Boundary element-free methods for exterior acoustic problems with arbitrary and high wavenumbers

This paper proposes the boundary element-free method (BEFM) for the numerical solution of exterior acoustic problems with arbitrary and high wavenumbers. A single layer BEFM and a double layer BEFM are developed by using acoustic single and double layer potentials to represent the solution, respectively. To eliminate the non-uniqueness drawback, an improved combined field integral equation is derived free of strongly singular and hypersingular integrals, and then a combined field BEFM is also developed for enhancing the solution accuracy, particularly in the neighborhood of the characteristic wavenumber. Compared with the original BEFM, boundary conditions in the proposed three BEFMs are implemented accurately and easily by using density functions. Numerical examples involving single and multiple objects show that the proposed methods offer reliable and efficient numerical solutions to exterior acoustic problems with arbitrary and high wavenumbers.