Computation of scattering of a plane wave from multiple prolate spheroids using the collocation multipole method

Area of Science:

• Acoustics
• Computational Physics
• Wave Scattering

Background:

• Solving three-dimensional acoustic scattering problems with multiple objects is computationally challenging.
• Existing methods often struggle with complex geometries like prolate spheroids and require approximations.
• Accurate prediction of acoustic fields is crucial for various engineering applications.

Purpose of the Study:

• To present a novel collocation multipole method for three-dimensional acoustic scattering.
• To address scattering problems involving multiple prolate spheroids under plane wave incidence.
• To accurately determine both near-field acoustic pressure and far-field scattering patterns.

Main Methods:

• Formulation of the scattered field using prolate spheroidal wave functions.
• Combination of the multipole method, directional derivative, and collocation technique for semi-analytical solution.
• Development of a normal derivative for sound-hard/Neumann conditions without truncation error.

Main Results:

• A finite linear algebraic system is derived by truncating multipole expansion terms.
• The method accurately calculates acoustic scattering for one, two, and three prolate spheroids.
• Validation against analytical and boundary element methods confirms the proposed approach's accuracy.

Conclusions:

• The collocation multipole method provides an efficient and accurate solution for multiple prolate spheroid acoustic scattering.
• The study investigates the influence of scatterer eccentricity, separation, and wave number on acoustic fields.
• This method offers a robust tool for analyzing complex acoustic scattering phenomena.