Higher order hierarchical Legendre basis functions for iterative integral equation solvers with curvilinear surface modeling

Numerical solution of Maxwell's equations is often based on a discretization of an unknown field quantity using a set of N basis functions. A set of higher order hierarchical vector basis functions for the electric surface current in MoM codes with curvilinear quad patches is investigated. The basis is based on Legendre polynomials, modified to enforce current continuity, and are rather simple to implement in addition to allowing for a flexible selection of the polynomial order. This flexibility is not provided by interpolatory bases that traditionally have been preferred due to the condition number of the matrix. Numerical results obtained with EFIE and CFIE show that the hierarchical Legendre basis provides a better condition number of the MoM matrix than existing interpolatory bases. This allows for convergence in very few iterations using basis functions as high as 10th order.