A Multiplicative Calderón Preconditioner for the B-Spline-Based Electric Field Integral Equation

We present a multiplicative Calderón preconditioner for the electric field integral equation (EFIE) when discretized with B-spline-based basis functions, that is, the resulting formulation is free from the dense-discretization breakdown. We obtain the preconditioner by establishing a set of suitable dual basis functions, which can be explicitly expressed as a superposition of a refined discretization, as is known from the (low-order) Buffa-Christiansen (BC) functions. In contrast to the BC functions, our approach applies to arbitrary polynomial degrees of the basis functions for single- and multi-patch (curvilinear) descriptions of the geometry, which can be open or closed. Numerical results demonstrate the optimal nature of the derived preconditioner.