Numerical solution of 2-D scattering problems using high-order methods

Abstract

We demonstrate that a method of moments scattering code employing high-order methods can compute accurate values for the scattering cross section of a smooth body more efficiently than a scattering code employing standard low-order methods. Use of a high-order code also makes it practical to provide meaningful accuracy estimates for computed solutions.Index Terms-Boundary integral equation, electromagnetic scattering, high-order numerical method, method of moments.

High Order Representations for Singular Currents at Corners

“…These are generally proposed to obtain high accuracy in computations or to reduce the number of required unknowns while ensuring sufficient (low to moderate) accuracy. A variety of results, obtained for structures with smooth surfaces, support the conclusion that high order methods provide improved accuracy relative to computational costs [2], [5], [6], [8]- [10], [12], [13], [16]. Furthermore, with high order representations for the equivalent surface currents, the error decreases at faster rates with reduced cell sizes than it does for low order basis functions.…”

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

“…4 7...~2 .!.! 13 5 ' 5' 5' 5' 5' , 5' 5' ... (1) Previous research by the authors suggests that for a given order expansion in the smooth regions of a structure, there is a trade-off between the number of singular terms used in corner cells, and the relative dimension of the corner cell. Reference [3] concluded that, for a wide range of problems, a nearly optimum solution was obtained with (1) corner cells that were twice the dimension of the other cells in the model, and (2) a representation that incorporated a number of singular terms equal to the number of regular terms.…”

“…High-order techniques have been proposed for obtaining high accuracy and rapid convergence in numerical solutions of integral equations for electromagnetics [1][2]. 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.…”

Optimal High-Order Method of Moment combined with NURBS for the scattering by a 2D cylinder.

“…Hamilton et all [23] used the product of Jacoby and Legendre polynomials. Although they did not impose the continuity, the results are corrects for EFIE in TM polarization.…”