Computing Geodesics on Riemannian Manifolds

Under construction.

Animations

Below, you can see an animation of the leapfrog method on the unit sphere.

Related Publications

• A single shooting method with approximate Fréchet derivative for computing geodesics on the Stiefel manifold, M. Sutti, Electron. Trans. Numer. Anal. (ETNA), Vol. 60, 501–519, September 2024.

bibtex



@article{Sutti:2024,
  author   = {Sutti, M.},
  title    = {A single shooting method with approximate {F}r\'{e}chet derivative for computing geodesics on the {S}tiefel manifold},
  fjournal = {Electronic Transactions on Numerical Analysis},
  journal  = {Electron. Trans. Numer. Anal.},
  volume   = {60},
  pages    = {501--519},
  month    = {Sep},
  year     = {2024},
  issn     = {1068–9613},
  doi      = {10.1553/etna_vol60s501},
  url      = {https://etna.math.kent.edu/vol.60.2024/pp501-519.dir/pp501-519.pdf}
}
close
• Nonlinear Schwarz methods to compute geodesics on manifolds, M. Sutti, T. Vanzan, Tech. report, September 2024.

bibtex



@article{Sutti_Vanzan:2024,
  author  = {Sutti, M. and Vanzan, T.},
  title   = {{N}onlinear {S}chwarz methods to compute geodesics on manifolds},
  journal = {arXiv preprint arXiv:2409.01023},
  month   = {Sep},
  year    = {2024}
}
close
• Shooting methods for computing geodesics on the Stiefel manifold, M. Sutti, Tech. report, September 2023.

bibtex



@article{Sutti:2023,
  author  = {Sutti, M.},
  title   = {Shooting methods for computing geodesics on the Stiefel manifold},
  journal = {arXiv preprint arXiv:2309.03585},
  month   = {Sept},
  year    = {2023}
}
close
• The leapfrog algorithm as nonlinear Gauss-Seidel, M. Sutti, B. Vandereycken, Tech. report, January 2023.

bibtex



@article{Sutti_V:2023,
  author  = {Sutti, M. and Vandereycken, B.},
  title   = {The leapfrog algorithm as nonlinear {G}auss--{S}eidel},
  journal = {arXiv preprint arXiv:2010.14137v3},
  month   = {Jan},
  year    = {2023}
}
close

Low-rank Problems

Under construction.

Related Publications

• Implicit low-rank Riemannian schemes for the time integration of stiff partial differential equations, M. Sutti, B. Vandereycken, Vol. 101, article number 3, J. Sci. Comput., 13 August 2024.

bibtex



@article{Sutti_V:2024,
  author   = {Sutti, M. and Vandereycken, B.},
  title    = {Implicit low-rank Riemannian schemes for the time integration of stiff partial differential equations},
  fjournal = {Journal of Scientific Computing},
  journal  = {J. Sci. Comput.},
  month    = {Aug},
  year     = {2024},
  day      = {13},
  volume   = {101},
  number   = {1},
  pages    = {3},
  issn     = {1573-7691},
  doi      = {10.1007/s10915-024-02629-8},
  url      = {https://doi.org/10.1007/s10915-024-02629-8}
}
close
• Riemannian multigrid line search for low-rank problems, M. Sutti, B. Vandereycken, SIAM J. Sci. Comput., 43(3), A1803–A1831, 2021.

bibtex



@article{Sutti_V:2021,
  author  = {Sutti, M. and Vandereycken, B.},
  title   = {Riemannian multigrid line search for low-rank problems},
  journal = {SIAM J. Sci. Comput.},
  volume  = {43},
  number  = {3},
  pages   = {A1803--A1831},
  year    = {2021},
  doi     = {10.1137/20M1337430}
}
close

Smoothed Particle Hydrodynamics (SPH)

The Smoothed Particle Hydrodynamics (SPH) is a meshfree particle method for computational fluid dynamics (CFD) simulations. The domain of interest is discretized by a set of particles (or points) not connected by a mesh (or grid).

Software

SPHM: A MATLAB package for SPH simulations, September 2022.

Related Publication

If you use SPHM for your work, please cite the following document:

• SPHM: a MATLAB package for for Smoothed Particle Hydrodynamics simulations, M. Sutti, Tech. report, September 2022.

bibtex



@article{Sutti:2022a,
  author  = {Sutti, M.},
  title   = {SPHM: a MATLAB package for Smoothed Particle Hydrodynamics simulations},
  journal = {arXiv preprint arXiv:2209.05189},
  month   = {Sept},
  year    = {2022}
}
close

Animations

Below, you can see two animations realized with SPHM.