A regularised electric field integral equation for scattering by perfectly conducting junctions

The electric field integral equations or EFIE can be used to describe the scattering of a time harmonic electromagnetic wave by a perfect electrical conductor. Unfortunately the linear system resulting upon its discretization becomes increasingly ill-conditioned as the mesh parameter decreases. Because of this, the solution time increases faster than the number of degrees of freedom, precluding the design of a truly fast solver. For uncomplicated geometries, Calderon preconditioners have been described that provide a solution to this problem. Unfortunately, it is not easy to extend Calderon preconditioning to structures containing junctions, a case relevant to many applications. In this contribution a Calderon preconditioner for the EFIE in the presence of junctions is described. The preconditioner is based on a generalisation of the dual basis functions introduced in the work of Buffa and Christiansen (2007). Numerical examples ares presented that are evidence of the scheme´s efficiency. Speed-up of about a factor of 20 are reported and in some cases preconditioning is a necessary step to enable to iterative solution of the system.