A Calderón preconditioner for the EFIE operator without barycentric refinement of the mesh

Among the techniques to solve the ill-conditioning of the electric field integral equation (EFIE), multiplicative approaches based on Calderón identities are peculiarly effective. They rely on the use of a dual basis, like the Buffa-Christiansen (BC) or Chen-Wilton (CW) basis functions, to stably discretize the H_div^-1/2-H_curl^-1/2 duality. These dual basis functions, unfortunately, require a barycentric refinement of the mesh resulting in an increase of the memory consumption. This work presents a multiplicative preconditioner for the EFIE operator that, differently from other Calderón preconditioning approaches, does not require the barycentric refinement of the mesh. The new preconditioner is obtained by chaining two standard system matrices (discretized on the standard, non-refined, mesh) with a suitably designed Gram matrix and appropriately chosen pre- and post-smoothers. A theoretical analysis proves the effectiveness of the proposed preconditioner and numerical results from realistic application scenarios corroborate the presented theory.