Determinant of the Finite Volume Laplacian

Thomas Doehrman, David Glickenstein

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
JournalDiscrete and Computational Geometry
DOIs
StateAccepted/In press - 2022

Keywords

  • Determinant
  • Finite volume
  • Laplacian

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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