Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods

The Journal of the Acoustical Society of America
Elliott S WiseBradley E Treeby

Abstract

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.

References

May 24, 2001·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·T D MastR C Waag
Feb 8, 2002·The Journal of the Acoustical Society of America·Makoto TabeiRobert C Waag
May 13, 2010·Journal of Biomedical Optics·Bradley E Treeby, B T Cox
Aug 20, 2016·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·Eleanor MartinBradley E Treeby
Apr 5, 2017·The Journal of the Acoustical Society of America·James L B RobertsonBradley E Treeby
Feb 3, 2018·The Journal of the Acoustical Society of America·Bradley E TreebyB T Cox

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Citations

Jan 1, 2021·The Journal of the Acoustical Society of America·Stefan Bilbao, Jens Ahrens
Nov 4, 2020·The Journal of the Acoustical Society of America·Bradley E TreebyB T Cox
May 5, 2021·The Journal of the Acoustical Society of America·Esra Aytac-KipergilErwin J Alles

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