Journal
COMPUTATIONAL MATERIALS SCIENCE
Volume 42, Issue 2, Pages 329-336Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.commatsci.2007.07.019
Keywords
density functional theory; ABINIT; eigenvalue; LOBPCG; SCALAPACK; FFT; parallelization; MPI; supercomputing
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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. (C) 2007 Elsevier B.V. All rights reserved.
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