Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:344

Article; Proceedings Paper

Chavez, Gustavo¹  Turkiyyah, George²  Zampini, Stefano¹  Keyes, David¹ 

[1] King Abdullah Univ Sci & Technol, Thuwal, Saudi Arabia

[2] Amer Univ Beirut, Beirut, Lebanon

关键词: Preconditioning;    Cyclic reduction;    Hierarchical matrices;   

DOI  :  10.1016/j.cam.2017.11.035

来源: Elsevier

【 摘 要 】

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 non-symmetry, 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. (C) 2017 The Author(s). Published by Elsevier B.V.

【 授权许可】

Free