A fast numerical method for a natural boundary integral equation for the Helmholtz equation (Q2389979)

First, the authors reduce a Neumann boundary value problem of the Helmholtz equation in an exterior circular domain into an equivalent natural boundary integral equation. The Galerkin method using trigonometric wavelets allows to obtain a stiffness matrix which is symmetric and circulant, and which leads to a fast numerical method based on the fast Fourier transform. The method is also efficient when the wave number in the Helmholtz equation is very large.