Task-Based Sparse Direct Solver for Symmetric Indefinite Systems

Abstract. Many applications in science and engineering require the solution of large sparse linear systems of equations. For solving such problems, direct methods are frequently employed because of their robustness, accuracy and usability as black-box solvers.

As modern architectures become more and more complex, with an increasing number of cores per chip, a deeper memory hierarchy and the integration of accelerators such as GPUs, it becomes all the more challenging to exploit the potential performance of such machines for sparse matrix factorization algorithms especially in the context of symmetric indefinite systems. Although significant efforts has gone into positive-definite systems, little progress has been reported in the much harder indefinite case. One major advance for tackling these problems is the design of the APTP (a posteriori threshold pivoting) strategy that has been implemented in the SSIDS solver and proven to be efficient on both multicores and GPUs while giving accurate solutions.

In this talk, we present the DAG-based solver SpLDLT that relies on a APTP strategy and uses the StarPU runtime system for implementing it parallel version. We demonstrate the benefits of this approach by showing our ability to exploit heterogeneity in the context of GPU-accelerated multicore systems.