Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements

We consider a two-dimensional wave di raction problem from a closed body such that the complex pro- gressive wave potential satis es the Sommerfeld condition and the Helmholtz equation. We are interested in the case where the wavelength is much smaller than any other length dimensions of the problem. We introduce new mapped wave envelope in nite elements to model the potential in the far eld, and test them for some simple Dirichlet boundary condition problems. They are used in conjuction with wave envelope nite elements developed earlier [1] to model the potential in the near eld. An iterative procedure is used in which an initial estimate of the phase is iteratively improved. The iteration scheme, by which the wave envelope and phase are recovered, is described in detail.