The International Conference for High Performance Computing, Networking, Storage, and Analysis
The International Conference for High Performance Computing, Networking, Storage, and Analysis
Workshop: ESPM2 2022: Seventh International Workshop on Extreme Scale Programming Models and Middleware
Authors: Valentin Le Fèvre (Barcelona Supercomputing Center (BSC)); Tetsuzo Usui (Next Generation Technical Computing Unit, Fujitsu Ltd); and Marc Casas (Barcelona Supercomputing Center (BSC))
Abstract: Sparse linear algebra routines are fundamental building blocks of a large variety of scientific applications. Direct solvers, which are methods for solving linear systems via the factorization of matrices into products of triangular matrices, are commonly used in many contexts. The Cholesky factorization is the fastest direct method for symmetric and definite positive matrices.
This presentation presents selective nesting, a method to determine the optimal task granularity for the parallel Cholesky factorization based on the structure of sparse matrices. We propose the OPT-D algorithm, which automatically and dynamically applies selective nesting. OPT-D leverages matrix sparsity to drive complex task-based parallel workloads in the context of direct solvers. We run an extensive evaluation campaign considering a heterogeneous set of 35 sparse matrices and a parallel machine featuring the A64FX processor. OPT-D delivers an average performance speedup of 1.46x with respect to the best state-of-the-art parallel method to run direct solvers.