GPU computing with Kaczmarz's and other iterative algorithms for linear systems.
GPU computing with Kaczmarz's and other iterative algorithms for linear systems.
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DOI：
10.1016/j.parco.2009.12.003
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发表时间：
2010-06-01
影响因子：
1.4
通讯作者：
Vouzis P
中科院分区：
文献类型：
--
作者：
Elble JM;Sahinidis NV;Vouzis P
图形处理单元(GPU)用于求解由偏微分方程组导出的大型线性系统。所研究的微分方程是强对流占优势的，大小不一，在许多领域都是通用的，包括计算流体力学、传热学和结构力学。本文比较了Kaczmarz迭代法、Cimmino迭代法、分量平均法、共轭梯度法(CGNR)、对称逐次超松弛预条件共轭梯度法、共轭梯度加速分量平均行投影法(CARP-CG)等几种迭代方法在GPU和CPU上的实现。计算是用稠密的和一般的带状系统进行的。结果表明，我们的GPU实现优于这些算法的CPU实现，以及先前研究的在Linux集群和共享存储系统上的并行实现。虽然CGNR方法在解决这类问题上已经开始失宠，但对于本文研究的问题，在GPU上实现的CGNR方法比其他方法，包括CARP-CG方法的集群实现，表现得更好。
The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradient-accelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out of favor for solving such problems, for the problems studied in this paper, the CGNR method implemented on the GPU performed better than the other methods, including a cluster implementation of the CARP-CG method.
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影响因子：
3.1
作者：
Gordon, D;Gordon, R
通讯作者：
Gordon, R
影响因子：
5.4
作者：
COMBETTES, PL
通讯作者：
COMBETTES, PL
DOI：
10.1137/0913003
发表时间：
1992-01-01
期刊：
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING
影响因子：
--
作者：
ARIOLI, M;DUFF, I;RUIZ, D
通讯作者：
RUIZ, D
DOI：
10.1137/0913010
发表时间：
1992-01-01
期刊：
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING
影响因子：
--
作者：
BRAMLEY, R;SAMEH, A
通讯作者：
SAMEH, A
影响因子：
2.7
作者：
Gordon, Dan;Gordon, Rachel
通讯作者：
Gordon, Rachel