Towards a Broadband-Stable Fast Method for the B-Spline Discretized Electric Field Integral Equation

Scattering problems in electromagnetics have a multitude of applications, including, but not limited to, remote sensing and radar systems, electromagnetic compatibility, and antenna design. A natural way to address these problems in free space are integral equations such as the electric field integral equation (EFIE). The EFIE can be approximated by a linear system of equations using the boundary element method (BEM). Typically, in the first step, a mesh is created on the surface of the geometry. Currents on the mesh are approximated by a superposition of basis functions. This results in a geometric discretization error that can be prevented by utilizing exact parametric descriptions of the geometry surface. One commonly employed technique involves the use of non-uniform rational B-splines (NURBS), where the surface is described by a union of patches. Basis functions are subsequently established using the same parametric representation by mapping them from a parametric space onto the patches [1]. This aligns well with common industrial design schemes that focus on computer-aided design (CAD) tools and integrates the design and simulation process. Existence and uniqueness of the solution of the BEM for the EFIE using a set of divergence-conforming basis functions have been established in [2].