An efficient and highly accurate solver for multi-body acoustic scattering problems involving rotationally symmetric scatterers

TL;DR

This paper introduces a high-accuracy, efficient numerical solver for multi-body acoustic scattering involving rotationally symmetric objects, capable of handling complex geometries with many scatterers on standard hardware.

Contribution

The paper presents a novel boundary integral equation approach combined with a hybrid solver and Fast Multipole acceleration specifically for rotationally symmetric scatterers, achieving high accuracy and efficiency.

Findings

Accurate solutions to seven digits for complex geometries.

Capable of handling several dozen scatterers simultaneously.

Efficient on personal workstations.

Abstract

A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries involving cavities, solutions accurate to seven digits or better were obtained. The method relies on a Boundary Integral Equation formulation of the scattering problem, discretized using a high-order accurate Nystr\"om method. A hybrid iterative/direct solver is used in which a local scattering matrix for each body is computed, and then GMRES, accelerated by the Fast Multipole Method, is used to handle reflections between the scatterers. The main limitation of the method described is that it currently applies only to scattering bodies that are rotationally symmetric.