Wise Elliott S, Cox B T, Jaros Jiri, Treeby Bradley E
Department of Medical Physics and Biomedical Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Centre of Excellence IT4Innovations, Faculty of Information Technology, Brno University of Technology, Brno, Czech Republic.
J Acoust Soc Am. 2019 Jul;146(1):278. doi: 10.1121/1.5116132.
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.
准确表示声源分布是超声模拟的重要组成部分。对于基于网格的配置方法而言，当此类分布与网格点不一致时，例如当声源是嵌入三维域中的二维曲面时，这具有挑战性。通常，靠近声源表面的网格点被定义为源点，但这可能会导致“阶梯状”以及所得声场中的重大误差。本文描述了一种在傅里叶配置方法中准确表示任意源分布的技术。该方法通过对连续源分布应用离散的带限卷积算子来工作，之后可以生成源网格权重。这使得可以在网格上定义任意形状的源，例如聚焦碗和圆形活塞，而不会产生阶梯状误差。通过对一系列超声源的模拟来检验该技术，与解析解的比较显示出优异的精度和收敛率。还讨论了该技术的扩展，包括应用于初值问题、分布式传感器和移动源。
