A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons

Area of Science:

• Acoustics
• Numerical Methods
• Signal Processing

Background:

• Calculating near-field acoustic pressure from apodized rectangular sources is computationally intensive.
• Existing methods like the Rayleigh-Sommerfeld integral and FIELD II program can be slow for complex pressure field analysis.
• The fast near-field method (FNM) has shown promise for uniformly excited pistons but requires extension for apodized sources.

Purpose of the Study:

• To develop and validate an analytical two-dimensional (2D) integral expression for fast near-field pressure calculations from apodized rectangular pistons.
• To extend the fast near-field method (FNM) to handle apodization, improving computational efficiency and accuracy.
• To provide a method that eliminates numerical singularities present in conventional models.

Main Methods:

• Derived analytical 2D integral expressions by extending the FNM for uniformly excited pistons.
• Subdivided the apodized rectangular piston into smaller rectangles and applied superposition.
• Utilized integration by parts and exchanged summation variables to obtain the 2D apodized FNM expression.
• Incorporated a simplified time-space decomposition method to further reduce transient calculation times.

Main Results:

• The 2D apodized FNM significantly reduces computation time compared to the Rayleigh-Sommerfeld integral and FIELD II program.
• For time-harmonic calculations, speedups of up to 155 times were observed at a 0.01 normalized root mean square error (NRMSE).
• For transient calculations, speedups of up to 24 times were achieved at a 0.01 NRMSE.
• The method effectively eliminates numerical singularities, ensuring accurate pressure field modeling.

Conclusions:

• The 2D apodized FNM is an efficient and accurate method for calculating near-field pressures from apodized rectangular pistons.
• This technique is ideal for applications requiring fast pressure calculations and serves as an accurate reference in the near-field region.
• The developed method offers substantial computational advantages over existing numerical approaches.