Efficient high-order discretization schemes for integral equation methods

Abstract

A high-order method is a method that provides extra digits of accuracy with only a modest increase in computational cost. A number of method of moment (MoM) techniques based on high-order basis and testing functions have been presented in the literature. Characteristically, these methods result in a substantial increase in precomputational cost principally due to the expensive numerical integration required for near interactions. This can be accelerated through the use of specialized quadrature schemes when available. Unfortunately, performing the double integration numerically over high-order functions can still be quite computationally intensive. A novel high-order technique based on a locally-corrected Nystrom scheme combined with advanced quadrature schemes is presented. It is shown that this method truly demonstrates high-order convergence for the solution of electromagnetic scattering problems with comparable computational cost to low-order schemes. The elegance of this technique is in its simplicity and ease of implementation. However, the power of the method is its ability to inexpensively provide true high-order convergence.