Implementing Parallel LU Factorization with Pipelining on a MultiCore Using OpenMP

Abstract

Recent developments in high performance computer architecture have a significant effect on all fields of scientific computing. Linear algebra and especially the solution of linear systems of equations lies at the heart of many applications in scientific computing. This paper describes and analyzes three parallel versions of the dense LU factorization method that is used in linear system solving on a multicore using OpenMP interface. More specifically, we present two naive parallel algorithms based on row block and row cyclic data distribution and we put special emphasis on presenting a third parallel algorithm based on the pipeline technique. Further, we propose an implementation of the pipelining technique in OpenMP. Experimental results on a multicore CPU show that the proposed OpenMP pipeline implementation achieves good overall performance compared to the other two naive parallel methods. Finally, in this work we propose a simple, fast and reasonably analytical model to predict the performance of the LU decomposition method with the pipelining technique.