A novel computational technique is presented in this thesis which improves Finite Element Method (FEM) in solving both direct and inverse problems for nondestructive evaluation (NDE) applications. Subregion method is used to select and isolate area of interest that design parameters need to be updated from entire domain. An elastic mesh generator is developed in this thesis to generate optimal meshes in the selected area to save connectivity matrix until having the most accurate design parameters. Using Subregion FEM (SFEM) in solving inverse problems will help in minimizing processing time and memory usage in addition of reducing solution complexity. An Eddy Current Testing (ECT) problem of detecting and characterizing the location and shape of surface and subsurface defects by separating the defects from entire domain is investigated to validate the presented SFEM algorithm. The elastic mesh generator is derived to update the pre-selected design parameters of the defect in each iteration. This novel meshing technique adds the specialty of using subregion method in inverse problems, where, elements and nodes numbering is saved inside and outside the defect region. Both of Genetic Algorithm (GA) and Simulated Annealing (SA) based optimization techniques are developed to get the accurate defect parameters. A parametric study of those defect parameters including size, depth and position is also presented to study the defect response problems by comparing with classical forward formulation. The presented SFEM results have been verified computationally using conventional FEM and COMSOL Multiphysics. Excellent results of signal agreement and processing time minimization with a reduction of 90% with an accuracy of 98% have been achieved. In addition, the presented SFEM algorithm has been verified experimentally using Aluminum (T6061-T6) and steel samples. The experiments are carried out for the first time using an elongated excitation coil in a fixed position mounted on the top of the sample and Tunneling Magnetoresistive (TMR) sensor to measure magnetic field. The measured magnetic fields were used as input to the inverse SFEM solver and machined artificial defects were characterized with excellent accuracy.
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