A spectral embedding method applied to the advection-diffusion equation

In order to solve partial differential equations in complex geometries with a spectral type method, one describes an embedding approach which essentially makes use of Fourier expansions and boundary integral equations. For the advection-diffusion equation, the method is based on an efficient open-quotes Helmholtz solver,close quotes the accuracy of which is tested by considering 1D and 2D advection-diffusion problem in a hexagonal geometry. 16 refs., 13 figs., 2 tabs