Computing Toroidal and Spherical Area-Preserving Mappings

🛠️ Under construction.

Related Publications

• Toroidal area-preserving parameterizations of genus-one closed surfaces
  M. Sutti, M.-H. Yueh
  Tech. report, to appear in Springer's Journal of Scientific Computing, 2026.
  Publisher's version arXiv preprint BibTeX

  @article{Sutti_Yueh:2025,
    author = {Sutti, M. and Yueh, M.-H.},
    title = {Toroidal area-preserving parameterizations of genus-one closed surfaces},
    journal = {Journal of Scientific Computing},
    year = {2025},
    month = {Aug},
    eprint = {2508.05111},
    archivePrefix = {arXiv},
    note = {To appear}
  }
• Riemannian gradient descent for spherical area-preserving mappings
  M. Sutti, M.-H. Yueh
  AIMS Math., Vol. 9(7), 19414–19445, 12 June 2024.
  Publisher's version arXiv preprint BibTeX

  @article{Sutti_Yueh:2024,
    author = {Sutti, M. and Yueh, M.-H.},
    title = {Riemannian gradient descent for spherical area-preserving mappings},
    journal = {AIMS Math.},
    year = {2024},
    volume = {9},
    number = {7},
    pages = {19414--19445},
    issn = {2473-6988},
    doi = {10.3934/math.2024946},
    eprint = {2403.11726},
    archivePrefix = {arXiv},
    url = {https://www.aimspress.com/article/doi/10.3934/math.2024946},
    fjournal = {AIMS Mathematics}
  }

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.
  Publisher's version arXiv preprint 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},
    journal = {Electron. Trans. Numer. Anal.},
    year = {2024},
    month = {Sep},
    volume = {60},
    pages = {501--519},
    issn = {1068-9613},
    doi = {10.1553/etna_vol60s501},
    eprint = {2404.04089},
    archivePrefix = {arXiv},
    url = {https://etna.math.kent.edu/vol.60.2024/pp501-519.dir/pp501-519.pdf},
    fjournal = {Electronic Transactions on Numerical Analysis}
  }
• Nonlinear Schwarz methods to compute geodesics on manifolds
  M. Sutti, T. Vanzan
  Tech. report, to appear in Springer's Lecture Notes in Computational Science and Engineering, 26 July 2026.
  Publisher's version arXiv preprint DDM28 proceedings (PDF) BibTeX

  @inproceedings{Sutti_Vanzan:2026,
    author = {Sutti, M. and Vanzan, T.},
    title = {{N}onlinear {S}chwarz methods to compute geodesics on manifolds},
    booktitle = {Lecture Notes in Computational Science and Engineering},
    year = {2026},
    month = {Jul},
    eprint = {2409.01023},
    archivePrefix = {arXiv},
    url = {https://www.ddm.org/DD28/proceedings/DD28_239.pdf}
  }
• Shooting methods for computing geodesics on the Stiefel manifold
  M. Sutti
  Tech. report, September 2023.
  arXiv preprint BibTeX

  @misc{Sutti:2023,
    author = {Sutti, M.},
    title = {Shooting methods for computing geodesics on the Stiefel manifold},
    year = {2023},
    month = {Sep},
    eprint = {2309.03585},
    archivePrefix = {arXiv},
    url = {https://arxiv.org/abs/2309.03585}
  }
• The leapfrog algorithm as nonlinear Gauss-Seidel
  M. Sutti, B. Vandereycken
  Tech. report, January 2023.
  arXiv preprint BibTeX

  @misc{Sutti_V:2023,
    author = {Sutti, M. and Vandereycken, B.},
    title = {The leapfrog algorithm as nonlinear {G}auss--{S}eidel},
    year = {2023},
    month = {Jan},
    eprint = {2010.14137},
    archivePrefix = {arXiv},
    url = {https://arxiv.org/abs/2010.14137}
  }

Low-rank Problems

🛠️ Under construction.

Related Publications

• Low-rank solutions to a class of parametrized systems using Riemannian optimization
  M. Sutti, T. Vanzan
  Tech. report, to appear in SIAM J. Sci. Comput., 2026.
  Publisher's version arXiv preprint BibTeX

  @article{Sutti_Vanzan:2026b,
    author = {Sutti, M. and Vanzan, T.},
    title = {Low-rank solutions to a class of parametrized systems using Riemannian optimization},
    journal = {SIAM Journal on Scientific Computing},
    year = {2026},
    month = {Apr},
    eprint = {2604.07136},
    archivePrefix = {arXiv},
    note = {To appear}
  }
• 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.
  Publisher's version arXiv preprint 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},
    journal = {J. Sci. Comput.},
    year = {2024},
    month = {Aug},
    day = {13},
    volume = {101},
    number = {1},
    pages = {3},
    issn = {1573-7691},
    doi = {10.1007/s10915-024-02629-8},
    eprint = {2305.11532},
    archivePrefix = {arXiv},
    url = {https://doi.org/10.1007/s10915-024-02629-8},
    fjournal = {Journal of Scientific Computing}
  }
• Riemannian multigrid line search for low-rank problems
  M. Sutti, B. Vandereycken
  SIAM J. Sci. Comput., 43(3), A1803–A1831, 2021.
  Publisher's version arXiv preprint 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.},
    year = {2021},
    volume = {43},
    number = {3},
    pages = {A1803--A1831},
    doi = {10.1137/20M1337430},
    eprint = {2005.06976},
    archivePrefix = {arXiv}
  }

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 Smoothed Particle Hydrodynamics simulations
  M. Sutti
  Tech. report, September 2022.
  arXiv preprint BibTeX

  @misc{Sutti:2022a,
    author = {Sutti, M.},
    title = {SPHM: a MATLAB package for Smoothed Particle Hydrodynamics simulations},
    year = {2022},
    month = {Sep},
    eprint = {2209.05189},
    archivePrefix = {arXiv},
    url = {https://arxiv.org/abs/2209.05189}
  }

Animations

Below, you can see two animations realized with SPHM.