TY - JOUR
T1 - Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
AU - Chavez Chavez, Gustavo Ivan
AU - Turkiyyah, George
AU - Zampini, Stefano
AU - Keyes, David E.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank the editors and the reviewers for their time and comments during the review process of this work. Support from the KAUST Supercomputing Laboratory and access to Shaheen Cray XC40 is gratefully acknowledged.
PY - 2017/12/7
Y1 - 2017/12/7
N2 - We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.
AB - We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.
UR - http://hdl.handle.net/10754/626377
UR - http://www.sciencedirect.com/science/article/pii/S0377042717305952
UR - http://www.scopus.com/inward/record.url?scp=85042652048&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2017.11.035
DO - 10.1016/j.cam.2017.11.035
M3 - Article
SN - 0377-0427
VL - 344
SP - 760
EP - 781
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -