Exact 3D scattering solutions for spherical symmetric scatterers

TL;DR

This paper develops exact analytical solutions for acoustic scattering by layered spherical elastic objects, enabling precise numerical evaluation and benchmarking for complex scattering scenarios.

Contribution

It introduces a comprehensive method for solving acoustic scattering by multilayered spherical elastic scatterers with added Neumann conditions, including numerical implementation and benchmark problems.

Findings

Numerical solutions are exact apart from round-off errors.

Benchmark problems are proposed for future validation.

Numerical examples demonstrate accuracy and applicability.

Abstract

In this paper, exact solutions to the problem of acoustic scattering by elastic spherical symmetric scatterers are developed. The scatterer may consist of an arbitrary number of fluid and solid layers, and scattering with single Neumann conditions (replacing Neumann-to-Neumann conditions) is added. The solution is obtained by separation of variables, resulting in an infinite series which must be truncated for numerical evaluation. The implemented numerical solution is exact in the sense that numerical error is solely due to round-off errors, which will be shown using the symbolic toolbox in MATLAB. A system of benchmark problems is proposed for future reference. Numerical examples are presented, including comparisons with reference solutions, far-field patterns and near-field plots of the benchmark problems, and time-dependent solutions obtained by Fourier transformation.