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The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

Publication ,  Journal Article
Marek, A; Blum, V; Johanni, R; Havu, V; Lang, B; Auckenthaler, T; Heinecke, A; Bungartz, H-J; Lederer, H
Published in: Journal of physics. Condensed matter : an Institute of Physics journal
May 2014

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem sizes arising in the field of electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a matrix of dimension 260,000, scalability up to 295,000 CPU cores has been shown on BlueGene/P.

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Published In

Journal of physics. Condensed matter : an Institute of Physics journal

DOI

EISSN

1361-648X

ISSN

0953-8984

Publication Date

May 2014

Volume

26

Issue

21

Start / End Page

213201

Related Subject Headings

  • Mathematical Concepts
  • Fluids & Plasmas
  • Electronics
  • Computational Biology
  • Algorithms
  • 5104 Condensed matter physics
  • 4018 Nanotechnology
  • 4016 Materials engineering
  • 1007 Nanotechnology
  • 0912 Materials Engineering
 

Citation

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Marek, A., Blum, V., Johanni, R., Havu, V., Lang, B., Auckenthaler, T., … Lederer, H. (2014). The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science. Journal of Physics. Condensed Matter : An Institute of Physics Journal, 26(21), 213201. https://doi.org/10.1088/0953-8984/26/21/213201
Marek, A., V. Blum, R. Johanni, V. Havu, B. Lang, T. Auckenthaler, A. Heinecke, H. -. J. Bungartz, and H. Lederer. “The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.Journal of Physics. Condensed Matter : An Institute of Physics Journal 26, no. 21 (May 2014): 213201. https://doi.org/10.1088/0953-8984/26/21/213201.
Marek A, Blum V, Johanni R, Havu V, Lang B, Auckenthaler T, et al. The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science. Journal of physics Condensed matter : an Institute of Physics journal. 2014 May;26(21):213201.
Marek, A., et al. “The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.Journal of Physics. Condensed Matter : An Institute of Physics Journal, vol. 26, no. 21, May 2014, p. 213201. Epmc, doi:10.1088/0953-8984/26/21/213201.
Marek A, Blum V, Johanni R, Havu V, Lang B, Auckenthaler T, Heinecke A, Bungartz H-J, Lederer H. The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science. Journal of physics Condensed matter : an Institute of Physics journal. 2014 May;26(21):213201.
Journal cover image

Published In

Journal of physics. Condensed matter : an Institute of Physics journal

DOI

EISSN

1361-648X

ISSN

0953-8984

Publication Date

May 2014

Volume

26

Issue

21

Start / End Page

213201

Related Subject Headings

  • Mathematical Concepts
  • Fluids & Plasmas
  • Electronics
  • Computational Biology
  • Algorithms
  • 5104 Condensed matter physics
  • 4018 Nanotechnology
  • 4016 Materials engineering
  • 1007 Nanotechnology
  • 0912 Materials Engineering