Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Robert Nürnberg"'
We propose a deep learning method for the numerical solution of partial differential equations that arise as gradient flows. The method relies on the Brezis--Ekeland principle, which naturally defines an objective function to be minimized, and so is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::156df5b50a7357db7c4d1c478879a2a7
http://arxiv.org/abs/2209.14115
http://arxiv.org/abs/2209.14115
Autor:
Klaus Deckelnick, Robert Nürnberg
Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler app
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f8c88e4432429773ed01f4180a443808
http://arxiv.org/abs/2209.06565
http://arxiv.org/abs/2209.06565
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first fabricates a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a9bc8fc0297e58d7c48a99e17f65db9
http://arxiv.org/abs/2207.03706
http://arxiv.org/abs/2207.03706
Publikováno v:
ESAIM: Mathematical Modelling and Numerical Analysis. 55:833-885
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the classical Willmore energy: the integral of the squared mean curvature. This geometric evolution law is of interest in differential geometry, image reco
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80be30ad265758533f2c6b73603dbdc8
https://doi.org/10.1051/m2an/2021014
https://doi.org/10.1051/m2an/2021014
Autor:
Robert Nürnberg, Klaus Deckelnick
Publikováno v:
SIAM Journal on Numerical Analysis. 59:2698-2721
We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a parameterization o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf06a05a18c990913fdb567a3ae44333
https://doi.org/10.1137/20m1374584
https://doi.org/10.1137/20m1374584
Autor:
Robert Nürnberg
We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins--Sekerka problem. The discretization uses finite elemen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c0a0c417d63e30317aa704cf49f65dcf
http://arxiv.org/abs/2111.15418
http://arxiv.org/abs/2111.15418
Publikováno v:
SIAM Journal on Numerical Analysis. 57:1987-2018
The elastic flow, which is the $L^2$-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fc0d9b535e6f9db5fb5317ed2d1d87f
https://doi.org/10.1137/18m1227111
https://doi.org/10.1137/18m1227111
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during constructio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d6a9e10fb6eb00a7f6fe55122eebcc6
Autor:
Harald Garcke, Robert Nürnberg
We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open curves we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::980dcac5e7da5ed459abaa138bb3b490
http://arxiv.org/abs/2012.02707
http://arxiv.org/abs/2012.02707
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature. The approa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d5daba06fb42f525b41b08bd87a9f131
https://doi.org/10.1016/bs.hna.2019.05.002
https://doi.org/10.1016/bs.hna.2019.05.002