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 language||English (US)|
|Number of pages||13|
|Journal||International Journal for Computational Methods in Engineering Science and Mechanics|
|State||Published - Apr 19 2018|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): URF/1/1401-01-01
Acknowledgements: This research was supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01-01.