Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Extreme Computing Research Center
Applied Mathematics and Computational Science Program
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AbstractWe 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.
CitationChávez G, Turkiyyah G, Zampini S, Keyes D (2017) Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. Journal of Computational and Applied Mathematics. Available: http://dx.doi.org/10.1016/j.cam.2017.11.035.
SponsorsWe 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.