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An issue on the surface integrals with face decomposition in the virtual element method and its improvement without the decomposition
Ist Teil von
Computer methods in applied mechanics and engineering, 2024-08, Vol.428, p.117107, Article 117107
Ort / Verlag
Elsevier B.V
Erscheinungsjahr
2024
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
The Virtual Element Method (VEM) is a promising approach developed in recent years. Within the energy-based framework of the VEM, we can directly compute the consistency and stabilization terms by automatically differentiating the separation of the energy functional. Surface integrals are involved in computing the consistency matrix, and we find that the results depend on the element-partitioning schemes for these integrals. Partitioning scheme that introduces facial centroids works well, but it can only be applied to star-convex polygons. Other partitioning schemes without introducing centroids cause significant errors since the integration weights are not computed from all nodes of the surface. In this paper, we provide a detailed derivation to illustrate these discrepancies. To overcome this challenge, we implement an integration scheme without element-partitioning, which converting the surface integrals into line integrals using a recursive procedure. We employ four examples to demonstrate the effectiveness of the proposed method for both convex and concave polyhedra.