Rapid solution of integral equations fast numerical algorithms

Summary form only given. The author discusses an algorithm for the rapid solution of boundary value problems for the Helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory. The algorithm requires an amount of work proportional to n/sup 4/3/, where n is the number of nodes in the discretization of the boundary of the scatterer, and, when it is combined with a generalized conjugate residual type algorithm, the resulting process takes very few iterations to converge, leading to an order n/sup 4/3/ algorithm for the solution of the original scattering problem. A fairly straightforward refinement of the scheme, reducing its CPU time requirements from O(n/sup 4/3/), to O(n log (n)), has also been considered.<>