Low-Frequency Stabilization for the B-Spline Based Isogeometric Discretization of the Electric Field Integral Equation

In order to low-frequency stabilize the electric field integral equation (EFIE) when discretized with divergence conforming B-spline based basis and testing functions in an isogeometric approach, we propose a corresponding quasi-Helmholtz preconditioner.To this end, we derive i) a loop-star decomposition for the B-spline basis in the form of sparse mapping matrices applicable to arbitrary polynomial orders of the basis as well as to open and closed geometries described by single-or multipatch parametric surfaces (as an example non-uniform rational Bsplines (NURBS) surfaces are considered).Based on the loopstar analysis, we show ii) that quasi-Helmholtz projectors can be defined efficiently.This renders the proposed low-frequency stabilization directly applicable to multiply-connected geometries without the need to search for global loops and results in betterconditioned system matrices compared to directly using the loopstar basis.Numerical results demonstrate the effectiveness of the proposed approach.