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

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  • 1Rechenzentrum Garching der Max-Planck-Gesellschaft am Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany.

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The Eigenvalue soLvers for Petascale Applications (ELPA) library efficiently solves large dense eigenvalue problems on parallel platforms. ELPA significantly outperforms existing libraries like ScaLAPACK for electronic structure theory and computational science.

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Area of Science:

  • Computational Science
  • Electronic Structure Theory
  • Numerical Analysis

Background:

  • Solving large dense eigenvalue problems is crucial for computational science and electronic structure theory.
  • Existing methods often face limitations in computational effort (O(N^3)) and scalability for large systems.
  • Iterative methods are ineffective when a significant fraction of eigenvalues/eigenvectors are required.

Purpose of the Study:

  • To review current developments in dense eigenvalue solvers.
  • To introduce and detail the Eigenvalue soLvers for Petascale Applications (ELPA) library.
  • To demonstrate the efficiency and scalability of ELPA on parallel computing platforms.

Main Methods:

  • Focus on the ELPA library for solving symmetric and Hermitian eigenvalue problems (standard and generalized).
  • ELPA utilizes the ScaLAPACK matrix layout but employs its own parallel subroutines for performance.
  • Employs both one-step and two-step tridiagonalization methods for matrix reduction and eigenvector backtransformation.

Main Results:

  • ELPA significantly outperforms ScaLAPACK routines and proprietary libraries (e.g., Intel MKL).
  • The two-step tridiagonalization is particularly efficient for larger matrices and core counts.
  • Demonstrated scalability beyond 10,000 CPU cores for electronic structure problems on high-performance architectures.
  • Achieved scalability up to 295,000 CPU cores for a matrix of dimension 260,000 on BlueGene/P.

Conclusions:

  • ELPA provides a highly efficient and scalable solution for large-scale dense eigenvalue problems.
  • The library is suitable for demanding applications in electronic structure theory and computational science.
  • ELPA represents a significant advancement in parallel eigenvalue solvers for petascale computing.