Calderon preconditioning of the local system in a single level BETI method

This paper will introduce a Calderon multiplicative preconditioner for the local problems appearing in the BETI formulation of the frequency domain electromagnetic transmission problem. The local problems in BETI involve the solution of local Neumann problems through the inversion of a block operator comprising the single and double layer operators for the Maxwell system. Like many formulations of scattering and transmission problems whose formulation includes the single layer operator, the spectral properties of this system are such that iterative solution times grow faster than the number of degrees of freedom in the domain under consideration. In this contribution it is demonstrates that the systems appearing in the local problems are amenable to regularisation through the application of a Calderon multiplicative preconditioner.