A high-order accurate, explicit kernel-split, panel-based, Fourier–Nyström discretization scheme is developed for integral equations associated with the Helmholtz equation in axially symmetric domains. Extensive incorporation of analytic information about singular integral kernels and on-the-fly computation of nearly singular quadrature rules allow for very high achievable accuracy, also in the...

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potential...

The recovery of the coe cient H(x) in the one-dimensional generalized Schrodinger equation d =dx + kH(x) = Q(x) ; where H(x) is a positive, piecewise continuous function with positive limits H as x ! 1; is studied. The large-k asymptotics of the wavefunctions and the scattering coe cients are analyzed. A factorization formula is given expressing the total scattering matrix as a product of simp...