Solvers currently supported in ELSI are:

  • ELPA: The Kohn-Sham eigenvalue problem can be explicitly solved by direct diagonalization. The massively parallel dense eigensolver ELPA facilitates the solution of symmetric or Hermitian eigenproblems on high-performance computers. Algorithm extensions and optimizations are ongoing within the ELPA-AEO project.
  • libOMM: The orbital minimization method (OMM) bypasses the Kohn-Sham eigenvalue problem by efficient iterative algorithms which directly minimize an unconstrained energy functional using a set of auxiliary Wannier functions. The Wannier functions are defined on the occupied subspace of the system, reducing the size of the problem. The density matrix is then obtained directly, without calculating the Kohn-Sham orbitals.
  • PEXSI: PEXSI is a Fermi operator expansion (FOE) based method which expands the density matrix in terms of a linear combination of a small number of rational functions (pole expansion). Evaluation of these rational functions exploits the sparsity of the Hamiltonian and overlap matrices using selected inversion to enable scaling to 100,000+ of MPI tasks for calculation of the electron density, energy, and forces in electronic structure calculations.
  • EigenExa: The EigenExa library consists of two massively parallel implementations of direct, dense eigensolver. Its eigen_sx method features an efficient transformation from full to pentadiagonal matrix. Eigenvalues and eigenvectors of the pentadiagonal matrix are directly solved with a divide-and-conquer algorithm. This method is particularly efficient when a large part of the eigenspectrum is of interest.
  • SLEPc-SIPs: SLEPc-SIPs is a parallel sparse eigensolver for real symmetric generalized eigenvalue problems. SLEPc-SIPs solves the eigenvalue problem with distributed spectrum slicing method and it is currently available through the SLEPc library built on top of the PETSc framework.
  • NTPoly: NTPoly is a massively parallel library for computing the functions of sparse, symmetric matrices based on polynomial expansions. For sufficiently sparse matrices, most of the matrix functions can be computed in linear time. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. Various density matrix purification algorithms which compute the density matrix as a function of the Hamiltonian matrix are implemented in NTPoly.

Other features available in the latest release of ELSI may be found on the Changelog page.