High-order treatment of corner singularities with the locally-corrected Nyström method

High-order techniques have been proposed for obtaining high accuracy and rapid convergence in numerical solutions of integral equations for electromagnetics. Results obtained for structures with smooth surfaces exhibit relatively low errors, and the rate of decrease in the error improves with reduced cell sizes as either the basis function or the representation order increases. Recent publications report a method-of-moments procedure that permits similar improvement in accuracy for structures with corners where the current density or charge density exhibits a singularity. In the following, a similar procedure is incorporated into the locally-corrected Nystrom (LCN) method. Extensions of the LCN for the special case of a knife-edge singularity were proposed by Gedney and Tong and Chew. The present work differs in that it is applicable to corners of any angle, and it incorporates multiple singular terms at each corner in order to achieve true high order behavior. Results indicate that as the order of the representation for the current density increases, the accuracy of the solution improves at rates identical to those observed for smooth geometries.