Full wavenumber high precision combined coupled double boundary element method for solving external acoustic problems

•Simultaneous equations can overcome the non-uniqueness of boundary element method.•The non-uniqueness of eigenfrequency can be overcome by adding complex damping.•The complex damping method is more accurate than Burton-Miller method.•Singular integrals can be calculated indirectly by matrix substitution.•The accuracy of boundary element method can be improved by using indirect matrix. In this paper, a high-precision combined coupled double boundary element method (CCD-BEM) with a full wavenumber unique solution is proposed by combining the boundary element method (BEM) equation with the virtual indirect BEM (VIBEM) equation and using the equivalent relationship between their coefficient matrices. This method only requires overcoming the non-uniqueness of the VIBEM equation to obtain the unique solution of full-wave number, thus avoiding the failure of interior-point configuration in the combined Helmholtz integral equation formulation (CHIEF) method and the calculation of hyper-singular integral in Burton-Miller method. In addition, the singular matrix in BEM can be calculated indirectly using the equivalent relationship between the BEM and VIBEM coefficient matrix, which completely avoids the direct calculation of weak singular or singular integral. The numerical results of acoustic radiation and scattering show that CCD-BEM has a lower condition number of the coefficient matrix and higher calculation accuracy than BEM.