Well-conditioned saddle point description for scattering by a metallic junction

In this contribution, a well-conditioned boundary integral based algorithm is described for the scattering of time-harmonic waves by metallic junctions, i.e. structures that contain lines where three or more sheets meet. The formulation is based on a saddle point description of the electric field integral equation that enforces the conservation of current at the junction by introduction of Lagrange multipliers. Upon discretisation, the system results in a finite dimensional saddle point system that is susceptible to dense grid breakdown, i.e. its solution by Krylov iterative solvers becomes increasingly more difficult as the mesh parameter tends to zero. To overcome this the system is regularised by providing preconditioners for the upper left block of the saddle system and its Schur complement. This requires the use of a finite element space that is a generalisation of the space of dual functions introduced by Buffa and Christiansen. As an additional benefit of using a saddle point method, continuity constraints of the current at the junction are weakened allowing for the use of geometrically non-conforming meshes. Numerical Results show the efficiency of the method.