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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2025-06-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1549 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849228792820662272 |
|---|---|
| author | Rory Conboye |
| author_facet | Rory Conboye |
| author_sort | Rory Conboye |
| collection | DOAJ |
| description |
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.
|
| format | Article |
| id | doaj-art-530ff509d3d34ce28029eeb8e8f84306 |
| institution | Kabale University |
| issn | 2457-6794 2501-059X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj-art-530ff509d3d34ce28029eeb8e8f843062025-08-22T15:39:18ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2025-06-0154110.33993/jnaat541-1549Stability of piecewise flat Ricci flow in three dimensionsRory Conboye0https://orcid.org/0000-0002-6463-2029Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue NW, Washington, DC 20016, USA. Current Address: Department of Mathematics, Munster Technological University, Bishopstown, Cork, T12 P928, Ireland 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. https://ictp.acad.ro/jnaat/journal/article/view/1549Numerical Ricci flow, piecewise flat, linear stability |
| spellingShingle | Rory Conboye Stability of piecewise flat Ricci flow in three dimensions Journal of Numerical Analysis and Approximation Theory Numerical Ricci flow, piecewise flat, linear stability |
| title | Stability of piecewise flat Ricci flow in three dimensions |
| title_full | Stability of piecewise flat Ricci flow in three dimensions |
| title_fullStr | Stability of piecewise flat Ricci flow in three dimensions |
| title_full_unstemmed | Stability of piecewise flat Ricci flow in three dimensions |
| title_short | Stability of piecewise flat Ricci flow in three dimensions |
| title_sort | stability of piecewise flat ricci flow in three dimensions |
| topic | Numerical Ricci flow, piecewise flat, linear stability |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1549 |
| work_keys_str_mv | AT roryconboye stabilityofpiecewiseflatricciflowinthreedimensions |