Asynchronous Approach to Memory Management in Sparse Multifrontal Methods on Multiprocessors

Abstract

This research covers the Intel ? Direct Sparse Solver for Clusters, the sof tware that implements a direct method for solving the Ax = b equation with sparse symmetric matrix A on a cluster. This met hod, 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 decompo sition 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.