A large domain complete basis functions for curved surfaces

The method of moments (MoM) with triangular surface discretization has become one of the most used techniques for solving electromagnetic scattering and radiation problems. This approach uses planar triangles to model the geometry and div-conforming basis functions to represent the surface current [1]. The planar triangle surface approximation, however, can lead to significant discretization errors when surfaces with high curvature are modelled. In near-field analysis the fidelity of the geometry modeling greatly impacts the accuracy of solutions so it is important to model curved features with curvilinear basis functions. We have recently introduced a complete analytical entire domain linear phase basis functions based on Shannon sampling theorem. These functions, called Linear-Phase Basis Functions (LPF) have been introduced in [2] for flat surfaces and are able to reconstruct the scattered field from a flat plate with a number of functions equal to the degrees of freedom of the scatterer. The GSF constitute a complete, discrete basis for any kind of equivalent currents on a flat finite surface. Their selection does not resort to any singular value decomposition (SVD) procedure, but they are selected in a non-redundant way by a Gram-Smith orthogonalization process. In this paper we present a generalization of the LPF introduced in [2] to curvilinear basis function able to represent any current on a curved surface.