The most parallel computing algorithms for solving tasks of heat and mass exchange
Journal Title: Metallurgical and Mining Industry - Year 2017, Vol 9, Issue 5
Abstract
Problems of mathematical modeling of Dirichlet problems are considered on the basis of use of parallel computing systems of cluster type. For solution of multivariate spatial tasks, it was offered to convert the task of three-dimensional distribution in the field of variables change to the sequence of the diagrams excluding unknown values only in one direction – alternately in longitudinal, cross and vertical. For this purpose it is recommended to use implicit schemes; it leads to systems of the linear algebraic equations with three-diagonal structure. It is shown that the greatest effect of the parallel processor is reached by application of elements of the linear algebra for matrix computation. In this regard, special attention is paid to development of the maximum parallel forms of algorithms of the differential schemes with three-diagonal structure. It is shown that the offered algorithm of a cyclic reduction of shifts allows the highest level of vectorization. Application of a method of “odd-even” reduction of lines for system of the linear algebraic equations allows to us to develop the parallel algorithm with the maximum extent of vectorization.
Authors and Affiliations
V. P. Ivashchenko, G. G. Shvachich, A. V. Sobolenko
Keywords
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