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Reliable numerical simulation techniques represent a very valuable tool for analysis. For this purpose we investigated the applicability of the local interaction simulation approach (LISA) to the study of the propagation of Lamb waves in complex structures. The LISA allows very fast and flexible simulations, especially in conjunction with parallel processing, and it is particularly useful for complex (heterogeneous, anisotropic, attenuative, and/or nonlinear) media. We present simulations performed on a glass fiber reinforced plate, initially undamaged and then with a hole passing through its thickness (passing-by hole). In order to give a validation of the method, the results are compared with experimental data. Then we analyze the interaction of Lamb waves with notches, delaminations, and complex structures. In the first case the discontinuity due to a notch generates mode conversion, which may be used to predict the defect shape and size. In the case of a single delamination, the most striking "signature" is a time-shift delay, which may be observed in the temporal evolution of the signal recorded by a receiver. We also present some results obtained on a geometrically complex structure. Due to the inherent discontinuities, a wealth of propagation mechanisms are observed, which can be exploited for the purpose of quantitative nondestructive evaluation (NDE).