# Boundary regularised integral equation formulation of the Helmholtz equation in acoustics

## TL;DR

This paper introduces a boundary integral method for the Helmholtz equation in acoustics that removes singularities analytically, enabling higher accuracy and efficiency in modeling acoustic radiation problems, even with complex geometries.

## Contribution

It develops a singularity-free boundary integral formulation for the Helmholtz equation, improving numerical precision and computational efficiency in acoustic simulations.

## Key findings

- Enhanced numerical accuracy with higher order elements
- Effective handling of complex geometries and aspect ratios
- Guaranteed solution uniqueness with the CHIEF method

## Abstract

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field due to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.