Modeling for ultrasonic testing is an important tool in industrial sectors concerned with advanced inspection methods. A significant amount of effort has been directed to building hybrid methods, which try to encompass advantages of both asymptotic and numerical methods. In our work, we consider a hybrid coupling method based upon reciprocity relations. By deriving specific formulations for the incident and diffracted fields, we apply this strategy to the case of surface and near-surface flaws. We illustrate this coupling strategy in some canonical 2D and 3D ultrasonic testing configurations.

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The transient spectral element method (SEM) is a specific high order finite element method that is particularly accurate and fast with a low memory footprint, hence enabling 3D ultrasonic testing simulations on a standard PC. However, particular care in its settings and hybridization with a semi-analytical solution remains a major challenge when seeking for both practicality and performance. A natural hybrid strategy consists of coupling a field calculated by ray tracing in the defect-free object to a SEM subdomain wherein the perturbation is enclosed, then synthesizing the signal with a reciprocity argument. The difficulty is to define the suited coupling strategy when the flaw response interacts with the back wall. In a highly heterogeneous medium, it may even become necessary to widen the numerical domain to the entire thickness of the inspected object and, therefore, to ensure the performance of the SEM through a custom discretization strategy. Here we present different customized uses of the SEM for practical ultrasonic inspection applications and discuss how they complement the ray tracing solution.