Nonlinear Heat Transfer - Revision history

Schuetz2 at 05:36, 17 June 2025

2025-06-17T05:36:23Z

← Older revision		Revision as of 05:36, 17 June 2025
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''Nonlinear Heat Transfer'''. MORwiki - Model Order Reduction Wiki, 2018. ~~http~~://modelreduction.org/~~index.php~~/Nonlinear_Heat_Transfer		::The MORwiki Community, '''Nonlinear Heat Transfer'''. MORwiki - Model Order Reduction Wiki, 2018. https://modelreduction.org/morwiki/Nonlinear_Heat_Transfer

	@MISC{morwiki_nheat,		@MISC{morwiki_nheat,
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	title = {Nonlinear Heat Transfer},		title = {Nonlinear Heat Transfer},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Nonlinear_Heat_Transfer}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Nonlinear_Heat_Transfer}</nowiki>,
	year = {20XX}		year = {20XX}
	}		}

Malhotra: infobox string

2023-11-30T09:34:19Z

infobox string

@@ Line 1: / Line 1: @@
 [[Category:benchmark]]
 [[Category:Oberwolfach]]
 ==Description==

Lund: /* Dimensions */ add F matrix

2023-04-24T16:43:51Z

Dimensions: add F matrix

← Older revision		Revision as of 16:43, 24 April 2023
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	:<math>		:<math>
	\begin{align}		\begin{align}
	E\dot{x}(t) &= Ax(t) + Bu(t) + f(x(t)) \\		E\dot{x}(t) &= Ax(t) + Bu(t) + F f(x(t)) \\
	y(t) &= Cx(t)		y(t) &= Cx(t)
	\end{align}		\end{align}
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	System dimensions:		System dimensions:

	~~<math>E \in \mathbb{R}^{N \times N}</math>,~~
	<math>A \in \mathbb{R}^{N \times N}</math>,		<math>A \in \mathbb{R}^{N \times N}</math>,
	<math>B \in \mathbb{R}^{N \times 2}</math>,		<math>B \in \mathbb{R}^{N \times 2}</math>,
	<math>C \in \mathbb{R}^{2 \times N}</math>,		<math>C \in \mathbb{R}^{2 \times N}</math>,
			<math>E \in \mathbb{R}^{N \times N}</math>,
			<math>F \in \mathbb{R}^{N \times N}</math>,
	<math>f : \mathbb{R}^N \to \mathbb{R}^N</math>.		<math>f : \mathbb{R}^N \to \mathbb{R}^N</math>.

Saak: /* Data */

2021-12-14T07:13:11Z

Data

← Older revision		Revision as of 07:13, 14 December 2021
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	\|+ style="caption-side:bottom;"\|		\|+ style="caption-side:bottom;"\|
	\|-		\|-
	\|[~~http~~://~~www2~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e1-n15-linear.zip NonlinearHeatTransfer-dim1e1-n15-linear.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e1-n15-linear.zip NonlinearHeatTransfer-dim1e1-n15-linear.zip]
	\|1 kB		\|1 kB
	\|-		\|-
	\|[~~http~~://~~www2~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e1-n15-nonlinear.zip NonlinearHeatTransfer-dim1e1-n15-nonlinear.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e1-n15-nonlinear.zip NonlinearHeatTransfer-dim1e1-n15-nonlinear.zip]
	\|1.2 kB		\|1.2 kB
	\|-		\|-
	\|[~~http~~://~~www2~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e2-n410-nonlinear.zip NonlinearHeatTransfer-dim1e2-n410-nonlinear.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e2-n410-nonlinear.zip NonlinearHeatTransfer-dim1e2-n410-nonlinear.zip]
	\|18.8 kB		\|18.8 kB
	\|}		\|}

Himpe: verify nonlinear heat transfer.

2018-07-27T08:05:54Z

verify nonlinear heat transfer.

← Older revision		Revision as of 08:05, 27 July 2018
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	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]
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	</math>		</math>

	We output of the model is the temperature <math>T(x,t)</math>, the degrees of freedom are the temperature from left to right.		The output of the model is the temperature <math>T(x,t)</math>, the degrees of freedom are the temperature from left to right.
	The right end of the beam (at <math>x=L</math>) is fixed at ambient temperature <math>0</math>;		The right end of the beam (at <math>x=L</math>) is fixed at ambient temperature <math>0</math>;
	this node does not occur in the model any more.		this node does not occur in the model any more.
	The model features two inputs: The first one is a time-dependent uniform heat flux <math>f</math> [W/m2] flowing in from the left end (at <math>x=0</math>).		The model features two inputs: The first one is a time-dependent uniform heat flux <math>f</math> [W/m<sup>2</sup>] flowing in from the left end (at <math>x=0</math>).
	The second one is a time dependent heat source <math>Q</math> [W/m3] in the beam volume, e.g. from an electric current.		The second one is a time dependent heat source <math>Q</math> [W/m<sup>3</sup>] in the beam volume, e.g. from an electric current.

	===Benchmark examples===		===Benchmark examples===
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	==Origin==		==Origin==

	This benchmark is part of the '''Oberwolfach Benchmark Collection'''<ref name="korvink2005"/>; No. 38883.		This benchmark is part of the '''Oberwolfach Benchmark Collection'''<ref name="korvink2005"/>; No. 38883, see <ref name="lienemann05"/>.

	==Data==		==Data==

	Details of the implementation are available in a separate report<ref name="~~lienemann05~~"/>.		Details of the implementation are available in a separate report<ref name="lienemann04"/>.
	A typical input to this system is a step response; periodic on/off switching is also possible.		A typical input to this system is a step response; periodic on/off switching is also possible.
	The reduced model should thus both represent the step response as well as the possible influence of higher order harmonics.		The reduced model should thus both represent the step response as well as the possible influence of higher order harmonics.
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	<tt>n15-nonlinear</tt>: <math>N = 15</math>,		<tt>n15-nonlinear</tt>: <math>N = 15</math>,
	<tt>n410-nonlinear</tt>: <math>N = 410</math>.		<tt>n410-nonlinear</tt>: <math>N = 410</math>.

			==Citation==

			To cite this benchmark, use the following references:

			* For the benchmark itself and its data:
			::The MORwiki Community, '''Nonlinear Heat Transfer'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Nonlinear_Heat_Transfer

			@MISC{morwiki_nheat,
			author = <nowiki>{{The MORwiki Community}}</nowiki>,
			title = {Nonlinear Heat Transfer},
			howpublished = {{MORwiki} -- Model Order Reduction Wiki},
			url = <nowiki>{http://modelreduction.org/index.php/Nonlinear_Heat_Transfer}</nowiki>,
			year = {20XX}
			}

			* For the background on the benchmark:

			@INPROCEEDINGS{LieYK04,
			author = <nowiki>{J. Lienemann, A. Yousefi, J.G. Korvink}</nowiki>,
			title = {Nonlinear heat transfer modelling},
			booktile = {12th Mediterranean Conference on Control and Automation},
			year = {2004}
			}



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	<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, In: Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>		<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, In: Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>

	<ref name="lienemann05"> J. Lienemann, A. Yousefi, J.G. Korvink, [https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer.pdf Nonlinear heat transfer modelling], 12th Mediterranean Conference on Control and Automation, 2004.</ref>		<ref name="lienemann05"> J. Lienemann, A. Yousefi, J.G. Korvink, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_13 Nonlinear Heat Transfer Modeling]</span>, In: Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 327--331, 2005.</ref>

			<ref name="lienemann04"> J. Lienemann, A. Yousefi, J.G. Korvink, [https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer.pdf Nonlinear heat transfer modelling], 12th Mediterranean Conference on Control and Automation, 2004.</ref>

	</references>		</references>

Himpe: /* References */

2018-07-17T10:41:11Z

References

← Older revision		Revision as of 10:41, 17 July 2018
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	<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, In: Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>		<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, In: Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>

	<ref name="lienemann05"> J. Lienemann, A. Yousefi, J.G. Korvink, [https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation/downloads/benchmark~~/~~Nonlinear%20heat%20transfer%20%2838883%29~~/~~files~~/~~fileinnercontentproxy.2010-02-05~~.~~0369225308~~ Nonlinear heat transfer modelling], 12th Mediterranean Conference on Control and Automation, 2004.</ref>		<ref name="lienemann05"> J. Lienemann, A. Yousefi, J.G. Korvink, [https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer.pdf Nonlinear heat transfer modelling], 12th Mediterranean Conference on Control and Automation, 2004.</ref>

	</references>		</references>

Himpe: /* Data */ Update benchmark data file links

2018-07-17T10:40:44Z

Data: Update benchmark data file links

← Older revision		Revision as of 10:40, 17 July 2018
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	\|+ style="caption-side:bottom;"\|		\|+ style="caption-side:bottom;"\|
	\|-		\|-
	\|[~~https~~://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Nonlinear%20heat%20transfer%20%2838883%29/files/fileinnercontentproxy.2010~~-02-05.~~0283505742 NonlinearHeatCond~~-n15-linear.zip]		\|[http://www2.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e1-n15-linear.zip NonlinearHeatTransfer-dim1e1-n15-linear.zip]
	\|1 kB		\|1 kB
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	\|[~~https~~://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Nonlinear%20heat%20transfer%20%2838883%29/files/fileinnercontentproxy.2010~~-02-05.~~0325677886 NonlinearHeatCond~~-n15-nonlinear.zip]		\|[http://www2.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e1-n15-nonlinear.zip NonlinearHeatTransfer-dim1e1-n15-nonlinear.zip]
	\|1.2 kB		\|1.2 kB
	\|-		\|-
	\|[~~https~~://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Nonlinear%20heat%20transfer%20%2838883%29/files/fileinnercontentproxy.2010~~-02-05.~~0347354187 NonlinearHeatCond~~-n410-nonlinear.zip]		\|[http://www2.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/NonlinearHeatTransfer-dim1e2-n410-nonlinear.zip NonlinearHeatTransfer-dim1e2-n410-nonlinear.zip]
	\|18.8 kB		\|18.8 kB
	\|}		\|}

Saak at 14:27, 6 March 2018

2018-03-06T14:27:42Z

← Older revision		Revision as of 14:27, 6 March 2018
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	[[Category:benchmark]]		[[Category:benchmark]]
			[[Category:Oberwolfach]]

	==Description==		==Description==

Saak: /* References */

2018-03-06T14:27:34Z

References

← Older revision		Revision as of 14:27, 6 March 2018
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	<references>		<references>

	<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>		<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, In: Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>

	<ref name="lienemann05"> J. Lienemann, A. Yousefi, J.G. Korvink, [https://portal.uni-freiburg.de/imteksimulation/downloads/benchmark/Nonlinear%20heat%20transfer%20%2838883%29/files/fileinnercontentproxy.2010-02-05.0369225308 Nonlinear heat transfer modelling], 12th Mediterranean Conference on Control and Automation, 2004.</ref>		<ref name="lienemann05"> J. Lienemann, A. Yousefi, J.G. Korvink, [https://portal.uni-freiburg.de/imteksimulation/downloads/benchmark/Nonlinear%20heat%20transfer%20%2838883%29/files/fileinnercontentproxy.2010-02-05.0369225308 Nonlinear heat transfer modelling], 12th Mediterranean Conference on Control and Automation, 2004.</ref>

	</references>		</references>

Himpe: Added dimension section and fixes

2018-03-01T09:55:21Z

Added dimension section and fixes

@@ Line 73: / Line 73: @@
 |<math>36</math>
 |}
 ====Nonlinear examples (heat conductivity temperature dependent)====
@@ Line 136: / Line 134: @@
 |<math>1.3852815 \cdot 10^{-10}</math>
 |}
 {| class="wikitable" style="margin: auto;"
@@ Line 197: / Line 193: @@
 |<math>1.3852815 \cdot 10^{-10}</math>
 |}
 The <tt>.m</tt> files contain matrices <math>E</math>, <math>A</math>, <math>B</math>, <math>F</math> and <math>C</math> and the vector <math>f</math> for the following system of equations:
@@ Line 234: / Line 228: @@
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 |}
 ==References==