An integral formulation in terms of a two-component electric vector potential (based on a tree-cotree decomposition of the mesh and edge-element basis functions) is used for the solution of the JSAEM Problem 6, which consists in the reconstruction of the shapes of various cracks from the impedance change of a pancake coil. The cracks are assumed to be infinitely thin. Superposition and reciprocity are employed in order to get more accurate impedance calculations. Woodbury's algorithm is used to speed up the solution process: the solution of each direct problem requires the inversion of a linear system whose order is less than the number of degrees of freedom related to the crack region. The inverse problem is formulated as the search of the mesh facets belonging to the crack. Due to the binary nature of the unknown, a genetic-like inversion algorithm is used for the determination of the unknown, a genetic-like inversion algorithm is used for the determination of the crack shape, minimizing the normalized root mean square error between the predictions and the measurements of the impedance variation.
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