Higher-Order Locally Corrected Nyström Solution of the Combined Field Integral Equation Based on Geometric Modelling with NURBS

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By: M. Shafieipour, C. Niu, and V. Okhmatovski

Abstract: Higher-order (HO) methods for electromagnetic (EM) analysis are of high practical interest as they control solution error exponentially more efficiently 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 EM 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.

This work was presented at: 2014 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium) along with a poster as follows:

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