Stability of piecewise flat Ricci flow in three dimensions

For a recently developed piecewise flat approximation of the Ricci flow, numerical instabilities are seen to arise for a particularly useful class of mesh-types. Here, a geometrically motivated adaptation to these meshes is introduced, and a linear stability analysis and numerical simulations used t...

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Veröffentlicht in:	Journal of numerical analysis and approximation theory Jg. 54; H. 1; S. 42 - 61
1. Verfasser:	Conboye, Rory
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Publishing House of the Romanian Academy 30.06.2025
Schlagworte:	Numerical Ricci flow, piecewise flat, linear stability
ISSN:	2457-6794, 2501-059X
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	For a recently developed piecewise flat approximation of the Ricci flow, numerical instabilities are seen to arise for a particularly useful class of mesh-types. Here, a geometrically motivated adaptation to these meshes is introduced, and a linear stability analysis and numerical simulations used to show that the instability is then suppressed. These adapted meshes have also been successfully used in a recently published paper to show the convergence of the piecewise flat Ricci flow to known smooth Ricci flow solutions for a variety of manifolds.
ISSN:	2457-6794 2501-059X
DOI:	10.33993/jnaat541-1549