Solution of radiation problems by collocation of integral formulations in terms of single and double layer potentials

Abstract

The purpose of this paper is the solution of the exterior steady state acoustic radiation problem for an arbitrary surface of which the normal velocity is specified, by using integral formulations. To obtain integral formulations, both a direct method, based on the surface Helmholtz integral equation, and an indirect method, based on single and double layer potentials, have been used. Filippi's method, with a hybrid potential, ensures uniqueness for any wavenumber. Three different surface elements have been used as a basis for obtaining approximate solutions by collocation of the integral equations. A comparison of the rates of convergence for the three surface elements is presented, based on a suitably defined overall error. There is no overall convergence for the double layer representation when a constant approximate solution is used for each surface element in spite of the good local convergence at the centers of the elements. The rate of convergence also appears to be highly dependent on the normal interpolation technique. Special care has been taken in the calculation of the singular integrals which are the terms of self-influence. The numerical implementation of the method, which has been tested for special cases, is applicable to general three dimensional sound radiation problems, since no special symmetry conditions are involved.