Abstract: Reflectometry is an electromagnetic probing process for fusion plasmas. It is modelled by Maxwell's equation with a specific dielectric tensor. This equation split into two different propagation modes, namely ordinary (O) and extraordinary (X). The O-mode equation is Helmholtz equation with a smooth vanishing coefficient. The X-mode equation is much more tricky, and known to have a singular solution.
The numerical method we developed for reflectometry, based on an Ultra-Weak Variational Formulation, is adapted to the main unusual feature of these equations. Since standard plane wave method are irrelevant when the local wave number vanishes , we designed generalized plane wave basis functions to overcome this problem. We achieve high order convergence, the order being linked to order of approximation of the coefficient.
The talk will focus on the design of such adapted basis functions and interpolation properties, together with the corresponding UWVF numerical method.