SIESTA‐SIPs: Massively parallel spectrum‐slicing eigensolver for an ab initio molecular dynamics package

Abstract

Integration of Shift-and-Invert Parallel Spectral Transformation (SIPs) eigensolver (as implemented in the SLEPc library) into an ab initio molecular dynamics package, SIESTA, is described. The effectiveness of the code is demonstrated on applications to polyethylene chains, boron nitride sheets, and bulk water clusters. For problems with the same number of orbitals, the performance of the SLEPc eigensolver depends on the sparsity of the matrices involved, favoring reduced dimensional systems such as polyethylene or boron nitride sheets in comparison to bulk systems like water clusters. For all problems investigated, performance of SIESTA-SIPs exceeds the performance of SIESTA with default solver (ScaLAPACK) at the larger number of cores and the larger number of orbitals. A method that improves the load-balance with each iteration in the self-consistency cycle by exploiting the emerging knowledge of the eigenvalue spectrum is demonstrated. © 2018 Wiley Periodicals, Inc.

ELSI: A unified software interface for Kohn–Sham electronic structure solvers

“…As of its 2.4.1 release, ELSI supports shared-memory eigensolvers LA-PACK [27] and MAGMA [28,29], distributed-memory eigensolvers ELPA [21,22,23], SLEPc-SIPc [13,14,24,25], and EigenExa [26], and distributedmemory density matrix solvers PEXSI [8,9,10,11], libOMM [30], and NT-Poly [31]. In the following sections, we cover a few algorithmic and technical aspects of the upgraded PEXSI solver and the newly added NTPoly and SLEPc-SIPs solvers.…”

A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation

“…The SIESTA-SIPs method of [Keçeli et al 2018] adopts a similar k-means strategy for tracking the eigenvalue migration throughout the SCF procedure to avoid costly methods to perform shift selection every SCF iteration. The SIESTA-SIPs method is not as sensitive to changes in the definitions of spectral slice intervals between SCF iterations as long as they are distributed such to allow for similar convergence rates between slices due to their use of SI-Lanczos.…”

“…These distributed calculations for each spectral probe may take place on a subset of the total number of MPI ranks, allowing leverage of massive parallelism on large computing clusters. We do not treat this particular parallelism scheme in this work, but it has been discussed at length in other related work [Keçeli et al 2016[Keçeli et al , 2018Zhang et al 2007].…”

“…• The shift-invert Lanczos method (SI-Lanczos). Historically, this has been the method of choice for spectrum slicing methods [Aktulga et al 2014;Campos and Roman 2012;Grimes et al 1994;Keçeli et al 2016Keçeli et al , 2018Zhang et al 2007]. However, the dependency among the sequence of linear systems the method must solve makes it difficult to achieve good parallel scalability.…”

“…The dynamic shift selection within each subdomain is similar to the sequential shift selection scheme presented by Grimes et al [1994]. More recently, the SIPs method has been extended to a dynamically scheduled two-level parallel scheme targeting the SCF eigenvalue problem (SIESTA-SIPs [Keçeli et al 2018]), which processes non-overlapping spectral subdomains with an improved dynamic shift selection within each domain as developed in the SLEPc library [Campos and Roman 2012]. While robust, this shift selection strategy does not maximize the potential for concurrency viz independent slices as the dynamic shift selection within a spectral subdomain still occurs sequentially.…”