Full-wave nonlinear ultrasound simulation on distributed clusters using the k-space pseudospectral method

Abstract

Performing realistic simulations of the propagation of nonlinear ultrasound waves through biological tissue is a computationally difficult task. This is because the domain size of interest is often very large compared to the wavelengths of the high-frequency harmonics generated as the ultrasound waves progress. Recently, the k-space pseudospectral method has been applied to this problem to reduce the number of grid points required per wavelength compared to finite difference methods. However, the global nature of the spectral gradient calculations used in this method introduces new challenges for tackling large-scale problems. Here, we discuss three important issues for pseudospectral methods in the context of distributed computing. (1) Decomposing the domain to allow distribution across multiple nodes while still retaining the global accuracy of the spectral gradient calculations. (2) Using non-uniform grids to allow grid points to be clustered around highly nonlinear regions. (3) Avoiding aliasing errors due to modeling nonlinear wave propagation on a fixed grid. For each issue, solutions that retain the efficiency advantages of the pseudospectral method are discussed. We then present recent results of large-scale 3D nonlinear ultrasound simulations in heterogeneous and absorbing media running on both shared memory computers and distributed computer clusters.