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

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.