The Use of Graphic Accelerators in Simulation of Nonlinear Ultrasonic Beams with Shock Fronts on the Basis of the Westerwelt Equation

The problem of accelerating the algorithm for calculating nonlinear effects is considered, when modeling high-intensity ultrasonic beams based on the one-way Westervelt equation. When constructing a numerical solution for strongly distorted waves with shock fronts, it is necessary to take into account large number of harmonics (up to 1000) on spatial grids with a matrix size of the order of 10 000 by 10 000, which requires the processing of large amounts of data and a long calculation time. In this paper, the implementation of the nonlinearity operator is carried out in a time representation using a Godunov-type shock-catching scheme, which allows modeling nonlinear waves with shock fronts with a small (3) number of grid nodes on the shock front. The paper compares the efficiency of using this method when it is implemented on central processing units (CPUs) and graphics processing units (GPUs) in comparison with the spectral method implemented earlier for quasi-linear wave propagation. An analysis is made of the speed of algorithm execution on the CPU and GPU, depending on the size of the input data arrays.