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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Vydané v:	Journal of numerical analysis and approximation theory Ročník 54; číslo 1; s. 42 - 61
Hlavný autor:	Conboye, Rory
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Publishing House of the Romanian Academy 30.06.2025
Predmet:	Numerical Ricci flow, piecewise flat, linear stability
ISSN:	2457-6794, 2501-059X
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Shrnutí:	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