Asynchronous Approach to Memory Management in Sparse Multifrontal Methods on Multiprocessors

Abstract

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.

Schur Complement Computations in Intel® Math Kernel Library PARDISO

“…In Kalinkin [17], the basic algorithm was implemented for symmetric, positive definite matrices. In the presentations [18] and [19], the proposed algorithm was significantly improved by balancing the dependency tree. In [20], the algorithm was expanded to non-positive definite matrices and nonsymmetric matrices.…”