On a general implementation of h- and p-adaptive curl-conforming finite elements
Visualitza/Obre
10.1016/j.advengsoft.2019.03.006
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/130851
Tipus de documentArticle
Data publicació2019-06
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
Edge (or Nédélec) finite elements are theoretically sound and widely used by the computational electromagnetics community. However, its implementation, especially for high order methods, is not trivial, since it involves many technicalities that are not properly described in the literature. To fill this gap, we provide a comprehensive description of a general implementation of edge elements of first kind within the scientific software project FEMPAR . We cover into detail how to implement arbitrary order (i.e., p-adaptive) elements on hexahedral and tetrahedral meshes. First, we set the three classical ingredients of the finite element definition by Ciarlet, both in the reference and the physical space: cell topologies, polynomial spaces and moments. With these ingredients, shape functions are automatically implemented by defining a judiciously chosen polynomial pre-basis that spans the local finite element space combined with a change of basis to automatically obtain a canonical basis with respect to the moments at hand. Next, we discuss global finite element spaces putting emphasis on the construction of global shape functions through oriented meshes, appropriate geometrical mappings, and equivalence classes of moments, in order to preserve the inter-element continuity of tangential components of the magnetic field. Finally, we extend the proposed methodology to generate global curl-conforming spaces on non-conforming hierarchically refined (i.e., h-adaptive) meshes with arbitrary order finite elements. Numerical results include experimental convergence rates to test the proposed implementation.
CitacióOlm, M.; Badia, S.; Martín, A. F. On a general implementation of h- and p-adaptive curl-conforming finite elements. "Advances in engineering software", Juny 2019, vol. 132, p. 1-29.
ISSN0965-9978
Versió de l'editorhttps://www.sciencedirect.com/science/article/pii/S096599781831113X
Altres identificadorshttps://arxiv.org/abs/1810.10314
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art032.pdf | final draft post-refereeing | 2,461Mb | Visualitza/Obre |