Numerical convergence of discrete exterior calculus on arbitrary surface meshes
| العنوان: | Numerical convergence of discrete exterior calculus on arbitrary surface meshes |
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| المؤلفون: | Mamdouh S. Mohamed, Anil N. Hirani, Ravi Samtaney |
| المصدر: | International Journal for Computational Methods in Engineering Science and Mechanics. 19:194-206 |
| بيانات النشر: | Informa UK Limited, 2018. |
| سنة النشر: | 2018 |
| مصطلحات موضوعية: | Computational Mechanics, 010103 numerical & computational mathematics, 02 engineering and technology, Computer Science::Computational Geometry, 01 natural sciences, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, Convergence (routing), FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, medicine, Applied mathematics, Polygon mesh, Mathematics - Numerical Analysis, 0101 mathematics, Hodge dual, Calculus (medicine), ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, Partial differential equation, 020207 software engineering, Numerical Analysis (math.NA), Surface (topology), medicine.disease, Computational Mathematics, Discrete exterior calculus, Poisson's equation, MathematicsofComputing_DISCRETEMATHEMATICS |
| الوصف: | 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 on curved surfaces. This paper presents numerical evidences 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. |
| تدمد: | 1550-2295 1550-2287 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59410515f14e06c1d0f55d3737d5eeb0Test https://doi.org/10.1080/15502287.2018.1446196Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....59410515f14e06c1d0f55d3737d5eeb0 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15502295 15502287 |
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