Nonlinear Acoustic Holography With Adaptive Sampling.

Area of Science:

• Acoustics
• Computational Physics
• Numerical Methods

Background:

• Accurate simulation of nonlinear ultrasound propagation is crucial for therapeutic and physical applications.
• Existing methods using uniform meshes are computationally expensive, especially for 3-D shock wave problems.
• High computational cost limits the widespread application of nonlinear ultrasound simulations.

Purpose of the Study:

• To develop an adaptive numerical algorithm for efficient nonlinear acoustic holography.
• To reduce the computational burden of simulating highly nonlinear ultrasound propagation.
• To enable rapid and efficient modeling of nonlinear high-intensity focused ultrasound (HIFU) wave propagation.

Main Methods:

• An adaptive algorithm that monitors harmonic content and adjusts discretization parameters at each propagation step.
• Incorporation of frequency-domain upsampling for forward propagation and downsampling for backward propagation.
• Active adaptation to the signal's nonlinearity level without requiring prior simulations.

Main Results:

• The adaptive algorithm achieves significant computational cost reduction for highly nonlinear 3-D problems.
• Demonstrated a nearly 50-fold speedup compared to uniform mesh implementations.
• Efficient local resolution of higher harmonics in areas of high nonlinearity.

Conclusions:

• The proposed adaptive algorithm offers a computationally efficient solution for nonlinear ultrasound simulations.
• This method facilitates faster and more accessible modeling of nonlinear acoustic phenomena, particularly for HIFU.
• Enables more rapid development and application of therapeutic and physical ultrasound technologies.