A FFT integral formulation using edge-elements for Eddy Current Testing

This paper presents a new approach for reducing the computational cost needed to solve the forward problem, i.e. the prediction of the measurements of a given ECT measurement system. This issue is mandatory in any inversion algorithm which, typically, requires the solution of a large number of direct problems. Integral formulations are attractive for ECT since they require the discretization of the conductive body only. However they also give rise to a full stiffness matrix whose inversion, typically obtained using direct solvers, has a computational cost that grows as O (n(3)) where n is the number of unknowns arising from the discretization. Iterative algorithms achieve a computational cost that is lower than direct solvers when the stiffness matrix is sparse. The approach proposed in this paper makes it possible to represent the stiffness matrix arising from an edge-elements based integral formulation, by means of the Fast Fourier Transform. This representation is achieved for bounded conductive domains meshed by a regular mesh and incurs a computational cost that grows as O(N log h).