A Robust Nonsingular Double-Boundary CHIEF Method for Full Wave Numbers

In this paper, a double-boundary CHIEF method is constructed based on the idea of the combined Helmholtz integral equation formulation (CHIEF) method by adding supplementary equation for overcoming the non-uniqueness of the boundary integral equation at the eigenfrequency. The conventional boundary element method (CBEM) equation is coupled with the virtual indirect boundary element method (VIBEM) equation. Because the CBEM equation and the VIBEM equation are located at different boundaries, their eigenfrequencies are not coincident, which theoretically avoids the failure of the supplementary equation in the traditional CHIEF method. At the same time, according to the equivalence of the coefficient matrix between the CBEM and VIBEM, the singular matrix is obtained indirectly by replacement calculation. Through the analysis and verification of numerical examples, the non-singular dual-boundary CHIEF method proposed in this paper can effectively overcome the non-uniqueness of the conventional boundary element method at the eigenfrequency, and can obtain high-precision and robust results in the full wavenumber domain. The accuracy of the proposed method is much higher than that of CBEM and Burton-Miller method without singular integral processing.