A more stable transition matrix for acoustic target scattering by highly oblate elastic objects

Area of Science:

• Acoustics
• Computational Physics
• Wave Scattering

Background:

• Previous T-matrix formulations struggled with stable acoustic scattering calculations for elongated elastic objects.
• Existing ansatzs for outgoing basis functions were effective for prolate shapes but not oblate ones.

Purpose of the Study:

• To adapt and evaluate an alternative T-matrix formulation for stable acoustic scattering analysis of highly oblate axisymmetric objects.
• To extend the frequency range of stable computations for oblate shapes using T-matrix methods.

Main Methods:

• Utilized an alternative basis of low-order spherical functions analytically continued into the complex plane.
• Distributed these functions along the imaginary axis of the complex plane to ensure completeness.
• Compared the stability and frequency range of the modified T-matrix formulation against existing methods.

Main Results:

• The alternative basis significantly extended the stability range of the T-matrix formulation for highly oblate axisymmetric objects.
• The achieved frequency range was comparable to spheroidal-basis T-matrix formulations.
• The stability range for oblate shapes was not as extensive as that for prolate shapes.

Conclusions:

• The adapted T-matrix formulation provides enhanced stability for acoustic scattering computations involving oblate axisymmetric objects.
• Further optimization of basis sets is needed to fully stabilize computations for highly oblate shapes and match prolate shape performance.
• Analysis of residual noise sources indicates potential for developing more optimal basis sets.