Agullo, Emmanuel and Amestoy, Patrick and Buttari, Alfredo and Guermouche, Abdou and Joslin, Guillaume and L'Excellent, Jean-Yves and Li, Xiaoye Sherry and Napov, Artem and Rouet, François-Henry and Sid-Lakhdar, Mohamed and Wang, Shen and Weisbecker, Clément and Yamazaki, Ichitaro Recent advances in sparse direct solvers. (2013) In: 22nd Conference on Structural Mechanics in Reactor Technology (SMIRT 2013), 18 August 2013 - 23 August 2013 (San Francisco, United States).
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Abstract
Direct methods for the solution of sparse systems of linear equations of the form A x = b are used in a wide range of numerical simulation applications. Such methods are based on the decomposition of the matrix into a product of triangular factors (e.g., A = L U ), followed by triangular solves. They are known for their numerical accuracy and robustness but are also characterized by a high memory consumption and a large amount of computations. Here we survey some research directions that are being investigated by the sparse direct solver community to alleviate these issues: memory-aware scheduling techniques, low-rank approximations, and distributed/shared memory hybrid programming.
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