Numerical Convergence of Discrete Exterior Calculus on Arbitrary Surface\n Meshes

2018/02/13 by Mamdouh S. Mohamed, Mohamed, Mamdouh S., Anil N. Hirani +3 · 2 citations
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1802.04506

openalex publication_date 2018/02/13 · openalex created_date 2022/08/18 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Parallelisation of Discrete Exterior Calculus via Representation Theory on Curved and Three-Dimensional Meshes
• A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms

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