A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements
Numerical Analysis
2017-12-27 v1
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 arithmetic complexity and memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the -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 -LU and that it can tackle problems where algebraic multigrid fails to converge.
Keywords
Cite
@article{arxiv.1604.00617,
title = {A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements},
author = {Gustavo Chávez and George Turkiyyah and David Keyes},
journal= {arXiv preprint arXiv:1604.00617},
year = {2017}
}