A Loop-Star Decomposition for the B-Spline Based Discretization of the Electric Field Integral Equation

The electric field integral equation (EFIE) is widely employed to determine the field that is scattered from perfectly electrically conducting (PEC) structures. However, it is known to suffer from a low-frequency breakdown. In order to overcome this breakdown for a B-spline based (isogeometric) discretization of arbitrary polynomial order of the EFIE employing the method of moments, we propose a loop-star decomposition of the discretized surface current density resulting in a preconditioner involving solely sparse matrices. The proposed decomposition is applicable to open and closed simply-connected surfaces described by a single or by multiple patches. To verify the correctness of the proposed method, numerical examples are provided.