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Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism
Abstract
It has been recognised that numerical computations of magnetic fields by the finite-element method may require new types of elements, whose degrees of freedom are not field values at mesh nodes, but other field-related quantities like e.g. circulations along edges of the mesh. A rationale for the use of these special ‘mixed’ elements can be obtained if one cxpresses basic equations in terms of differential forms, instead of vector fields. The paper gives an elementary introduction to this point of view, presents Whitney forms (the mixed finite elements alluded to), and sketches two numerical methods (dual, in some sense), for eddy-current studies, based on these elements.
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Citations
Cited by
Multigrid Method for Maxwell's Equations
Hiptmair, R. (1998) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142997326203 · Cited by 403
Enhancement of Light Extraction from Light Emitting Diodes
Zhmakin, A. I. (2011) · Physics Reports · doi:10.1016/j.physrep.2010.11.001 · Cited by 312
Metadata
- Authors
- Bossavit, A.
- Venue
- IEE Proceedings A Physical Science, Measurement and Instrumentation, Management and Education, Reviews
- Published
- 1988
- Volume
- 135
- Issue
- 8
- Pages
- 493
- ISSN
- 0143-702X (ISSN-L)
- OpenAlex
- W4242566991
- Cited by
- 524
- References
- 0
- FWCI
- 3.05
- Type
- journal article
- Language
- en
- Open access
- closed
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- Bossavit, A. (1988). Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism. IEE Proceedings A Physical Science, Measurement and Instrumentation, Management and Education, Reviews. https://doi.org/10.1049/ip-a-1.1988.0077
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
