A Parallel Sparse Direct Solver via Hierarchical DAG Scheduling

Abstract

We present a parallel sparse direct solver for multicore architectures based on Directed Acyclic Graph (DAG) scheduling. Recently, DAG scheduling has become popular in advanced Dense Linear Algebra libraries due to its efficient asynchronous parallel execution of tasks. However, its application to sparse matrix problems is more challenging as it has to deal with an enormous number of highly irregular tasks. This typically results in substantial scheduling overhead both in time and space, which causes overall parallel performance to be suboptimal. We describe a parallel solver based on two-level task parallelism: tasks are first generated from a parallel tree traversal on the assembly tree; next, those tasks are further refined by using algorithms - by - blocks to gain fine-grained parallelism. The resulting fine-grained tasks are asynchronously executed after their dependencies are analyzed. Our approach is distinct from others in that we adopt two-level task scheduling to mirror the two-level parallelism. As a result, we reduce scheduling overhead, and increase efficiency and flexibility. The proposed parallel sparse direct solver is evaluated for the particular problems arising from the hp -Finite Element Method where conventional sparse direct solvers do not scale well.