Current recovery for the RWG-based method of moments

摘要

Derivative recovery through local smoothing, is a well-known approach to obtain an estimate of a solution field's derivative, to one polynomial order higher than its direct representation. In the finite element method context, this is often referred to as `gradient recovery'. The method of moments (MoM) is routinely used to solve electromagnetic field integral equations in terms of the electric surface current density, which is often represented by mixed first-order, Rao-Wilton-Glisson (RWG) basis functions upon a mesh of triangle elements. A procedure for recovering a mixed second-order, approximate solution from an RWG-based MoM solution is presented. Recovery of the solution itself rather than its derivative, is made possible by exploiting specific properties of the mixed-order, surface divergence-conforming function spaces. The procedure is not strictly local, however, only sparse, positive-definite global linear systems must be solved. The procedure is independent of the integral operator. Computational complexity is lower than that of existing residual-based MoM error estimators. Results are shown with the recovered solution being a better approximation than the original solution. The procedure is useful for post-processing and for local or global a posteriori error estimation. It can be incorporated into any RWG-based MoM code.