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

  • Gustavo Chávez
  • George Turkiyyah
  • David E. KeyesEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 116)


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.


Arithmetic Complexity Cyclic Reduction Nest Dissection Hierarchical Matrice Block Tridiagonal Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Gustavo Chávez
    • 1
  • George Turkiyyah
    • 1
  • David E. Keyes
    • 1
    Email author
  1. 1.Extreme Computing Research CenterKing Abdullah University of Science and TechnologyThuwalSaudi Arabia

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