Higher-order Locally Corrected Nystrom solution of the combined field integral equation based on geometric modelling with NURBS

Summary form only given. Higher-order (HO) methods for electromagnetic analysis are of high practical interest as they are exponentially more efficient than their low-order counterparts (Jeffrey, et.al., IEEE AP Mag. pp. 294-308, vol. 55, no. 3, June 2013). Such methods also can produce the same accuracy of solution with greatly reduced number of unknowns. The HO Method of Moments (MoM) and HO Locally Corrected Nystrom (LCN) method are two common techniques which yield such benefits. The former, however, is known to require prolonged system matrix fill times compared to that of the LCN method (Notaros, IEEE Trans. Antennas Propag., 56, 2251-2276, 2008). Being an element-based method the HO MoM also renders acceleration techniques such as the multilevel fast multipole algorithm (MLFMA) to be less efficient than the point-based LCN method. For the above reasons MLFMA accelerated HO LCN method is a preferred approach to efficient error-controllable large-scale electromagnetic analysis (Jeffrey, et. al., IEEE AP Mag. pp. 294-308, vol. 55, no. 3, June 2013).In this work we show that the HO convergence to the true solution can be achieved in the LCN solution of CFIE only if a certain degree of geometry smoothness is preserved in the discretized model. Our numerical experiments show that the surface must exhibit continuity to at least first-order spatial derivatives. Surface discretizations leading to the discontinuity in first-order spatial derivatives produce infinite electromagnetic fields at the junctions between the mesh elements. This type of discontinuities is artificially introduced to a smooth surface when bilinear and interpolation curvilinear quadrilaterals are used to discretize the geometry. This calls for the introduction of NonUniform Rational B-Spline (NURBS) surfaces into HO-LCN since continuity of spatial derivatives of NURBS surfaces can be controlled. Furthermore since NURBS surfaces are usually a mixture of arbitrary sized quadrilateral and triangular- patches, we demonstrate that one can utilize quadrilateral quadrature rules on triangular patches as a special case of quadrilateral elements when one edge approaches zero.