Near- and Far-Field Boundary Conditions for a Finite Element Method for the Helmholtz Equation in Axisymmetric Problems of Underwater Acoustics

We consider the Helmholtz equation in a stratified cylindrically symmetric waveguide overlying a rigid bottom. Nonlocal boundary conditions are posed at a near- and a far-field artificial boundary. At the near-field boundary a nonhomogeneous DtN-type condition that takes into account the effects of the source and of the backscattering from the rest of the waveguide is posed. At the far-field boundary is used a condition associated with the DtN map of the exterior problem. The problem is discretized by a standard Galerkin/finite element method and is implemented in a Fortran code called FENL². The code is tested on some small scale problems and its results are compared with those of COUPLE and are found to be in excellent agreement.