Modeling of wave fields generated by ultrasonic transducers using a quasi-Monte Carlo method

The sound fields generated by ultrasonic transducers are modeled using the quasi-Monte Carlo (QMC) method, which is found to overcome the conflict between accuracy and efficiency that occurs in existing wave field calculation methods. The RI equation, which is frequently used as a model equation in ultrasonic field calculation, is used here as an exact method and for comparison purposes. In the QMC method, the judgment sampling method and Halton sequence are used for pseudo-random sampling from the sound source, and then the sound field distributions are found by solving the integral solution using the sample mean. Numerical examples and results are presented when modeling unfocused, focused, and steered and focused beam fields. The accuracy and efficiency of the QMC method are discussed by comparing the results obtained using different modeling methods. The results show that the proposed method has a high level of efficiency due to the nature of the QMC algorithm and a high level of accuracy because no approximation is required. In addition, wave fields can be modeled with the QMC method as long as sound sources can be effectively pseudo-randomly sampled, allowing the proposed method to be applied to various types of transducers.