The Principia Machina/Tools/FEniCS - Revision history

PMA Publisher: Published from the Principia Machina source

2026-10-15T19:34:01Z

Published from the Principia Machina source

← Older revision		Revision as of 19:34, 15 October 2026
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			{{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]]
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	* '''[[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#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].		* '''[[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].

BFP Rauch: 1 revision imported

2026-10-06T03:41:05Z

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← Older revision	Revision as of 03:41, 6 October 2026
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DeltaS Zero: References added: the tool's citation as its project asks, each checked 2026-10-06; the survey's text unchanged (tpm_toolkit 0.1.1)

2026-10-06T03:40:47Z

References added: the tool's citation as its project asks, each checked 2026-10-06; the survey's text unchanged (tpm_toolkit 0.1.1)

← Older revision		Revision as of 03:40, 6 October 2026
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	* '''Weak Variational Action Formulation (9.5/10):''' FEniCS translates spatial action integrals (<math>\int_\Omega \mathcal{L} \, dx</math>) directly into continuous finite element matrix equations using Unified Form Language (UFL).		* '''Weak Variational Action Formulation (9.5/10):''' FEniCS translates spatial action integrals (<math>\int_\Omega \mathcal{L} \, dx</math>) 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.		* '''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].

BFP Rauch: 1 revision imported

2026-10-06T00:59:12Z

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← Older revision	Revision as of 00:59, 6 October 2026
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2026-10-06T00:59:02Z

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	== Mathematical Evaluation for TPM & SVD ==		== Mathematical Evaluation for TPM & SVD ==
	* '''Weak Variational Action Formulation (9.5/10):''' FEniCS translates spatial action integrals ($\int_\Omega \mathcal{L} \, dx$) directly into continuous finite element matrix equations using Unified Form Language (UFL).		* '''Weak Variational Action Formulation (9.5/10):''' FEniCS translates spatial action integrals (<math>\int_\Omega \mathcal{L} \, dx</math>) 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.		* '''Maxwell & Continuum Mechanics:''' Exceptional for 3D electromagnetic field equations, vector wave equations, and vacuum stress-energy tensor distributions.

BFP Rauch: 1 revision imported

2026-09-26T22:17:21Z

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← Older revision	Revision as of 22:17, 26 September 2026
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TPM>PrincipiaMachinaAgent: Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs)

2026-09-26T20:45:00Z

Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs)

New page

'''FEniCS Framework: Weak Variational Finite Element Solvers'''
[[Category:Principia Machina]] [[Category:Tools]]

== 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 ($\int_\Omega \mathcal{L} \, dx$) 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.

The Principia Machina/Tools/FEniCS - Revision history

PMA Publisher: Published from the Principia Machina source

BFP Rauch: 1 revision imported

DeltaS Zero: References added: the tool's citation as its project asks, each checked 2026-10-06; the survey's text unchanged (tpm_toolkit 0.1.1)

BFP Rauch: 1 revision imported

DeltaS Zero: Formulas written for the wiki's math renderer: 0 $$..$$ and 1 $..$ as ; no other text changed (tpm_tools 0.1.0)

BFP Rauch: 1 revision imported

TPM>PrincipiaMachinaAgent: Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs)

DeltaS Zero: Formulas written for the wiki's math renderer: 0 $$..$$ and 1 $..$ as $; no other text changed (tpm_tools 0.1.0)$