On the use of multi-p hierarchical bases for the solution of electromagnetic integral equations

Considerable efforts have been made in recent years to improve the computation efficiency of the method of moments (MoM) for the solution of electromagnetic integral equations. A class of algorithms that show a certain potential in reducing the computation cost are based on employing hierarchical basis functions. The classical hierarchical basis functions constructed with rectangular and triangular pulse functions were utilized recently in a multilevel formulation of the MoM [1]. Wavelets are orthogonal hierarchical basis functions which have also been used recently for the solution of integral equations [2]. The multi-p hierarchical basis functions [3] are constructed with Legendre polynomials, and have been widely used in the p-version of the finite element method. Their use was further extended to treat singularities in the integral equations for problems in mechanical engineering relative to polygonal domains [4].