Singular boundary method for acoustic eigenanalysis

This paper applies the singular boundary method (SBM) to two- (2D) and three-dimensional (3D) acoustics eigenproblems in simply- and multiply-connected domains. The SBM is a strong-form boundary discretization numerical method and is meshless, integration-free, and easy-to-implement. By introducing the concept of the source intensity factors, the singularity of fundamental solutions can be isolated to avoid the singular numerical integrals in the boundary element method (BEM). Similar to the BEM, the spurious eigenvalues may arise in the SBM computation. In order to extract out spurious eigenvalues from SBM results, the singular value decomposition updating techniques and the Burton–Miller method are implemented. Several 2D and 3D benchmark examples subjected to Dirichlet and Neumann boundaries are tested to examine the accuracy and stability of the present SBM strategy.