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Libkrylov: A modular open-source software library for extremely large on-the-fly matrix computations.

Dmitrij Rappoport1, Samuel Bekoe1, Luke Nambi Mohanam1,2

  • 1Department of Chemistry, University of California Irvine, Irvine, California, USA.

Journal of Computational Chemistry
|January 13, 2023
PubMed
Summary
This summary is machine-generated.

We developed libkrylov, an open-source library for solving complex matrix equations using Krylov subspace methods. It offers flexible integration and various preconditioning options for enhanced performance in scientific computing.

Keywords:
Krylov space methodsTDDFTTDHFiterative algorithmsopen-source software

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Area of Science:

  • Computational physics and chemistry
  • Numerical analysis and scientific computing

Background:

  • Krylov subspace methods are essential for solving large-scale linear and eigenvalue problems in computational science.
  • Existing libraries often lack flexibility in handling matrix-free computations and customizable preconditioning strategies.

Purpose of the Study:

  • To design and implement libkrylov, an open-source library for matrix-free eigenvalue, linear, and shifted linear equation solutions.
  • To provide a flexible API and modular structure for easy integration with specialized matrix-vector evaluation engines.
  • To offer pluggable preconditioning, orthonormalization, and tunable convergence control for diverse numerical challenges.

Main Methods:

  • Implementation of Krylov subspace methods for matrix-free computations.
  • Inclusion of pluggable components for preconditioning (Diagonal/Conjugate Gradient, Davidson, Jacobi-Davidson) and orthonormalization (orthonormal, nonorthonormal/nKs).
  • Exposing all functionalities through Fortran and C application programming interfaces (APIs).

Main Results:

  • Successful design and implementation of the libkrylov library.
  • Demonstrated performance for eigenvalue calculations in time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA).
  • Analysis of convergence behavior influenced by preconditioning and orthonormalization choices.

Conclusions:

  • Libkrylov provides a flexible and modular open-source solution for matrix-free computations.
  • The library's design facilitates integration and customization for specific scientific applications.
  • Performance analysis in TDDFT-TDA highlights the impact of preconditioning and orthonormalization on convergence.