Publication Details
Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods
Fourier collocation method, acoustic source, acoustic sensor, staircaisng
Accurately representing acoustic source distributions is an important part of
ultrasound simulation. This is challenging for grid-based collocation methods
when such distributions do not coincide with the grid points, for instance when
the source is a curved, two-dimensional surface embedded in a three-dimensional
domain. Typically, grid points close to the source surface are defined as source
points, but this can result in "staircasing" and substantial errors in the
resulting acoustic fields. This paper describes a technique for accurately
representing arbitrary source distributions within Fourier collocation methods.
The method works by applying a discrete, band-limiting convolution operator to
the continuous source distribution, after which source grid weights can be
generated. This allows arbitrarily shaped sources, for example, focused bowls and
circular pistons, to be defined on the grid without staircasing errors. The
technique is examined through simulations of a range of ultrasound sources, and
comparisons with analytical solutions show excellent accuracy and convergence
rates. Extensions of the technique are also discussed, including application to
initial value problems, distributed sensors, and moving sources.
@article{BUT158066,
author="Elliott {Wise} and Ben {Cox} and Jiří {Jaroš} and Bradley {Treeby}",
title="Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods",
journal="Journal of the Acoustical Society of America",
year="2019",
volume="146",
number="1",
pages="278--288",
doi="10.1121/1.5116132",
issn="1520-8524",
url="https://asa.scitation.org/doi/10.1121/1.5116132"
}