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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.

Asynchronous Approach to Memory Management in Sparse Multifrontal Methods on Multiprocessors