Thermal Model - Revision history

Schuetz2 at 05:41, 17 June 2025

2025-06-17T05:41:26Z

← Older revision		Revision as of 05:41, 17 June 2025
Line 156:		Line 156:

	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	:: Oberwolfach Benchmark Collection, '''Thermal Model'''. hosted at MORwiki - Model Order Reduction Wiki, 2018. ~~http~~://modelreduction.org/~~index.php~~/Thermal_Model		:: Oberwolfach Benchmark Collection, '''Thermal Model'''. hosted at MORwiki - Model Order Reduction Wiki, 2018. https://modelreduction.org/morwiki/Thermal_Model

	@MISC{morwiki_thermal,		@MISC{morwiki_thermal,
Line 162:		Line 162:
	title = {Thermal Model},		title = {Thermal Model},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Thermal_Model}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Thermal_Model}</nowiki>,
	year = 20XX		year = 20XX
	}		}

Malhotra: infobox string

2023-11-30T09:42:48Z

infobox string

@@ Line 8: / Line 8: @@
 [[Category:MIMO]]
 [[Category:Sparse]]
 ==Description: Boundary Condition Independent Thermal Model==

Lund: /* Dimensions */ update with .mat indices

2023-04-26T12:48:52Z

Dimensions: update with .mat indices

← Older revision		Revision as of 12:48, 26 April 2023
Line 108:		Line 108:
	:<math>		:<math>
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A + ~~h_{top}A_{top}~~ + ~~h_{bottom}A_{bottom}~~ + ~~h_{side}A_{side}~~) x(t) + B \\		E \dot{x}(t) & = (A_1 + h_2 A_2 + h_3 A_3 + h_4 A_4) x(t) + B \\
	y(t) & = Cx(t)		y(t) & = Cx(t)
	\end{align}		\end{align}
Line 117:		Line 117:

	<math>E \in \mathbb{R}^{4257 \times 4257}</math>,		<math>E \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>A \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_1 \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>~~A_{top}~~ \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_2 \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>~~A_{bottom}~~ \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_3 \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>~~A_{side}~~ \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_4 \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>B \in \mathbb{R}^{4257 \times 1}</math>,		<math>B \in \mathbb{R}^{4257 \times 1}</math>,
	<math>C \in \mathbb{R}^{7 \times 4257}</math>.		<math>C \in \mathbb{R}^{7 \times 4257}</math>.
Line 127:		Line 127:
	Parameter ranges:		Parameter ranges:

	<math>~~h_{top}~~ \in [1,10^9]</math>,		<math>h_2 \in [1,10^9]</math>,
	<math>~~h_{bottom}~~ \in [1,10^9]</math>,		<math>h_3 \in [1,10^9]</math>,
	<math>~~h_{side}~~ \in [1,10^9]</math>.		<math>h_4 \in [1,10^9]</math>.

			In the original Matrix Market data, <math>A_{top} = A_2, A_{bottom} = A_3, A_{side} = A_4</math>.

	==Citation==		==Citation==

Lund: b --> B

2022-09-01T15:06:20Z

b --> B

← Older revision		Revision as of 15:06, 1 September 2022
Line 44:		Line 44:
	:<math id="eq3">		:<math id="eq3">
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A + \sum_{i} h_{i} A_{i})x(t) + b, & (3)		E \dot{x}(t) & = (A + \sum_{i} h_{i} A_{i})x(t) + B, & (3)
	\end{align}		\end{align}
	</math>		</math>
Line 73:		Line 73:
	:<math>		:<math>
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A - h_{top} A_{top} - h_{bottom} A_{bottom} - h_{side} A_{side}) x(t) + b \\		E \dot{x}(t) & = (A - h_{top} A_{top} - h_{bottom} A_{bottom} - h_{side} A_{side}) x(t) + B \\
	y & = Cx(t)		y & = Cx(t)
	\end{align}		\end{align}
	</math>		</math>

	where <math>E</math> and <math>A</math> are the symmetric sparse system matrices (heat capacity and heat conductivity matrix), <math>b</math> is the load vector, <math>C</math> is the output matrix, <math>A_{top}</math>, <math>A_{bottom}</math>, and <math>A_{side}</math> are the diagonal matrices from the discretization of the convection boundary conditions and <math>T</math> is the vector of unknown temperatures.		where <math>E</math> and <math>A</math> are the symmetric sparse system matrices (heat capacity and heat conductivity matrix), <math>B</math> is the load vector, <math>C</math> is the output matrix, <math>A_{top}</math>, <math>A_{bottom}</math>, and <math>A_{side}</math> are the diagonal matrices from the discretization of the convection boundary conditions and <math>T</math> is the vector of unknown temperatures.

	The numerical values of film coefficients, <math>h_{top}</math>, <math>h_{bottom}</math>, and <math>h_{side}</math> can be from <math>1</math> to <math>10^9</math>.		The numerical values of film coefficients, <math>h_{top}</math>, <math>h_{bottom}</math>, and <math>h_{side}</math> can be from <math>1</math> to <math>10^9</math>.
Line 108:		Line 108:
	:<math>		:<math>
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A + h_{top}A_{top} + h_{bottom}A_{bottom} + h_{side}A_{side}) x(t) + b \\		E \dot{x}(t) & = (A + h_{top}A_{top} + h_{bottom}A_{bottom} + h_{side}A_{side}) x(t) + B \\
	y(t) & = Cx(t)		y(t) & = Cx(t)
	\end{align}		\end{align}
Line 121:		Line 121:
	<math>A_{bottom} \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_{bottom} \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>A_{side} \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_{side} \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>b \in \mathbb{R}^{4257 \times 1}</math>,		<math>B \in \mathbb{R}^{4257 \times 1}</math>,
	<math>C \in \mathbb{R}^{7 \times 4257}</math>.		<math>C \in \mathbb{R}^{7 \times 4257}</math>.

Himpe at 13:01, 25 August 2022

2022-08-25T13:01:53Z

← Older revision		Revision as of 13:01, 25 August 2022
Line 6:		Line 6:
	[[Category:first differential order]]		[[Category:first differential order]]
	[[Category:time invariant]]		[[Category:time invariant]]
	~~[[Category:parametric 2-5 parameters]]~~
	[[Category:MIMO]]		[[Category:MIMO]]
	[[Category:Sparse]]		[[Category:Sparse]]

Himpe: load vector fixes

2022-04-23T16:01:47Z

load vector fixes

← Older revision		Revision as of 16:01, 23 April 2022
Line 45:		Line 45:
	:<math id="eq3">		:<math id="eq3">
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A + \sum_{i} h_{i} A_{i})x(t) + ~~Bu(t)~~, & (3)		E \dot{x}(t) & = (A + \sum_{i} h_{i} A_{i})x(t) + b, & (3)
	\end{align}		\end{align}
	</math>		</math>
Line 74:		Line 74:
	:<math>		:<math>
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A - h_{top} A_{top} - h_{bottom} A_{bottom} - h_{side} A_{side}) x(t) + ~~B u~~ \\		E \dot{x}(t) & = (A - h_{top} A_{top} - h_{bottom} A_{bottom} - h_{side} A_{side}) x(t) + b \\
	y & = Cx(t)		y & = Cx(t)
	\end{align}		\end{align}
	</math>		</math>

	where <math>E</math> and <math>A</math> are the symmetric sparse system matrices (heat capacity and heat conductivity matrix), <math>B</math> is the load vector, <math>C</math> is the output matrix, <math>A_{top}</math>, <math>A_{bottom}</math>, and <math>A_{side}</math> are the diagonal matrices from the discretization of the convection boundary conditions and <math>T</math> is the vector of unknown temperatures.		where <math>E</math> and <math>A</math> are the symmetric sparse system matrices (heat capacity and heat conductivity matrix), <math>b</math> is the load vector, <math>C</math> is the output matrix, <math>A_{top}</math>, <math>A_{bottom}</math>, and <math>A_{side}</math> are the diagonal matrices from the discretization of the convection boundary conditions and <math>T</math> is the vector of unknown temperatures.

	The numerical values of film coefficients, <math>h_{top}</math>, <math>h_{bottom}</math>, and <math>h_{side}</math> can be from <math>1</math> to <math>10^9</math>.		The numerical values of film coefficients, <math>h_{top}</math>, <math>h_{bottom}</math>, and <math>h_{side}</math> can be from <math>1</math> to <math>10^9</math>.
Line 109:		Line 109:
	:<math>		:<math>
	\begin{align}		\begin{align}
	E \dot{x}(t) & = (A + h_{top}A_{top} + h_{bottom}A_{bottom} + h_{side}A_{side}) x(t) + B \\		E \dot{x}(t) & = (A + h_{top}A_{top} + h_{bottom}A_{bottom} + h_{side}A_{side}) x(t) + b \\
	y(t) & = Cx(t)		y(t) & = Cx(t)
	\end{align}		\end{align}
Line 122:		Line 122:
	<math>A_{bottom} \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_{bottom} \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>A_{side} \in \mathbb{R}^{4257 \times 4257}</math>,		<math>A_{side} \in \mathbb{R}^{4257 \times 4257}</math>,
	<math>B \in \mathbb{R}^{4257 \times 1}</math>,		<math>b \in \mathbb{R}^{4257 \times 1}</math>,
	<math>C \in \mathbb{R}^{7 \times 4257}</math>.		<math>C \in \mathbb{R}^{7 \times 4257}</math>.

Himpe at 15:48, 26 January 2022

2022-01-26T15:48:27Z

← Older revision		Revision as of 15:48, 26 January 2022
Line 174:		Line 174:
	<ref name="feng2004">L. Feng, E.B. Rudnyi, J.G. Korvink, "<span class="plainlinks">[http://modelreduction.com/doc/papers/feng04THERMINIC.pdf Parametric Model Reduction to Generate Boundary Condition Independent Compact Thermal Model]</span>", THERMINIC 2004, 10th International Workshop on Thermal Investigations of ICs and Systems, 29 September - 1 October 2004, Sophia Antipolis, Cote d'Azur, France.</ref>		<ref name="feng2004">L. Feng, E.B. Rudnyi, J.G. Korvink, "<span class="plainlinks">[http://modelreduction.com/doc/papers/feng04THERMINIC.pdf Parametric Model Reduction to Generate Boundary Condition Independent Compact Thermal Model]</span>", THERMINIC 2004, 10th International Workshop on Thermal Investigations of ICs and Systems, 29 September - 1 October 2004, Sophia Antipolis, Cote d'Azur, France.</ref>

	<ref name="feng2005">L. Feng, E. B. Rudnyi, J. G. Korvink, "<span class="plainlinks">[10.1109/TCAD.2005.852660 Preserving the film coefficient as a parameter in the compact thermal model for fast electro-thermal simulation]</span>", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 24(12): 1838--1847, 2005.</ref>		<ref name="feng2005">L. Feng, E. B. Rudnyi, J. G. Korvink, "<span class="plainlinks">[https://doi.org/10.1109/TCAD.2005.852660 Preserving the film coefficient as a parameter in the compact thermal model for fast electro-thermal simulation]</span>", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 24(12): 1838--1847, 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>, 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>, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>

Saak: /* Data */

2021-12-14T09:04:04Z

Data

← Older revision		Revision as of 09:04, 14 December 2021
Line 99:		Line 99:
	The matrices of this benchmark can be downloaded in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format:		The matrices of this benchmark can be downloaded in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format:

	* [https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/ThermalModel-dim1e3-T2DAL_BCI.tar.gz ThermalModel-dim1e3-T2DAL_BCI.tar.gz], 218.7 kB.		* [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/ThermalModel-dim1e3-T2DAL_BCI.tar.gz ThermalModel-dim1e3-T2DAL_BCI.tar.gz], 218.7 kB.

	The matrix name is used as an extension of the matrix file. File <tt>T2DAL_BCI.C.names</tt> contains a list of output names written consecutively.		The matrix name is used as an extension of the matrix file. File <tt>T2DAL_BCI.C.names</tt> contains a list of output names written consecutively.

Himpe: Fix CrossRefs

2021-08-27T07:50:13Z

Fix CrossRefs

← Older revision		Revision as of 07:50, 27 August 2021
Line 57:		Line 57:

	Unfortunately, the benchmark from <ref name="lasance2001"/> is not available in the computer readable format.		Unfortunately, the benchmark from <ref name="lasance2001"/> is not available in the computer readable format.
	For research purposes, we have modified a [[Micropyros_Thruster\|Micropyros Thruster benchmark]] (see ~~<xr id="fig1"/>~~).		For research purposes, we have modified a [[Micropyros_Thruster\|Micropyros Thruster benchmark]] (see Fig. 1).
	In the context of the present work, the model is as a generic example of a device with a single heat source when the generated heat dissipates through the device to the surroundings. The exchange between surrounding and the device is modeled by convection boundary conditions with different film coefficients at the top, <math>h_{top}</math>, bottom, <math>h_{bottom}</math>, and the side, <math>h_{side}</math>.		In the context of the present work, the model is as a generic example of a device with a single heat source when the generated heat dissipates through the device to the surroundings. The exchange between surrounding and the device is modeled by convection boundary conditions with different film coefficients at the top, <math>h_{top}</math>, bottom, <math>h_{bottom}</math>, and the side, <math>h_{side}</math>.
	From this viewpoint, it is quite similar to a chip model used as a benchmark in <ref name="lasance2001"/>.		From this viewpoint, it is quite similar to a chip model used as a benchmark in <ref name="lasance2001"/>.

Himpe: minor fixes.

2018-08-01T08:35:32Z

minor fixes.

← Older revision		Revision as of 08:35, 1 August 2018
Line 12:		Line 12:
	==Description: Boundary Condition Independent Thermal Model==		==Description: Boundary Condition Independent Thermal Model==
	<figure id="fig1">[[File:ThermalModel.jpg\|490px\|thumb\|right\|<caption>A 2D-axisymmetrical model of the micro-thruster unit (not scaled). A heater is shown by a red spot.</caption>]]</figure>		<figure id="fig1">[[File:ThermalModel.jpg\|490px\|thumb\|right\|<caption>A 2D-axisymmetrical model of the micro-thruster unit (not scaled). A heater is shown by a red spot.</caption>]]</figure>
			A benchmark for the heat transfer problem with variable [[wikipedia:Heat_transfer_coefficient\|film coefficients]] is presented.
	A benchmark for the heat transfer problem with variable film coefficients is presented.
	It can be used to apply parametric model reduction algorithms to a linear first-order problem.		It can be used to apply parametric model reduction algorithms to a linear first-order problem.

	===Modeling===		===Modeling===

	~~One of~~ important requirements for a compact thermal model is that it should be boundary condition ~~independent~~.		An important requirements for a compact thermal model is that it should be independent from the boundary condition.
	This means that a chip producer does not know conditions under which the chip will be used and hence the chip compact thermal model must allow an engineer to research on how the change in the environment influences the chip temperature.		This means that a chip producer does not know conditions under which the chip will be used and hence the chip compact thermal model must allow an engineer to research on how the change in the environment influences the chip temperature.
	The chip benchmarks representing boundary condition independent requirements are described in <ref name="lasance2001"/>.		The chip benchmarks representing boundary condition independent requirements are described in <ref name="lasance2001"/>.
Line 62:		Line 61:
	From this viewpoint, it is quite similar to a chip model used as a benchmark in <ref name="lasance2001"/>.		From this viewpoint, it is quite similar to a chip model used as a benchmark in <ref name="lasance2001"/>.
	The goal of parametric model reduction in this case is to preserve <math>h_{top}</math>, <math>h_{bottom}</math>, and <math>h_{side}</math> in the reduced model in the symbolic form.		The goal of parametric model reduction in this case is to preserve <math>h_{top}</math>, <math>h_{bottom}</math>, and <math>h_{side}</math> in the reduced model in the symbolic form.

			===Discretization===

	We have used a 2D-axisymmetric microthruster model (T2DAL in [[Micropyros_Thruster\|Micropyros Thruster]]).		We have used a 2D-axisymmetric microthruster model (T2DAL in [[Micropyros_Thruster\|Micropyros Thruster]]).

	The model has been made in [http://www.ansys.com/ ANSYS] and system matrices have been extracted by means of [http://portal.uni-freiburg.de/imteksimulation/downloads/mor4fem mor4fem] <ref name="rudnyi2004"/>.		The model has been made in [http://www.ansys.com/ ANSYS] and system matrices have been extracted by means of [http://portal.uni-freiburg.de/imteksimulation/downloads/mor4fem mor4fem] <ref name="rudnyi2004"/>.
	~~The benchmark contains a constant load vector. The input function equal to one corresponds to the constant input power of <math>15 mW</math>.~~

	~~===Discretization===~~

	~~A 2D-axisymmetric microthruster model (T2DAL).~~
	The model has been made in ANSYS and system matrices have been extracted by means of [http://www.cadfem.de/produkte/cadfem-ansys-extensions/model-reduction-inside-ansys.html mor4ansys] <ref name="rudnyi2004"/>.
	The benchmark contains a constant load vector.		The benchmark contains a constant load vector.
	The input function equal to one corresponds to the constant input power of 15 mW.		The input function equal to one corresponds to the constant input power of <math>15 mW</math>.

	The linear ordinary differential equations of first order are written as:		The linear ordinary differential equations of first order are written as:
Line 141:		Line 137:

	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	:: Oberwolfach Benchmark Collection, '''Thermal Model'''. hosted at MORwiki - Model Order Reduction Wiki, ~~2005~~. http://modelreduction.org/index.php/Thermal_Model		:: Oberwolfach Benchmark Collection, '''Thermal Model'''. hosted at MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Thermal_Model

	@MISC{~~morwiki_steel~~,		@MISC{morwiki_thermal,
	author = <nowiki>{{Oberwolfach Benchmark Collection}}</nowiki>,		author = <nowiki>{{Oberwolfach Benchmark Collection}}</nowiki>,
	title = {Thermal Model},		title = {Thermal Model},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{http://modelreduction.org/index.php/Thermal_Model}</nowiki>,		url = <nowiki>{http://modelreduction.org/index.php/Thermal_Model}</nowiki>,
	year = ~~2005~~		year = 20XX
	}		}

Line 155:		Line 151:
	@TechReport{morFenRK04,		@TechReport{morFenRK04,
	author = {Feng, L. and Rudnyi, E.~B. and Korvink, J.~G.},		author = {Feng, L. and Rudnyi, E.~B. and Korvink, J.~G.},
	title = {Parametric Model Reduction to Generate Boundary		title = {Parametric Model Reduction to Generate Boundary Condition Independent Compact Thermal Model},
	Condition Independent Compact Thermal Model},
	institution = {IMTEK-Institute for Microsystem Technology},		institution = {IMTEK-Institute for Microsystem Technology},
	type = {Technical report},		type = {Technical report},
	year = 2004,		year = {2004},
	url = <nowiki>{http://modelreduction.com/doc/papers/feng04THERMINIC.pdf}</nowiki>		url = <nowiki>{http://modelreduction.com/doc/papers/feng04THERMINIC.pdf}</nowiki>
	}		}