Virtual element approximation of magnetostatic | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Virtual element approximation of magnetostatic

By Donatella Marini

Appears in collection : POEMs - POlytopal Element Methods in Mathematics and Engineering

We present a lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic eld H on each edge, and the vertex values of the Lagrange multiplier p (used to enforce the solenoidality of the magnetic induction B = µH). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called ”first kind N´ed´elec” elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions. Hints on a whole family of elements will also be given.

Information about the video

Date of recording 29/04/2019
Date of publication 28/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19528503
Cite this video Marini, Donatella (29/04/2019). Virtual element approximation of magnetostatic. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19528503
URL https://dx.doi.org/10.24350/CIRM.V.19528503

Domain(s)

Numerical Analysis

Bibliography

DA VEIGA, L. Beirao, BREZZI, F., DASSI, F., et al. Virtual element approximation of 2d magnetostatic problems. Computer Methods in Applied Mechanics and Engineering, 2017, vol. 327, p. 173-195. - https://doi.org/10.1016/j.cma.2017.08.013
KIKUCHI, Fumio. Mixed formulations for finite element analysis of magnetostatic and electrostatic problems. Japan Journal of Applied Mathematics, 1989, vol. 6, no 2, p. 209. - [ DOI https://doi.org/10.1007/BF03167879ISTEX ]( DOI https://doi.org/10.1007/BF03167879ISTEX )
BEIRÃO DA VEIGA, L., BREZZI, F., DASSI, F., et al. A family of three-dimensional virtual elements with applications to magnetostatic. arXiv preprint arXiv:1804.10497, 2018. - https://arxiv.org/abs/1804.10497

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2024

Give feedback