In Beirão da Veiga et al. 2019, the authors proposed a virtual element method for domains with fixed curved boundary that tends to be locally straight when the discretisation gets finer and finer. In this paper, we properly modify this method so that it can also deal with curved mesh edges which are not necessarily located along boundaries and do not tend to be straight when refining the mesh. To achieve this goal, we assume that curved edges are described by polynomials and we increase the dimension of the virtual element space used in Beirão da Veiga et al. 2019. In the numerical experiments, we compare these two methods. Furthermore, we apply the proposed approach to the benchmark “TEAM 25” problem, an optimal shape design problem in magnetostatics characterised by curved edges.

Dassi, F., Di Barba, P. (2024). Enriched Virtual Element space on curved meshes with an application in magnetics. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 161(1 May 2024), 43-50 [10.1016/j.camwa.2024.02.036].

Enriched Virtual Element space on curved meshes with an application in magnetics

Dassi, F.;
2024

Abstract

In Beirão da Veiga et al. 2019, the authors proposed a virtual element method for domains with fixed curved boundary that tends to be locally straight when the discretisation gets finer and finer. In this paper, we properly modify this method so that it can also deal with curved mesh edges which are not necessarily located along boundaries and do not tend to be straight when refining the mesh. To achieve this goal, we assume that curved edges are described by polynomials and we increase the dimension of the virtual element space used in Beirão da Veiga et al. 2019. In the numerical experiments, we compare these two methods. Furthermore, we apply the proposed approach to the benchmark “TEAM 25” problem, an optimal shape design problem in magnetostatics characterised by curved edges.
Articolo in rivista - Articolo scientifico
Curved meshes; Magnetic field; Virtual elements;
English
28-feb-2024
2024
161
1 May 2024
43
50
none
Dassi, F., Di Barba, P. (2024). Enriched Virtual Element space on curved meshes with an application in magnetics. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 161(1 May 2024), 43-50 [10.1016/j.camwa.2024.02.036].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/461743
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
Social impact