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arXiv 0707.3405cond-mat.mtrl-sci
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基于三级并行的大规模从头计算

Large scale ab initio calculations based on three levels of parallelization

François Bottin, Stéphane Leroux, Andrew Knyazev, Gilles Zérah

摘要:

我们建议并实现了一个并行化方案的基础上,一个有效的多频带特征值求解器,称为局部最优块预处理共轭梯度LOBPCG方法,并使用优化的三维(3D)快速傅立叶变换(FFT)的从头算平面波代码ABINIT。除了对应于不同的k点的处理器上的标准数据划分之外,我们还介绍了相对于频带块的数据划分以及在ABINIT中使用的平面波基组上的系数的傅立叶空间中的空间划分。这种k点多带FFT并行化避免了整个处理器集合上的任何集体通信,而是仅依赖于一维通信。对于单个k点,由于广泛使用硬件优化的BLAS、LAPACK和SCALAPACK例程(主要在LOBPCG例程中),可在多达100个处理器上实现超线性缩放。我们观察到高达200个处理器的良好性能。使用10个k点,我们的三路数据分区导致用于测试的实际系统的线性扩展到1000个处理器。

英文摘要:

We suggest and implement a parallelization scheme based on an efficient multiband eigenvalue solver, called the locally optimal block preconditioned conjugate gradient LOBPCG method, and using an optimized three-dimensional (3D) fast Fourier transform (FFT) in the ab initio}plane-wave code ABINIT. In addition to the standard data partitioning over processors corresponding to different k-points, we introduce data partitioning with respect to blocks of bands as well as spatial partitioning in the Fourier space of coefficients over the plane waves basis set used in ABINIT. This k-points-multiband-FFT parallelization avoids any collective communications on the whole set of processors relying instead on one-dimensional communications only. For a single k-point, super-linear scaling is achieved for up to 100 processors due to an extensive use of hardware optimized BLAS, LAPACK, and SCALAPACK routines, mainly in the LOBPCG routine. We observe good performance up to 200 processors. With 10 k-points our three-way data partitioning results in linear scaling up to 1000 processors for a practical system used for testing.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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