Determinant of the finite volume Laplacian
Abstract
The finite volume Laplacian can be defined in all dimensions and is a natural way to approximate the operator on a simplicial mesh. In the most general setting, its definition with orthogonal duals may require that not all volumes are positive; an example is the case corresponding to two-dimensional finite elements on a non-Delaunay triangulation. Nonetheless, in many cases two- and three-dimensional Laplacians can be shown to be negative semidefinite with a kernel consisting of constants. This work generalizes work in two dimensions that gives a geometric description of the Laplacian determinant; in particular, it relates the Laplacian determinant on a simplex in any dimension to certain volume quantities derived from the simplex geometry.
Keywords
Cite
@article{arxiv.2108.07308,
title = {Determinant of the finite volume Laplacian},
author = {Thomas Doehrman and David Glickenstein},
journal= {arXiv preprint arXiv:2108.07308},
year = {2021}
}