The Principia Machina/Tools/FEniCS: Difference between revisions
m 1 revision imported |
Published from the Principia Machina source |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{DISPLAYTITLE:FEniCS Framework}} | |||
'''FEniCS Framework: Weak Variational Finite Element Solvers''' | '''FEniCS Framework: Weak Variational Finite Element Solvers''' | ||
[[Category:Principia Machina]] [[Category:Tools]] | [[Category:Principia Machina]] [[Category:Tools]] | ||
| Line 9: | Line 10: | ||
* '''Maxwell & Continuum Mechanics:''' Exceptional for 3D electromagnetic field equations, vector wave equations, and vacuum stress-energy tensor distributions. | * '''Maxwell & Continuum Mechanics:''' Exceptional for 3D electromagnetic field equations, vector wave equations, and vacuum stress-energy tensor distributions. | ||
== References == | |||
''Added on 2026-10-06 by the [[The Principia Machina/Research Toolkit|Research Toolkit]]: the tool's citations, each checked against the registry or the project's own page that day. The text above is the survey's own.'' | |||
The project's citing page now asks for the DOLFINx paper (first below), two Basix papers and the UFL paper, which are not listed here; the 2012 book and the FEniCS 1.5 paper are the earlier citations (checked 2026-10-06). | |||
* '''[[The Principia Machina/Research Toolkit/Bibliography#DOLFINX23|DOLFINX23]]''' – Baratta, I. A., Dean, J. P., Dokken, J. S., Habera, M., Hale, J. S., Richardson, C. N., Rognes, M. E., Scroggs, M. W., Sime, N., Wells, G. N. (2023). DOLFINx: The next generation FEniCS problem solving environment. Zenodo preprint v1, 31 Dec 2023. [https://doi.org/10.5281/zenodo.10447666 doi:10.5281/zenodo.10447666]. | |||
* '''[[The Principia Machina/Research Toolkit/Bibliography#FENICS15|FENICS15]]''' – Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M. E., Wells, G. N. (2015). The FEniCS Project Version 1.5. Archive of Numerical Software 3(100). [https://doi.org/10.11588/ans.2015.100.20553 doi:10.11588/ans.2015.100.20553]. | |||
* '''[[The Principia Machina/Research Toolkit/Bibliography#FENICS12|FENICS12]]''' – Logg, A., Mardal, K.-A., Wells, G. N. (eds.) (2012). Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. Springer, Lecture Notes in Computational Science and Engineering (ISSN 1439-7358). [https://doi.org/10.1007/978-3-642-23099-8 doi:10.1007/978-3-642-23099-8]. | |||
Latest revision as of 19:34, 15 October 2026
FEniCS Framework: Weak Variational Finite Element Solvers
Overview & Architectural Fit
The FEniCS Framework is an automated finite element library engineered to solve continuous spatial partial differential equations using weak variational formulations.
Mathematical Evaluation for TPM & SVD
- Weak Variational Action Formulation (9.5/10): FEniCS translates spatial action integrals () directly into continuous finite element matrix equations using Unified Form Language (UFL).
- Maxwell & Continuum Mechanics: Exceptional for 3D electromagnetic field equations, vector wave equations, and vacuum stress-energy tensor distributions.
References
Added on 2026-10-06 by the Research Toolkit: the tool's citations, each checked against the registry or the project's own page that day. The text above is the survey's own. The project's citing page now asks for the DOLFINx paper (first below), two Basix papers and the UFL paper, which are not listed here; the 2012 book and the FEniCS 1.5 paper are the earlier citations (checked 2026-10-06).
- DOLFINX23 – Baratta, I. A., Dean, J. P., Dokken, J. S., Habera, M., Hale, J. S., Richardson, C. N., Rognes, M. E., Scroggs, M. W., Sime, N., Wells, G. N. (2023). DOLFINx: The next generation FEniCS problem solving environment. Zenodo preprint v1, 31 Dec 2023. doi:10.5281/zenodo.10447666.
- FENICS15 – Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M. E., Wells, G. N. (2015). The FEniCS Project Version 1.5. Archive of Numerical Software 3(100). doi:10.11588/ans.2015.100.20553.
- FENICS12 – Logg, A., Mardal, K.-A., Wells, G. N. (eds.) (2012). Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. Springer, Lecture Notes in Computational Science and Engineering (ISSN 1439-7358). doi:10.1007/978-3-642-23099-8.