Numerical convergence of discrete exterior calculus on arbitrary surface meshes

Mamdouh S. Mohamed, Anil N. Hirani, Ravi Samtaney

Research output: Contribution to journalArticlepeer-review

Abstract

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.

Original languageEnglish (US)
Pages (from-to)194-206
Number of pages13
JournalInternational Journal of Computational Methods in Engineering Science and Mechanics
Volume19
Issue number3
DOIs
StatePublished - May 4 2018

Keywords

  • Discrete exterior calculus (DEC)
  • Hodge star
  • Poisson equation
  • incompressible Navier–Stokes equations
  • non-Delaunay mesh
  • structure-preserving discretizations

ASJC Scopus subject areas

  • Computational Mechanics
  • Computational Mathematics

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