Abstract: The propagation of ultrasonic waves is generally studied in homogeneous media, although in certain industrial applications the conditions of propagation differ from the ideal conditions and the predicted results are not valid. This work is focused on the resolution of the Helmholtz equation for the study of the ultrasonic propagation in nonhomogeneous media. In this way, the solution of the Helmholtz equation has been obtained by means of Finite Differences, using a nonconventional scheme that substantially improves the results obtained with other techniques such as standard Finite Differences or Finite Elements. Moreover, it decreases the computational cost in the calculation of the coefficients about 85%. The effects on the ultrasonic echoes in propagation environments with high gradients of propagation's speed have been analyzed by simulation using the method presented, and the results obtained have been experimentally validated through a set of measurements.

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