A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements

Gustavo Ivan Chavez Chavez, George Turkiyyah, David E. Keyes

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $\mathcal{H}$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $\mathcal{H}$ -LU and that it can tackle problems where algebraic multigrid fails to converge.
Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIII
PublisherSpringer Nature
Number of pages9
ISBN (Print)9783319523880
StatePublished - Mar 18 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01


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