Numerical solution to Maxwell's equations in singular waveguides

This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. The geometry is called singular, as its boundary includes reentrant corners or edges, which generate, in their neighborhood, strong electromagnetic fields. We have built a method which allows to compute the time-dependent electromagnetic field, based on a splitting of the spaces of solutions: First, the subspace of regular fields, which coincides with the whole space of solutions, in the case of convex or smooth boundary; Second, a singular subspace, defined and characterized via the singularities of the Laplace operator. Numerical results illustrate the influence of frequency of the ingoing electromagnetic waves in a L-shaped waveguide.