Finite difference solutions of the acoustic radiation equation in the near field

Numerical methods for the solution of the finite difference approximation to the acoustic radiation equation are discussed. For a spherical radiator, the Gauss-Seidel iterative method and the alternating direction implicit method are employed to solve the discrete approximation of the Helmholtz equation in the near field. Emphasis is on the development of the general numerical method and on the extrapolation scheme used to increase the rate of convergence. Measures of the number of calculations needed for various methods of solution are reported. A discussion of the nature of the acoustic radiation problem in numerical computation is also presented.