A numerical method for calculating the acoustic field in a smoothly inhomogeneous medium, based on the use of a three-dimensional wide-angle parabolic model and the expansion of a modified propagator of the one-way wave equation into operator Fourier series, is presented. The problem of focusing of an ultrasound beam generated by a transducer with parameters characteristic of non-invasive ultrasound surgery devices is considered in a medium with smooth inhomogeneity, simulating the inhomogeneities of soft biological tissues. An optimization search for the best values of the free parameters of the modified propagator has been conducted to achieve the smallest approximation error of the propagator using a Fourier series with a finite number of harmonics. A comparison of the simulation results obtained using the developed method and the reference full-wave pseudo-spectral numerical model “k-Wave” has been carried out.
E.O. Konnova (2025) studied this question.