Abstract
The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation serves as today’s workhorse for the modeling and simulation of high‐intensity focused ultrasound. This approximation of the full nonlinear wave equation allows serial algorithms to compute the pressure distribution produced by circular transducers usually in several hours on a modern workstation. However, more complicated transducer geometries preclude axisymmetric modeling, and extending into the third spatial dimension requires significantly more computational power, making serial algorithms intractable. This presentation details a parallel implementation of a combination time and frequency domain algorithm for rapid solution of the KZK equation. A split step method is used in which the linear terms in KZK are solved in the frequency domain and the nonlinear term is solved in the time domain. In the frequency domain, each harmonic may be computed independently, so this task is distributed over the available processors. In the time domain, the transverse spatial domain may be partitioned and distributed for independent solution of the nonlinear term. Near‐linear scaling (acceleration vs number of processors) using this algorithm is demonstrated.
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