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arXiv · 1604.00617

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

Gustavo Chávez·George Turkiyyah·David Keyes
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Abstract

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 $O(N \log^2 N)$ arithmetic complexity and $O(N \log N)$ 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 with a parallel implementation 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.

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Gustavo Chávez, George Turkiyyah, David Keyes. 2016-04-03. A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements. https://doi.org/10.1007/978-3-319-52389-7_12

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