Fast direct higher-order solution of complex large scale electromagnetic scattering problems via Locally Corrected Nystrom Discretization of CFIE

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

Work done by: D. Faircloth; T. Killian ; M. Horn ; M. Shafieipour ; I. Jeffrey ; J. Aronsson ; V. Okhmatovski

Abstract: Solutions of the large-scale electromagnetic scattering problems are typically obtained with Rao-Wilton-Glisson (RWG) Method of Moments (MoM) accelerated with Multi-Level-Fast-Multipole-Algorithm (MLFMA). Due to the low-order RWG MoM discretization and iterative nature of MLFMA such solutions present various challenges when realistic large-scale targets are considered. The most salient of these challenges are: 1) inefficient error control of solution beyond 2-3 digits, 2) poor conditioning of the matrix resulting from multiscale discretization of the model and/or the presence of highly resonant phenomena, and 3) the necessity to repeat solution for each excitation. In this work we present a novel computational framework, which efficiently overcomes these three challenges. Our method is based on Non-Uniform-Rational-B-Splines (NURBS) representation of the scatterer geometries and Higher-Order (HO) Locally Corrected Nystrom (LCN) discretization of the pertinent Combined Field Integral Equation (CFIE). Due to the HO nature of the LCN scheme, scattering solutions of desired precision are obtained with exponentially higher efficiency compared to the RWG MoM (Jeffrey, et.al., IEEE AP Mag. pp. 294-308, vol. 55, no. 3, June 2013). The second and third challenges are addressed through fast direct solution of the matrix equation resultant from LCN discretization of the CFIE. Our fast direct solution of the matrix equation is based on the block-LU decomposition aided with Adaptive-Cross-Approximation (ACA) compression of the blocks similar to Shaeffer’s algorithm (Shaeffer, IEEE TAP, no. 8, pp. 2306-2313, 2008). To overcome the computational complexity of the fast direct solution, the block LU decomposition is performed on multiple Graphics Processing Units (GPUs) with fast Out-of-Core memory augmentation.

This work was presented in a poster session, with the following poster:

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