Stability of piecewise flat Ricci flow in three dimensions
DOI:
https://doi.org/10.33993/jnaat541-1549Keywords:
Numerical Ricci flow, piecewise flat, linear stabilityAbstract
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.
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