A simple method avoiding non-uniqueness in the boundary element method for acoustic scattering problem.

Area of Science:

• Acoustics and Computational Mechanics
• Numerical Methods for Wave Propagation

Background:

• The boundary element method (BEM) is a standard for sound field analysis but suffers from non-uniqueness issues in exterior domains.
• Existing solutions to BEM non-uniqueness are often complex and not readily applicable to BEM implementations.

Purpose of the Study:

• To introduce a simple and effective method, the ICA-Ring (inner cavity ringing) method, to overcome BEM non-uniqueness problems.
• To demonstrate the applicability and efficacy of the ICA-Ring method in both single and plural domain BEM analyses.

Main Methods:

• The ICA-Ring method involves hollowing a scatterer into a shell, effectively shifting its eigenfrequencies to a higher range.
• The study explains the non-uniqueness mechanism in plural domains and justifies the ICA-Ring method's application in such scenarios.
• The method was applied to BEM simulations of a cylinder in two-dimensional free space.

Main Results:

• The ICA-Ring method successfully eliminated calculational errors in BEM simulations within the 1-6000 Hz range for a cylinder.
• Effective results were achieved for both single and plural domain scenarios with a shell thickness of 20 mm.
• The ICA-Ring method requires no modifications to existing conventional BEM computer programs.

Conclusions:

• The ICA-Ring method provides a straightforward and robust solution to the BEM non-uniqueness problem in acoustic analysis.
• This method enhances the reliability of BEM for complex sound field problems across various domain configurations.
• The technique's compatibility with existing BEM software facilitates its practical adoption.