An inverse problem in nondestructive evaluation of spot-welds

In this work, we investigate the problem of determining a heat source at the bottom of a plate from thermal measurements obtained at the top. This problem arises in a novel nondestructive evaluation technique for assessing the quality of a spot-weld. We devise a simple algorithm that takes thermal images and produces estimates of the heat source. The computational approach, which uses Tikhonov regularization, is shown to be convergent. Numerical examples illustrate the behaviour of the inversion algorithm.