A complex variable boundary element-free method for the Helmholtz equation using regularized combined field integral equations

Based on the combined field integral equation (CFIE) and the complex variable moving least squares (CVMLS) approximation, a complex variable boundary element-free method is developed for the exterior Neumann problem for the Helmholtz equation. To eliminate both strongly singular and hypersingular integrals and to ensure the stability and efficiency of the method for all wavenumbers, a regularized CFIE is derived. To facilitate the application of the method and the approximation of the gradient of the boundary function, the CVMLS approximation is used to discretize the CFIE. Numerical results reveal that the method is pollution-free and efficient for solving the Helmholtz equation with arbitrary and large wavenumbers.