A tearing-based hybrid parallel sparse linear system solver

Date

2010-09-15

Author

NAUMOV, Maxim
Manguoğlu, Murat
SAMEH, Ahmed

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We propose a hybrid sparse system solver for handling linear systems using algebraic domain decomposition-based techniques. The solver consists of several stages. The first stage uses a reordering scheme that brings as many of the largest matrix elements as possible closest to the main diagonal. This is followed by partitioning the coefficient matrix into a set of overlapped diagonal blocks that contain most of the largest elements of the coefficient matrix. The only constraint here is to minimize the size of each overlap. Separating these blocks into independent linear systems with the constraint of matching the solution parts of neighboring blocks that correspond to the overlaps, we obtain a balance system. This balance system is not formed explicitly and has a size that is much smaller than the original system. Our novel solver requires only a one-time factorization of each diagonal block, and in each outer iteration, obtaining only the upper and lower tips of a solution vector where the size of each tip is equal to that of the individual overlap. This scheme proves to be scalable on clusters of nodes in which each node has a multicore architecture. Numerical experiments comparing the scalability of our solver with direct and preconditioned iterative methods are also presented.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/40196

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2010.04.016

Collections

Department of Computer Engineering, Article

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Citation Formats

M. NAUMOV, M. Manguoğlu, and A. SAMEH, “A tearing-based hybrid parallel sparse linear system solver,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 3025–3038, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40196.