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

Abstract

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 largescale 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.INDEX TERMS Aerospace control, bi-static radar, Doppler radar, digital beamforming, low earth orbit satellites, parallel machines, supercomputers, radar tracking, real-time systems, space surveillance and tracking, sparse array, very-high frequencies, wide area surveillance, finite element methods, finite element tearing and interconnecting, FETI, domain decomposition methods, VHF band, FACTOPO.

Improvement of DDM Preprocessing for the Simulation of the GRAVES Radar Densified Sparse Array for Space Surveillance and Tracking

“…One main particularity in our implementation remains in the fact that we do not mesh the initial global sparse array before the resolution of the electromagnetic problem. The global array is geometrically broken down in few generic sub-domains (3 unit-cell in [1]) each equipped with its own local mesh. They are generated separately with an automatic procedure of the GID preprocessor and as a consequence we do not use METIS [11] for partitionning the large scale initial mesh into sub-domains.…”

“…Since the method is implemented on parallel machines, each computing core with at least 4 GB of memory is allocated exclusively to a sub-domain (elementary cell of the sparse array). The strategy used in a recent work [1] was to populate a regular grid of regular periodicity with three types of sub-domains: 1) Antenna sub-domain: It embeds the antenna geometry with surrounding Absorbing Boundary Conditions (ABC) and a Perfect Electrical Conductor (PEC) at z=0 as shown in Fig. 2.…”

“…Recently [1], to overcome the calculation difficulties indicated above, the simulation of the large size GRAVES sparse array has been performed with the Finite Element Tearing and Interconnecting using two Lagrange multipliers (FETI-2LM) technique [3], [9], [10] implemented in ONERA's FACTOPO code. The originality is that the complete mesh is not built upstream of the resolution of the electromagnetic problem avoiding the use of specific mesh splitter tools such as METIS [11] to decompose the large scale initial mesh.…”

“…Abstract-In a recent work [1] we have discussed our implementation of the Finite Element Tearing and Interconnecting method (FETI-2LM) a Domain Decompositon Method (DDM) for the full-wave simulation of the large GRAVES sparse array (60 m diameter disk). Due to the non-regular distribution of the antennas of the sparse array, such simulations in reasonable times are not accessible with existing FETI methods optimized for repetitive geometries and who do not benefit from an effective parallelization technique.…”

Simulation of Active Reflection Coefficient Phenomena of Large Antenna Array Using FEM Domain Decomposition Methods

“…However, the methodology to extract the scattering matrix of the array is based on a mix of periodic approximations (for the center elements) and partial local embedded zones for the border elements of the array. In this work, so as to efficiently calculate the embedded radiation patterns of all the radiating elements (internal and boundary radiating elements) as well as the complete Scattering Matrix [6] of the array, we discuss the interest of the implementation of the FETI-2LM domain decomposition methods taking into account the finitude o f t he a rray on massively parallel computers initially developed in [14] and optimized in [15] and [16] for large size sparse arrays. The main goal is to implement a method allowing in a first step to calculate the radiating elements radiation patterns and the GSM of the array, and in a second post processing step to calculate the gain patterns of the antenna array for azimuth and elevation scanning directions while taking into account the active reflection c oefficient.…”