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.

📑 BibTeX

@article{Sutti_Yueh:2025,
      author  = {Sutti, M. and Yueh, M.-H.},
      title   = {Toroidal area-preserving parameterizations of genus-one closed surfaces},
      journal = {arXiv preprint arXiv:2508.05111},
      month   = {Aug},
      year    = {2025}
    }

• Riemannian gradient descent for spherical area-preserving mappings, M. Sutti, M.-H. Yueh, AIMS Math., Vol. 9(7), 19414–19445, 12 June 2024.

📑 BibTeX

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

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}
    }

• 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.

📑 BibTeX

@article{Sutti_Vanzan:2026,
      author  = {Sutti, M. and Vanzan, T.},
      title   = {{N}onlinear {S}chwarz methods to compute geodesics on manifolds},
      journal = {Lecture Notes in Computational Science and Engineering},
      month   = {Jul},
      year    = {2026},
      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.

📑 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}
    }

• 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}
    }

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}
    }

• 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}
    }

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.

📑 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}
    }

Animations

Below, you can see two animations realized with SPHM.