Floating-point Complex Research Articles

Distributed Real-Time Image Processing of Formation Flying SAR Based on Embedded GPUs

<b>Formation flying synthetic aperture radar (FF-SAR) systems, as an important development direction of multichannel SAR, can achieve high-resolution wide-swath (HRWS) imaging. Coherently combining data from satellite receivers puts a strain on traditional real-time processing systems based on individual satellites. Characteristics such as the power of real-time on-orbit processing platform must be properly balanced with constrained memory and parallel computational resources. This paper proposes a distributed SAR real-time imaging method based on embedded Graphics Processing Units (GPUs). The parallel computing method of chirp scaling (CS) algorithm is designed based on parallel programming model of compute unified device architecture (CUDA), and the optimization methods of memory and performance are proposed for the hardware architecture of embedded GPUs. In particular, unified memory management method is used to avoid data copying and communication delays between the CPU and GPU. A hardware verification system for distributed SAR real-time imaging processing based on multiple embedded GPUs is constructed. The proposed algorithm takes 5.86 seconds to process single-precision floating-point complex imaging with a data size of 8192 &#x00D7; 8192 on a single Jetson Nano platform. The actual power consumption is less than 5 W, and the performance-to-power ratio is greater than 1.7&#x0025;. The experimental results show that the real-time processing method based on embedded GPUs proposed in this paper has high performance and low power consumption.</b>

English

English

Algorithmic Construction of Hurwitz Maps

We describe an algorithm that, given a k-tuple of permutations representing the monodromy of a rational map, constructs an arbitrarily precise floating-point complex approximation of that map. We then explain how it has been used to study a problem in dynamical systems raised by Cui.

Parallel algebraic hybrid solvers for large 3D convection-diffusion problems

In this paper we study the parallel scalability of variants of an algebraic additive Schwarz preconditioner for the solution of large three dimensional convection diffusion problems in a non-overlapping domain decomposition framework. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32- and 64-bit calculation. The robustness and the scalability of the preconditioners are investigated through extensive parallel experiments on up to 2,000 processors. Their efficiency from a numerical and parallel performance view point are reported.

Parallel scalability study of hybrid preconditioners in three dimensions

In this paper we study the parallel scalability of variants of additive Schwarz preconditioners for three dimensional non-overlapping domain decomposition methods. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32- and 64-bit calculation. The robustness of the preconditioners is illustrated on a set of linear systems arising from the finite element discretization of elliptic PDEs through extensive parallel experiments on up to 1000 processors. Their efficiency from a numerical and parallel performance view point are studied.

Concurrent Source Iteration in the Solution of Three-Dimensional, Multigroup Discrete Ordinates Neutron Transport Equations

A strategy for implementing source iteration on massively parallel computers for use in solving multigroup discrete ordinates neutron transport equations on three-dimensional Cartesian grids is proposed and analyzed. Based on an analysis of the memory requirement and floating-point complexity of the formal matrix-vector multiplication effected by a single source iteration, a data decomposition and communication strategy is presented that is designed to achieve good scalability with respect to all phase-space variables, i.e., neutron position, energy, and direction. A performance model is developed to analyze the scalability properties of the algorithm and to provide computational and heuristic strategies for determining a data decomposition that minimizes wall clock execution time. Numerical results are presented to demonstrate the performance of a specific implementation of this approach on a 1,024-node nCUBE/2.