An Explicit Higher-Order Dual Basis for a Multiplicatively Calderón Preconditioned Electric Field Integral Equation

Abstract

One of the most effective means to precondition the electric field integral equation (EFIE) discretized with Rao-Wilton-Glisson (RWG) functions is the multiplicative Calderón preconditioner employing Buffa-Christiansen (BC) functions as a basis dual to the RWG basis. It results in a formulation that is free from the dense-discretization and the low-frequency breakdown. To generalize the multiplicative Calderón preconditioner from the low-order BC and RWG basis to higher orders, we utilize B-spline-based basis functions and establish the first explicit high-order dual basis. It can be regarded as a generalization of the BC functions to arbitrary polynomial degrees and constitutes a fundamental building block for other approaches that rely on a dual basis. Numerical results for the obtained preconditioner demonstrate a low and constant number of generalized minimum residual (GMRES) iterations independent of the number of unknonws and the polynomial degree for canonical and realistic perfectly electrically conducting (PEC) scatterers; a key to enable the full potential of higher-order bases.