A Mixed Spatial–Spectral Eddy-Current Formulation for Pieces With One Symmetry Axis

A combination of the mesh-based finite integration technique with a modal expansion is proposed for the solution of the eddy-current induction problem in geometries involving workpieces with translational or rotational symmetry and an arbitrary 3-D current excitation. The solution is expanded in a series of modes along the symmetry axis, and thus, the reduced Helmholtz equation is discretized and solved independently for each mode in the transversal plane. Finally, the impedance variation of the eddy-current probe is evaluated by means of the reciprocity theorem. The main advantage of the proposed decomposition relies on the use of a 2-D instead of the 3-D grid with the consequent reduction of the numerical noise and the smaller size of the resulting linear system, which allows the simultaneous treatment of different sources.