amkatrutsa / shift4sai_krylov

Practical shift choice for Shift-And-Invert method

Practical shift choice in Shift-And-Invert Krylov method for matrix exponential evaluation

Prerequisites:

• NumPy >= 1.16, SciPy >= 1.1, Matplotlib >= 3
• PyAmg >= 4.0

Examples

• Convection-diffusion equation with piecewise-constant coefficients:

  • Optimize-and-run method
  • Inceremental method

• Anisotropic diffusion equation

  • Optimize-and-run method
  • Inceremental method

• Source code for the SAI Krylov method is available here

Citing

If you use this code in your research, please cite our preprint:

@article{katrutsa2019practical,
  title={Practical shift choice in the shift-and-invert Krylov subspace evaluations of the matrix exponential},
  author={Katrutsa, Alexandr and Botchev, Mike and Oseledets, Ivan},
  journal={arXiv preprint arXiv:1909.13059},
  year={2019}
}