Numerical convergence of discrete exterior calculus on arbitrary surface meshes |
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Authors: | Mamdouh S Mohamed Anil N Hirani Ravi Samtaney |
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Affiliation: | 1. Mechanical Engineering, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;2. Department of Mathematics, University of Illinois at Urbana-Champaign, IL, USA |
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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. |
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Keywords: | Discrete exterior calculus (DEC) Hodge star incompressible Navier–Stokes equations non-Delaunay mesh Poisson equation structure-preserving discretizations |
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