Geodesic
Implementation of iteration methods for solution of linear equation systems in problems of mathematical physics on reconfigurable computer systems
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 4, pp. 5-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we consider unique features of implementation of iteration methods for solution of linear equation systems in problems of mathematical physics on parallel computer systems, such as geometric decomposition of the computational domain and data parallelization in sequentially performed iterations with intensive data exchange between processors and memory. Standard methods of implementation of iteration methods of solution of linear equation systems with multiple exchanges with memory and between processors, which considerably reduce the performance, require a big number of communication channels in the computer system for implementation of complex topologies and hierarchic schemes of data storage. The solution of this problem is use of multiprocessor systems with reconfigurable architecture which allow adaptation of their architecture to the structure of iteration algorithms of mathematical physics owing to iteration parallelization. In this paper we analyze implementation of the Jacobi method for the Dirichlet problem for the Laplace equation on a reconfigurable computer system. This implementation is an example which illustrates reduction of the number of external data exchange channels, which are the most critical resource of the reconfigurable computer system.
Keywords: reconfigurable computer systems, FPGAs, numerical methods of mathematical physics, iteration parallelization, computational pipeline. 
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I. I. Levin; A. I. Dordopulo; A. V. Pelipets. Implementation of iteration methods for solution of linear equation systems in problems of mathematical physics on reconfigurable computer systems. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 4, pp. 5-18. http://geodesic.mathdoc.fr/item/VYURV_2016_5_4_a0/

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