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This paper presents the massively parallel implementation of the FETI-2LM techniques (Finite Element Tearing and Interconnecting with two Lagrange Multipliers) in the FACTOPO code to solve large-scale sparse receiving array evolutions of the GRAVES bistatic radar in the VHF band. There are four main ingredients in the proposed work and methodology: 1) the implementation of a total field weak formulation of FETI-2LM algorithms for multi-sources modeling using an efficient block Krylov recycling strategy for the calculation of the hundreds of antenna embedded radiation patterns of the sparse array; 2) the implementation of a meshing strategy consisting in generating the sparse array by populating a regular periodic grid; 3) the implementation of the proposed methodology on massively parallel clusters; 4) the investigation of performances of the optimized GRAVES elementary antenna in the VHF band, followed by the demonstration of the expected gain performances even with stronger interferences due to the densification of the array. These simulations of the GRAVES sparse array requiring the resolution of sparse linear systems with 10.47 billion unknowns have been made possible thanks to recent developments of the FETI-2LM domain decomposition method and the use of 13, 692 Intel Xeon Broadwell E5–2680v4 computing cores. A total of 3.8 million cumulated hours have been invested in the interest of the augmentation of the antennas. Until now FETI-2LM methods have been successfully implemented for antenna and diffraction electromagnetic simulations in the S-C-X-Ku and Ka bands and to the best to our knowledge this is the first time that they have been used in the VHF band.

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Massively Parallel Implementation of FETI-2LM Methods for the Simulation of the Sparse Receiving Array Evolution of the GRAVES Radar System for Space Surveillance and Tracking