Multifrontal Sparse Matrix Factorization on Graphics Processing Units

Robert F. Lucas, Gene Wagenbreth, John J. Tran, Dan M. Davis
Information Sciences Institute, University of Southern California, Marina del Rey, California
University of Southern California, Technical Report ISI-TR-677, 2012


   title={Multifrontal Sparse Matrix Factorization on Graphics Processing Units},

   author={Lucas, R.F. and Wagenbreth, G. and Tran, J.J. and Davis, D.M.},



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For many finite element problems, when represented as sparse matrices, iterative solvers are found to be unreliable because they can impose computational bottlenecks. Early pioneering work by Duff et al, explored an alternative strategy called multifrontal sparse matrix factorization. This approach, by representing the sparse problem as a tree of dense systems, maps well to modern memory hierarchies. Furthermore, it promotes the effective use of highly-tuned dense matrix arithmetic kernels, especially on novel and specialized hardware. The graphics processing units (GPUs) are architected differently than general-purpose hosts and offer an order of magnitude more processing power. This paper explores the hypothesis that GPUs can accelerate the speed of a multifrontal linear solver, even when only processing a small number of the largest frontal matrices. We show that GPUs can more than double the throughput of the sparse matrix factorization. This, in turn, promises to offer a very cost-effective speedup to many science and engineering problems in disciplines such as Mechanical Computer Aided Engineering (MCAE).
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