two steps. First the background field is calculated and stored for later use. Then the test object is meshed with scripts to sequence the elements, nodes, as well as vectorial edges and evaluate the elemental matrices for an arbitrary tetrahedral element. Finally, with the boundary conditions, use the Biot-Savart's law as well as Galerkin equations to obtain the magnetic vector potential of each edge and electric scalar potential of each node. Consequently, the electric field, eddy current and electric scalar potential of each point can be obtained. This treatment avoids the need for re-meshing and simulation results suggest the superiority of this method especially in NDT applications. Furthermore, this solver is suitable for both high frequency and low frequency conditions, which means that the solver can be applied to an extensive scale of skin depth. For instance, the surface of the object can be finely meshed for high frequency simulations in order to accurately describe the skin effect and the flow of surface eddy currents. Finally, the solver can be optimized for small flaws, which is because the elements around the flaw can be meshed more finely. Moreover, there is no need to mesh the target several times as the excitation field can be solved just once and applied a priori, which means only one meshing for the object is enough.