A filtered convolution method for the numerical evaluation of very large‐scale ultrasound problems

The pulsed ultrasound field in nonlinear biomedical tissue may be computed by the recurrent evaluation of the field of a distributed contrast source in a linear homogeneous background medium. For human organs, the computational domain may easily measure hundreds of wavelengths or periods in each spatiotemporal dimension. Even with today’s supercomputers, the evaluation of the transient field from the contrast sources in these very large inhomogeneous domains is a big challenge, and is only feasible if the applied numerical method is extremely efficient in terms of memory usage and computational speed. Using a Green’s function method, the critical operation is a spatiotemporal convolution over the entire computational domain. It is shown how a systematic filtering and windowing of the involved functions yield accurate numerical convolutions with a discretization approaching the Nyquist limit of two points per wavelength or period of the highest frequency. This minimizes the storage requirement. Application...