Thermal Block - Revision history

Schuetz2 at 05:41, 17 June 2025

2025-06-17T05:41:00Z

← Older revision		Revision as of 05:41, 17 June 2025
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	:: S. Rave and J. Saak, '''Thermal Block'''. MORwiki - Model Order Reduction Wiki, 2020. ~~http~~://modelreduction.org/~~index.php~~/Thermal_Block		:: S. Rave and J. Saak, '''Thermal Block'''. MORwiki - Model Order Reduction Wiki, 2020. https://modelreduction.org/morwiki/Thermal_Block

	@MISC{morwiki_thermalblock,		@MISC{morwiki_thermalblock,
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	title = {Thermal Block},		title = {Thermal Block},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Thermal_Block}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Thermal_Block}</nowiki>,
	year = 2020		year = 2020
	}		}

Malhotra: infobox string

2023-11-30T09:42:29Z

infobox string

← Older revision		Revision as of 09:42, 30 November 2023
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	[[Category:MIMO]]		[[Category:MIMO]]
	[[Category:Sparse]]		[[Category:Sparse]]

			{{Infobox
			\|Title = Thermal Block
			\|Benchmark ID = thermalBlock_n7488m1q4
			\|Category = misc
			\|System-Class = AP-LTI-FOS
			\|nstates = 7488
			\|ninputs = 1
			\|noutputs = 4
			\|nparameters = 4
			\|components = A, B, C, E
			\|License = BSD 2-Clause "Simplified" License
			\|Creator = [[User:Saak]]
			\|Editor =
			* [[User:Saak]]
			* [[User:Himpe]]
			* [[User:Mlinaric]]
			\|Zenodo-link = https://zenodo.org/record/3691894/files/ABCE.mat
			}}

Lund: /* Dimensions */ re-index

2023-05-09T14:44:06Z

Dimensions: re-index

← Older revision		Revision as of 14:44, 9 May 2023
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	:<math>		:<math>
	\begin{align}		\begin{align}
	E\dot{x}(t) &= (~~A_0~~ + \mu_1 ~~A_1~~ + \mu_2 ~~A_2~~ + \mu_3 ~~A_3~~ + \mu_4 ~~A_4~~) x(t) + Bu(t), \\		E\dot{x}(t) &= (A_1 + \mu_1 A_2 + \mu_2 A_3 + \mu_3 A_4 + \mu_4 A_5) x(t) + Bu(t), \\
	y(t) &= Cx(t)		y(t) &= Cx(t)
	\end{align}		\end{align}
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	<math>E \in \mathbb{R}^{N \times N}</math>,		<math>E \in \mathbb{R}^{N \times N}</math>,
	<math>~~A_0 \in \mathbb~~{~~R}^{N \times N}</math>,~~		<math>A_{1,...,5} \in \mathbb{R}^{N \times N}</math>,
	~~<math>A_1 \in \mathbb{R}^{N \times N}</math>~~,
	~~<math>A_2 \in \mathbb{R}^{N \times N}</math>~~,
	~~<math>A_3 \in \mathbb{R}^{N \times N~~}~~</math>,~~
	~~<math>A_4~~ \in \mathbb{R}^{N \times N}</math>,
	<math>B \in \mathbb{R}^{N \times 1}</math>,		<math>B \in \mathbb{R}^{N \times 1}</math>,
	<math>C \in \mathbb{R}^{4 \times N}</math>,		<math>C \in \mathbb{R}^{4 \times N}</math>,

Himpe at 13:01, 25 August 2022

2022-08-25T13:01:45Z

← Older revision		Revision as of 13:01, 25 August 2022
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	[[Category:first differential order]]		[[Category:first differential order]]
	[[Category:time invariant]]		[[Category:time invariant]]
	~~[[Category:Parametric]]~~
	[[Category:MIMO]]		[[Category:MIMO]]
	[[Category:Sparse]]		[[Category:Sparse]]

Himpe at 13:01, 25 August 2022

2022-08-25T13:01:37Z

← Older revision		Revision as of 13:01, 25 August 2022
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	[[Category:first differential order]]		[[Category:first differential order]]
	[[Category:time invariant]]		[[Category:time invariant]]
	[[Category:~~parametric 2-5 parameters~~]]		[[Category:Parametric]]
	[[Category:MIMO]]		[[Category:MIMO]]
	[[Category:Sparse]]		[[Category:Sparse]]

Himpe: /* Citation */ Updated

2021-08-26T07:04:17Z

Citation: Updated

← Older revision		Revision as of 07:04, 26 August 2021
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	:: S. Rave and J. Saak, <span class="plainlinks">[https://arxiv.org/abs/2003.00846 '''A Non-Stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction''']. e-prints 2003.00846, arXiv, math.NA (2020).		:: S. Rave and J. Saak, <span class="plainlinks">[https://arxiv.org/abs/2003.00846 '''A Non-Stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction''']. e-prints 2003.00846, arXiv, math.NA (2020).

	@~~TECHREPORT~~{~~morRavS20~~,		@INPROCEEDINGS{morRavS21,
	author = {Rave, S. and Saak, J.},		author = {Rave, S. and Saak, J.},
	title = {A Non-Stationary Thermal-Block Benchmark Model for Parametric		title = {A Non-Stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction},
	Model Order Reduction},		booktitle = {Model Reduction of Complex Dynamical Systems},
	~~institution~~ = {~~arXiv~~},		series = {International Series of Numerical Mathematics},
	~~type~~ = {~~e-print~~},		volume = {171},
	~~number~~ = {~~2003.00846~~},		publisher = {Springer},
	~~note~~ = {~~math.NA~~},		year = 2021,
	year = ~~2020~~,		doi = {10.1007/978-3-030-72983-7_16}
	~~url~~ = ~~<nowiki>~~{~~https://arxiv~~.~~org~~/~~abs/2003.00846~~}~~</nowiki>~~
	}		}

Himpe: /* References */ Updated references

2021-08-26T07:00:57Z

References: Updated references

← Older revision		Revision as of 07:00, 26 August 2021
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	==References==		==References==
	<references>		<references>
	<ref name="morBenW20c">P. Benner, S. W. R. Werner, <span class="plainlinks">[https://~~arxiv~~.org/~~abs~~/~~2002.12682~~ MORLAB -- the Model Order Reduction LABoratory]</span>,		<ref name="morBenW20c">P. Benner, S. W. R. Werner, <span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_19 MORLAB -- the Model Order Reduction LABoratory]</span>,
	e-~~print 2002.12682~~, ~~arXiv, cs.MS (2020)~~.</ref>		Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 393--415, 2021.</ref>
	<ref name="morHim20">C. Himpe, <span class="plainlinks">[https://~~arxiv~~.org/~~abs~~/~~2002.12226~~ Comparing (empirical-Gramian-based) model order reduction algorithms]</span>, e-~~prints 2002.12226, arXiv~~, ~~math.OC (2020)~~.</ref>		<ref name="morHim20">C. Himpe, <span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_7 Comparing (empirical-Gramian-based) model order reduction algorithms]</span>,
	<ref name="morBenKS20">P. Benner, M. Köhler, J. Saak, <span class="plainlinks">[https://~~arxiv~~.org/~~abs~~/~~2003.02088~~ Matrix equations, sparse solvers: M-M.E.S.S.-2.0.1 – philosophy, features and application for (parametric) model order reduction]</span>, ~~eprints 2003.02088~~, ~~arXiv~~, ~~cs.MS (2020)~~.</ref>		Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 141--164, 2021.</ref>
	<ref name="morRavS20">S. Rave, J. Saak, <span class="plainlinks">[https://~~arxiv~~.org/~~abs~~/~~2003.00846~~ An ~~Instationary~~ Thermal-Block Benchmark Model for Parametric Model Order Reduction]</span>, e-~~prints 2003.00846, arXiv~~, ~~math.NA (2020)~~.</ref>		<ref name="morBenKS20">P. Benner, M. Köhler, J. Saak, <span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_18 Matrix equations, sparse solvers: M-M.E.S.S.-2.0.1 – philosophy, features and application for (parametric) model order reduction]</span>, Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 369--392, 2021.</ref>
	<ref name="morMliRS20">P. Mlinarić, S. Rave, J. Saak, <span class="plainlinks">[https://~~arxiv~~.org/~~abs~~/~~2003.05825~~ Parametric model order reduction using pyMOR]</span>, e-~~prints 2003.05825~~, ~~arXiv, cs.MS (2020)~~.</ref>		<ref name="morRavS20">S. Rave, J. Saak, <span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_16 An Non-Stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction]</span>, Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 349-356, 2021.</ref>
	</references>		<ref name="morMliRS20">P. Mlinarić, S. Rave, J. Saak, <span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_17 Parametric model order reduction using pyMOR]</span>, Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 357--367 , 2021.</ref>
			</references>

	==Contact==		==Contact==
	'' [[User:Saak]]''		'' [[User:Saak]]''

Mlinaric: Fix typos

2020-10-27T12:25:28Z

Fix typos

← Older revision		Revision as of 12:25, 27 October 2020
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	==Description==		==Description==
	A parametric semi-discretized heat transfer problem with varying heat transfer coefficients, the parameters, on subdomains. This model is also called ''cookie baking problem'', and can be viewed as a flattened 2-D version of the ''skyscraper problem'' from high performance computing.		A parametric semi-discretized heat transfer problem with varying heat transfer coefficients, the parameters, on subdomains. This model is also called the ''cookie baking problem'', and can be viewed as a flattened 2-D version of the ''skyscraper problem'' from high-performance computing.

	<figure id="fig1">[[File:ThermalBlockDomain.svg\|490px\|thumb\|right\|<caption>The computational domain and boundaries.</caption>]]</figure>		<figure id="fig1">[[File:ThermalBlockDomain.svg\|490px\|thumb\|right\|<caption>The computational domain and boundaries.</caption>]]</figure>
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	==Data==		==Data==
	The benchmark includes the basic domain description as a gmsh input file, Python scripts for the matrix assembly, simulation in pyMOR and visualization as VTK, together with the matrices both as one combined file <code>ABCE.mat</code> or separate matrix market files for all matrices. The sources and the <code>ABCE.mat</code> are available for download at [https://doi.org/10.5281/zenodo.3691894 Zenodo].		The benchmark includes the basic domain description as a gmsh input file, Python scripts for the matrix assembly, simulation in pyMOR, and visualization as VTK, together with the matrices both as one combined file <code>ABCE.mat</code> or separate matrix market files for all matrices. The sources and the <code>ABCE.mat</code> are available for download at [https://doi.org/10.5281/zenodo.3691894 Zenodo].

	Note that the heat transfer coefficients are designed as characteristic functions on the domains, such that the system is only well-posed when all entries in <math>\mu</math> are positive.		Note that the heat transfer coefficients are designed as characteristic functions on the domains, such that the system is only well-posed when all entries in <math>\mu</math> are positive.
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	* For the background on the benchmark:		* For the background on the benchmark:
	:: S. Rave and J. Saak, <span class="plainlinks">[https://arxiv.org/abs/2003.00846 '''A Non-~~Sstationary~~ Thermal-Block Benchmark Model for Parametric Model Order Reduction''']. e-prints 2003.00846, arXiv, math.NA (2020).		:: S. Rave and J. Saak, <span class="plainlinks">[https://arxiv.org/abs/2003.00846 '''A Non-Stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction''']. e-prints 2003.00846, arXiv, math.NA (2020).

	@TECHREPORT{morRavS20,		@TECHREPORT{morRavS20,

Saak: /* Citation */

2020-06-05T06:00:47Z

Citation

← Older revision		Revision as of 06:00, 5 June 2020
Line 97:		Line 97:

	* For the background on the benchmark:		* For the background on the benchmark:
	:: S. Rave and J. Saak, <span class="plainlinks">[https://arxiv.org/abs/2003.00846 '''~~An Instationary~~ Thermal-Block Benchmark Model for Parametric Model Order Reduction''']. e-prints 2003.00846, arXiv, math.NA (2020).		:: S. Rave and J. Saak, <span class="plainlinks">[https://arxiv.org/abs/2003.00846 '''A Non-Sstationary Thermal-Block Benchmark Model for Parametric Model Order Reduction''']. e-prints 2003.00846, arXiv, math.NA (2020).

	@TECHREPORT{morRavS20,		@TECHREPORT{morRavS20,

Saak: /* Citation */

2020-06-05T06:00:15Z

Citation

← Older revision		Revision as of 06:00, 5 June 2020
Line 101:		Line 101:
	@TECHREPORT{morRavS20,		@TECHREPORT{morRavS20,
	author = {Rave, S. and Saak, J.},		author = {Rave, S. and Saak, J.},
	title = {~~An Instationary~~ Thermal-Block Benchmark Model for Parametric		title = {A Non-Stationary Thermal-Block Benchmark Model for Parametric
	Model Order Reduction},		Model Order Reduction},
	institution = {arXiv},		institution = {arXiv},