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Asynchronous Approach to Memory Management in Sparse Multifrontal Methods on Multiprocessors

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DOI: 10.4236/am.2013.412A004    3,354 Downloads   4,817 Views Citations


This research covers the Intel? Direct Sparse Solver for Clusters, the software that implements a direct method for solving the Ax = b equation with sparse symmetric matrix A on a cluster. This method, researched by Intel, is based on Cholesky decomposition and could be considered as extension of functionality PARDISO from Intel? MKL. To achieve an efficient work balance on a large number of processes, the so-called “multifrontal” approach to Cholesky decomposition is implemented. This software implements parallelization that is based on nodes of the dependency tree and uses MPI, as well as parallelization inside a node of the tree that uses OpenMP directives. The article provides a high-level description of the algorithm to distribute the work between both computational nodes and cores within a single node, and between different computational nodes. A series of experiments shows that this implementation causes no growth of the computational time and decreases the amount of memory needed for the computations.

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A. Kalinkin and K. Arturov, "Asynchronous Approach to Memory Management in Sparse Multifrontal Methods on Multiprocessors," Applied Mathematics, Vol. 4 No. 12A, 2013, pp. 33-39. doi: 10.4236/am.2013.412A004.

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