Modeling ultrasonic wave fields using a Quasi-Monte Carlo method: Wave transmission through complicated interfaces

The sound fields generated by ultrasonic transducers can be modeled using the Quasi-Monte Carlo (QMC) method with a high level of accuracy and efficiency from Zhang [J. Acoust. Soc. Am. 149(1), 7-15 (2021)]. In this work, this method is extended to simulate transmitted wave fields through complicated interfaces. When a wave propagates in two-layer media, the vibrating waves over the interface radiated by the transducer can be treated as the source for generating waves in the second medium, thus, a nested-form Rayleigh integral expression can be used as a model equation for the transmitted wave calculation. When the QMC method is used to solve the nested integral, pseudo-random samples for constructing the transducer and the interface are sampled separately and the transmitted wave fields are obtained using the final sample mean. Numerical examples and results are presented when the wave transmits normally or obliquely through planar or curved interfaces. The results indicate that the high level of accuracy and efficiency remains when the QMC method is used to model the transmitted wave fields. One important advantage is that wave fields can be well simulated using the QMC method when the wave transmits through a complicated interface as long as the interface can be constructed using pseudo-random samples.