A novel numerical method for solving the Kirchhoff-Helmholtz integral equation based on the sound field representation using the reproducing kernel in the frequency domain

The paper introduces a unique numerical solution method for the Kirchhoff-Helmholtz integral equation. This method is based on the representation of the sound field using the reproducing kernel in the solution space of the homogeneous Helmholtz equation. When compared to the conventional boundary element method, the proposed method holds numerous advantages. This paper presents the analysis theory of the proposed method and demonstrates its validity by calculating bounded and unbounded sound fields. The accuracy of the calculation is assessed by computing the sound field in a rectangular room under various conditions. Furthermore, although some theoretical issues remain, the proposed method effectively avoids the non-uniqueness of solutions in unbounded domain problems.