  Model-based treatment planning and exposimetry for high-intensity focused
ultrasound (HIFU) requires the numerical simulation of nonlinear ultrasound
propagation through heterogeneous and absorbing media. This is a
computationally demanding problem due to the large distances travelled by the
ultrasound waves relative to the wavelength of the highest frequency harmonic.
Here, the k-space pseudospectral method is used to solve a set of coupled
partial differential equations equivalent to a generalised Westervelt equation.
The model is implemented in C++ and parallelised using the message passing
interface (MPI) for solving large-scale problems on distributed clusters. The
domain is partitioned using a 1D slab decomposition, and global communication
is performed using a sparse communication pattern. Operations in the spatial
frequency domain are performed in transposed space to reduce the communication
burden imposed by the 3D fast Fourier transform. The performance of the model
is evaluated using grid sizes up to 4096 x 2048 x 2048 grid points distributed
over a cluster using up to 1024 compute cores. Given the global nature of the
gradient calculation, the model shows good strong scaling behaviour, with a
speed-up of 1.7x whenever the number of cores is doubled. This means
large-scale simulations can be distributed across high numbers of cores on a
cluster to minimise execution times with a relatively small computational
overhead. The efficacy of the model is demonstrated by simulating the
ultrasound beam pattern for a HIFU sonication of the kidney.
