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.

中文翻译：

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使用准蒙特卡罗方法对超声换能器产生的波场建模

使用准蒙特卡罗（QMC）方法对超声换能器产生的声场进行建模，发现该方法克服了现有波场计算方法中出现的精度与效率之间的冲突。在超声场计算中经常用作模型方程的RI方程在这里用作精确方法并用于比较目的。在QMC方法中，将判断采样方法和Halton序列用于从声源进行伪随机采样，然后通过使用样本均值求解积分解来找到声场分布。在对未聚焦，聚焦，转向和聚焦光束场进行建模时，将提供数值示例和结果。通过比较使用不同建模方法获得的结果，讨论了QMC方法的准确性和效率。结果表明，该方法由于QMC算法的性质而具有很高的效率，并且由于不需要逼近而具有很高的精度。此外，只要可以有效地伪随机采样声源，就可以使用QMC方法对波场进行建模，从而使该方法可以应用于各种类型的换能器。