4. TITLE AND SUBTITLE Hybrid asymptotic-numerical methods: in scattering

We have developed and studied hybrid asymptotic-numerical methods to compute the acoustic field scattered by a large object. IThe asymptotic approximation xs based on a short wavelength expansion of the scattered field in the form of uniformly valid geometrical theory of diffraction. These were combined with two numerical methods: finite elements and boundary spectral strip methods. The coupling to finite elements was achieved with the introduction of a new variational priciple to couple two incompatible approximations. The boundary spectral strip method is a spectral approximation applied to a boundary integral formulation of the boundary value problem. With this method, we have succesfully evaluated diffraction coefficients, surface wave excitation coefficients, and solved large scattering problems with several diffraction points: We have also studied the error introduced by joining the numerical and asymptotic approximations, and determined its properties and scalings