A numerical method is presented for simulating the acoustic field in a smoothly inhomogeneous medium, based on the use of a three-dimensional wide-angle parabolic model and expansion of a modified propagator of the one-way wave equation into operator Fourier series. The problem of focusing an ultrasound beam generated by a transducer with parameters characteristic of noninvasive 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. The simulation results obtained using the developed method and the reference full-wave pseudospectral numerical “k-Wave” model are compared.
Konnova et al. (2025) studied this question.