On the numerical computation of Killing and conformally Killing vector fields on compact Riemannian manifolds
Numerical Analysis
2020-02-24 v2 Numerical Analysis
Differential Geometry
Abstract
The defining equations for Killing vector fields and conformal Killing vector fields are overdetermined systems of PDE. This makes it difficult to solve the systems numerically. We propose an approach which reduces the computation to the solution of a symmetric eigenvalue problem. The eigenvalue problem is then solved by finite element techniques. The formulation itself is valid in any dimension and for arbitrary compact Riemannian manifolds. The numerical results which validate the method are given in two dimensional case.
Keywords
Cite
@article{arxiv.1903.02763,
title = {On the numerical computation of Killing and conformally Killing vector fields on compact Riemannian manifolds},
author = {Gaëlle Brunet and Maryam Samavaki and Jukka Tuomela},
journal= {arXiv preprint arXiv:1903.02763},
year = {2020}
}