Dr. Lennard Kamenski

Publications Research Teaching Talks CV Contact


Reseach listings in: AMS MathSciNet, Google Scholar, arXiv.

Books

  1. Numerical Geometry, Grid Generation and Scientific Computing
    V. A. Garanzha, L. Kamenski, and H. Si (Eds.),
    Lecture Notes in Computational Science and Engineering, Vol. 131 (2019),
    Springer International Publishing.

Research articles

  1. L. Kamenski:
    On the smallest eigenvalue of finite element equations with meshes without regularity assumptions,
    Submitted, arXiv:1908.03460.

  2. K. Gärtner and L. Kamenski:
    Why do we need Voronoi cells and Delaunay meshes? Essential properties of the Voronoi finite volume method.
    Comput. Math. Math. Phys. 59 (12) (2019), pp. 1930–1944, arXiv:1905.01738v2.
  3. K. Gärtner and L. Kamenski:
    Why do we need Voronoi cells and Delaunay meshes?
    Numerical Geometry, Grid Generation and Scientific Computing (NUMGRID-2018),
    Lect. Notes Comput. Sci. Eng. 131 (2019), pp. 45–60, arXiv:1905.01738v1.
  4. W. Huang, L. Kamenski, and J. Lang:
    Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes,
    J. Comput. Appl. Math. (2019) 112497, arXiv:1703.06463.
  5. F. Dassi, L. Kamenski, P. Farrell, and H. Si:
    Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction,
    Comput.-Aided Des. 103 (2018), pp. 2–13, arXiv:1703.07007.
  6. W. Huang and L. Kamenski:
    On the mesh nonsingularity of the moving mesh PDE method,
    Math. Comp. 87 (2018), pp. 1887–1911, arXiv:1512.04971.
  7. F. Dassi, L. Kamenski, and H. Si:
    Tetrahedral mesh improvement using moving mesh smoothing and lazy searching flips,
    Procedia Eng. 163 (2016), pp. 302–314, WIAS Preprint No. 2270 (2016).
    IMR Best Technical Paper Award.
  8. W. Huang, L. Kamenski, and J. Lang:
    Stability of explicit one-step methods for P1-finite element approximation of linear diffusion equations on anisotropic meshes,
    SIAM J. Numer. Anal. 54 (3) (2016), pp. 1612–1634, WIAS Preprint 1869 (2013), arXiv:1602.08055.
  9. W. Huang, L. Kamenski, and J. Lang:
    Stability of explicit Runge-Kutta methods for high order FE approximation of linear parabolic equations,
    Numerical Mathematics and Advanced Appllications — ENUMATH 2013,
    Lect. Notes Comput. Sci. Eng. 103, Springer, Berlin (2015), pp. 165–173, WIAS Preprint 1904 (2013), arXiv:1908.05374.
  10. W. Huang, L. Kamenski, and R. D. Russell:
    A comparative numerical study of meshing functionals for variational mesh adaptation,
    J. Math. Study 48 (2) (2015), pp. 168–186, WIAS Preprint No. 2086 (2015), arXiv:1503.04709.
  11. W. Huang and L. Kamenski:
    A geometric discretization and a simple implementation for variational mesh generation and adaptation,
    J. Comput. Phys. 301 (2015), pp. 322–337, WIAS Preprint No. 2035 (2014), arXiv:1410.7872.
  12. L. Kamenski and W. Huang:
    A study on the conditioning of FE equations with arbitrary anisotropic meshes via a density function approach,
    J. Math. Study 47 (2) (2014), pp. 151–172, arXiv:1302.6868.
  13. L. Kamenski and W. Huang:
    How a nonconvergent recovered Hessian works in mesh adaptation,
    SIAM J. Numer. Anal. 52 (4) (2014), pp. 1692–1708, arXiv:1211.2877.
  14. L. Kamenski, W. Huang, and H. Xu:
    Conditioning of finite elements equations with arbitrary anisotropic meshes,
    Math. Comp. 83 (2014), pp. 2187–2211, arXiv:1201.3651.
  15. W. Huang, L. Kamenski, and J. Lang:
    Adaptive finite elements with anisotropic meshes,
    Numerical Mathematics and Advanced Appllications 2011 (2013), pp. 33–42, arXiv:1201.4090.
  16. L. Kamenski:
    A study on using hierarchical basis error estimates in anisotropic mesh adaptation for the FE method,
    Eng. Comput. 28 (4) (2012), pp. 451–460, arXiv:1106.6031.
  17. W. Huang, L. Kamenski, and J. Lang:
    A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates,
    J. Comput. Phys. 229 (6) (2010), pp. 2179–2198, TU Darmstadt Preprint 2570 (2008), arXiv:1908.04242.
  18. L. Kamenski:
    A study on using hierarchical basis error estimates in anisotropic mesh adaptation for the FE method,
    Proceedings of the 19th International Meshing Roundtable (2010), pp. 297–314, eprint (pdf).
    Corrigendum: p. 13, Sect. 5, $\theta$ in the diffusion matrix $\mathbb{D}$: correct is $\theta = \pi \sin x \cos y$, (not $\pi/4$).
  19. W. Huang, L. Kamenski and X. Li:
    Anisotropic mesh adaptation for variational problems using error estimation based on hierarchical bases,
    Canad. Appl. Math. Q. 17 (3) (2009), pp. 501–522, arXiv:1006.0191.

Research notes

  1. W. Huang, L. Kamenski, and H. Si:
    Mesh smoothing: an MMPDE approach,
    Research Note, 24th International Meshing Roundtable (2015), WIAS Preprint 2130 (2015).
  2. L. Kamenski and H. Si:
    A study on generation of M-uniform tetrahedral meshes in practice,
    Research Note, 22nd International Meshing Roundtable (2013).
  3. W. Huang, L. Kamenski, and J. Lang:
    A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates,
    Research Note, 18th International Meshing Roundtable (2009).

Miscellaneous

Theses