Multifrontal QR Factorization for Multicore Architectures over Runtime Systems

Abstract

To face the advent of multicore processors and the ever increasing complexity of hardware architectures, programming models based on DAG parallelism regained popularity in the high performance, scientific computing community. Modern runtime systems offer a programming interface that complies with this paradigm and powerful engines for scheduling the tasks into which the application is decomposed. These tools have already proved their effectiveness on a number of dense linear algebra applications. This paper evaluates the usability of runtime systems for complex applications, namely, sparse matrix multifrontal factorizations which constitute extremely irregular workloads, with tasks of different granularities and characteristics and with a variable memory consumption. Experimental results on real-life matrices show that it is possible to achieve the same efficiency as with an ad hoc scheduler which relies on the knowledge of the algorithm. A detailed analysis shows the performance behavior of the resulting code and possible ways of improving the effectiveness of runtime systems.