Higher order surface integral equation solutions employing spherical harmonics based multilevel fast multipole method

Method of moments (MoM) is a powerful numerical tool for solving integral equation (IE) formulations of the boundary value problems in electromagnetics. The widely used low-order (LO) vector basis functions often require dense geometrical discretization to achieve sufficiently good accuracies. Great reduction of the number of unknowns for a given problem and desired accuracy is achievable through the use of higher-order (HO) basis functions. The tangentially continuous set of HO basis functions available, suitable for the modeling of field intensities, have been transformed to the normally continuous counterparts, by taking their cross product with the outward directed unit surface normal. The transformed basis functions have then been utilized to model the surface current densities for the MoM solution of IEs. Furthermore, because the accuracy of the electromagnetic solution is normally limited by the curl of the basis functions, the gradient space of the second-order basis functions have not been included in this work. The adaptive singularity cancellation approach has been used for the efficient and fully numerical evaluation of the singular and hyper-singular integrals.