Iterative solutions of boundary integral equations in acoustics

Abstract

It is shown that exterior problems for the Helmholtz equation may be solved iteratively for all frequencies. A general class of boundary-value problems for the Helmholtz equation is reduced to boundary integral equations. Using modified Green’s functions these boundary integral equations are known to be uniquely solvable. Even though the boundary integral operators are not self-adjoint they may be transformed into a form appropriate for iterative solution by a method developed for linear operator equations. Rates of convergence of the iteration are given and an example is presented to show the method.