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Title: Determinant of the Finite Volume Laplacian
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.  more » « less
Award ID(s):
1760538
PAR ID:
10469775
Author(s) / Creator(s):
;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Discrete & Computational Geometry
ISSN:
0179-5376
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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