Research of a parallel implementationof the splitting method for the heat conductivity problem on clustered computersystems

The paper consideres a parallel implementation of the splitting methods for heat conductivityproblem, provides results of the numeric simulation performed on clustered computer system,diagrams of the speedup factors dependencies on a number of elementary machines, and definesdependence of the optimal computer systems size on the size of the model.The goal of the research performed, is a determination of the optimal parameters of the parallelalgorithm and computer system that would minimize the programs execution time.A parallel implementation of splitting method for the heat conductivity problemt xx U =U +Uyy, defined in a square area with known initial and boundary conditions, has beenselected as a point of research. Numeric model was built upon a mesh that is uniformly set forspatial and time coordinates. The splitting method reduces solution of the chosen problem to anumeric solving of 2TN sets of linear equations with square tridiagonal N  N matrices(here N stands for the size of models mesh on spatial coordinates, T is the mesh size on timecoordinate). Thomas algorithm has been applied to solve matrices.A linear array of p elementary machines has been chosen as a special structure of the computersystem. The definition domain has been decomposed into p uniform sub-domains along one of thespatial axis. A separate thread of the parallel program calculates data within each sub-domain. Thechosen algorithm assumes point-to-point data exchange operations between neighbor threads.Program code has been written in C++. MPICH 1.21 library has been utilized to establish inter-communication between threads of the parallel program. Numeric simulation has carried on asegment of the distributed multi-cluster computer system of CPCT SibSUTIS.

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