Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods.

Area of Science:

• Acoustics and Ultrasound Simulation
• Computational Physics
• Numerical Methods

Background:

• Accurate representation of acoustic source distributions is crucial for ultrasound simulations.
• Grid-based collocation methods struggle with sources not aligned with grid points, leading to staircasing errors.
• Curved or arbitrary 2D sources in 3D domains present significant challenges for existing methods.

Purpose of the Study:

• To develop a technique for accurately representing arbitrary acoustic source distributions in Fourier collocation methods.
• To overcome limitations of grid-based methods in handling non-coincident source geometries.
• To eliminate staircasing errors and improve accuracy in simulated acoustic fields.

Main Methods:

• Applied a discrete, band-limiting convolution operator to continuous source distributions.
• Generated source grid weights from the convolved continuous distribution.
• Validated the technique through simulations of various ultrasound sources, including focused bowls and circular pistons.

Main Results:

• The proposed method accurately represents arbitrarily shaped acoustic sources on the grid.
• Eliminated staircasing errors, significantly improving the fidelity of simulated acoustic fields.
• Simulations demonstrated excellent accuracy and convergence rates when compared to analytical solutions.

Conclusions:

• The developed technique provides a robust solution for accurately embedding arbitrary acoustic sources in Fourier collocation ultrasound simulations.
• The method shows high accuracy and convergence, outperforming traditional approaches.
• Potential extensions include applications to initial value problems, distributed sensors, and moving sources.