Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
复制标题
变系数三维椭圆偏微分方程的并行加速循环约简预处理器
DOI：
10.1016/j.cam.2017.11.035
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
D. Keyes
中科院分区：
文献类型：
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作者：
Gustavo Chavez;G. Turkiyyah;S. Zampini;D. Keyes
我们提出了一个强大的和可扩展的预处理器的解决方案，产生的离散化的椭圆偏微分方程服从秩压缩的大规模线性系统。预条件是基于分层低秩近似和循环约简方法。的预处理器的设置和应用阶段实现对数线性复杂性的内存占用和操作的数量，和数值实验表现出良好的弱和强的可扩展性，在大处理器数量在分布式内存环境中。对对称与非对称、确定与不确定、常系数与变系数线性系统的数值实验表明了预条件的适用性和鲁棒性。此外，可以通过分级矩阵近似及其算术运算的精度阈值以及容许条件参数的调整来控制迭代次数。这些参数一起允许优化预处理器的存储器要求和性能。
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.
DOI：
10.1137/1.9780898718003
发表时间：
2003-05
期刊：
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影响因子：
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作者：
Y. Saad
通讯作者：
Y. Saad