A regularized approach evaluating the near-boundary and boundary solutions for three-dimensional Helmholtz equation with wideband wavenumbers

Abstract

Efficient evaluation of near-boundary and boundary solutions for the Helmholtz equation with wideband wavenumbers by the boundary collocation method has been a difficult task for a long time. This study provides a regularized approach to bypass this limitation. The singular boundary method avoids the near singularity by using the nearly singular factors to replace the corresponding nearly singular terms. The core idea of the regularized approach is to substitute an artificially constructed general solution of the Helmholtz equation into the boundary integral equation or hyper boundary integral equation to determine the nearly singular factors. The core difficulty is the construction of the appropriate general solutions. The proposed regularized approach is free of integrations, easy-to-use and independent with particular wavenumbers. Numerical experiments show that accuracy of the near-boundary and boundary solutions of the singular boundary method improved by several orders of magnitude through application of the proposed regularized approach.