Windscreen - Revision history

Schuetz2 at 05:42, 17 June 2025

2025-06-17T05:42:34Z

← Older revision		Revision as of 05:42, 17 June 2025
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	:: Oberwolfach Benchmark Collection, '''Windscreen'''. hosted at MORwiki - Model Order Reduction Wiki, 2018. ~~http~~://modelreduction.org/~~index.php~~/Windscreen		:: Oberwolfach Benchmark Collection, '''Windscreen'''. hosted at MORwiki - Model Order Reduction Wiki, 2018. https://modelreduction.org/morwiki/Windscreen

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

Malhotra: infobox string

2023-11-30T09:46:13Z

infobox string

@@ Line 6: / Line 6: @@
 [[Category:SISO]]
 [[Category:Sparse]]
 ==Description==

Lund: replace K_d with K, and -M with M (to be consistent with SOS model); replace B^T with C

2022-08-31T14:34:43Z

replace K_d with K, and -M with M (to be consistent with SOS model); replace B^T with C

← Older revision		Revision as of 14:34, 31 August 2022
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	:<math>		:<math>
	\begin{align}		\begin{align}
	~~K_d~~ x - \omega^2 M x & = B \\		K x + \omega^2 M x & = B \\
	y & = ~~B^T~~ x		y & = C x
	\end{align}		\end{align}
	</math>		</math>

	where <math>B</math> represents a unit point load in one unknown of the state vector.		where <math>B</math> represents a unit point load in one unknown of the state vector, <math>C = B^T </math>,
	<math>M</math> is a symmetric positive-definite matrix and <math>~~K_d~~ = (1+i\gamma) K</math> ~~where~~ <math>K</math> is symmetric positive ~~semi-definite~~.		<math>M</math> is a symmetric positive-definite matrix, and <math>K = (1+i\gamma) \widetilde{K}</math> with <math>\widetilde{K}</math> symmetric positive semidefinite.

	The test problem is a structural model of a car windscreen. <ref name="meerbergen2007"/>		The test problem is a structural model of a car windscreen. <ref name="meerbergen2007"/>
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	* [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Windscreen-dim1e4-windscreen.tar.gz Windscreen-dim1e4-windscreen.tar.gz] (21.5 MB)		* [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Windscreen-dim1e4-windscreen.tar.gz Windscreen-dim1e4-windscreen.tar.gz] (21.5 MB)

	The archive contains files <tt>windscreen.K</tt>, <tt>windscreen.M</tt> and <tt>windscreen.B</tt> representing <math>~~K_d~~</math>, <math>-M</math> and <math>f</math> accordingly.		The archive contains files <tt>windscreen.K</tt>, <tt>windscreen.M</tt> and <tt>windscreen.B</tt> representing <math>K</math>, <math>M</math> and <math>B</math> accordingly.

	==Dimensions==		==Dimensions==
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	\begin{align}		\begin{align}
	(K + \omega^2 M) x & = B \\		(K + \omega^2 M) x & = B \\
	y & = ~~B^{\mathrm{T}}~~ x		y & = C x
	\end{align}		\end{align}
	</math>		</math>
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	<math>K \in \mathbb{C}^{22692 \times 22692}</math>,		<math>K \in \mathbb{C}^{22692 \times 22692}</math>,
	<math>M \in \mathbb{R}^{22692 \times 22692}</math>,		<math>M \in \mathbb{R}^{22692 \times 22692}</math>,
	<math>B \in \mathbb{R}^{22692 \times 1}</math>.		<math>B \in \mathbb{R}^{22692 \times 1}</math>,
			<math>C \in \mathbb{R}^{1 \times 22692}</math>,

	==Citation==		==Citation==

Lund: /* Description */ change f to B

2022-08-31T14:30:02Z

Description: change f to B

← Older revision		Revision as of 14:30, 31 August 2022
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	:<math>		:<math>
	\begin{align}		\begin{align}
	K_d x - \omega^2 M x & = f \\		K_d x - \omega^2 M x & = B \\
	y & = f^* x		y & = B^T x
	\end{align}		\end{align}
	</math>		</math>

	where <math>f</math> represents a unit point load in one unknown of the state vector.		where <math>B</math> represents a unit point load in one unknown of the state vector.
	<math>M</math> is a symmetric positive-definite matrix and <math>K_d = (1+i\gamma) K</math> where <math>K</math> is symmetric positive semi-definite.		<math>M</math> is a symmetric positive-definite matrix and <math>K_d = (1+i\gamma) K</math> where <math>K</math> is symmetric positive semi-definite.

Lund: Undo revision 3452 by Lund (talk)

2022-08-31T14:00:24Z

Undo revision 3452 by Lund (talk)

← Older revision		Revision as of 14:00, 31 August 2022
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	System dimensions:		System dimensions:

	<math>K \in \mathbb{C}^{~~45384~~ \times ~~45384~~}</math>,		<math>K \in \mathbb{C}^{22692 \times 22692}</math>,
	<math>M \in \mathbb{R}^{~~45384~~ \times ~~45384~~}</math>,		<math>M \in \mathbb{R}^{22692 \times 22692}</math>,
	<math>B \in \mathbb{R}^{~~45384~~ \times 1}</math>.		<math>B \in \mathbb{R}^{22692 \times 1}</math>.

	==Citation==		==Citation==

Himpe at 12:59, 25 August 2022

2022-08-25T12:59:58Z

← Older revision		Revision as of 12:59, 25 August 2022
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	[[Category:Affine parameter representation]]		[[Category:Affine parameter representation]]
	[[Category:Parametric]]		[[Category:Parametric]]
	~~[[Category:Parametric 1 parameter]]~~
	[[Category:SISO]]		[[Category:SISO]]
	[[Category:Sparse]]		[[Category:Sparse]]

Lund: correct dimensions of matrices

2022-07-07T12:58:48Z

correct dimensions of matrices

← Older revision		Revision as of 12:58, 7 July 2022
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	System dimensions:		System dimensions:

	<math>K \in \mathbb{C}^{~~22692~~ \times ~~22692~~}</math>,		<math>K \in \mathbb{C}^{45384 \times 45384}</math>,
	<math>M \in \mathbb{R}^{~~22692~~ \times ~~22692~~}</math>,		<math>M \in \mathbb{R}^{45384 \times 45384}</math>,
	<math>B \in \mathbb{R}^{~~22692~~ \times 1}</math>.		<math>B \in \mathbb{R}^{45384 \times 1}</math>.

	==Citation==		==Citation==

Himpe: fix broken xref

2022-04-14T10:25:46Z

fix broken xref

← Older revision		Revision as of 10:25, 14 April 2022
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	The test problem is a structural model of a car windscreen. <ref name="meerbergen2007"/>		The test problem is a structural model of a car windscreen. <ref name="meerbergen2007"/>
	This is a 3D problem discretized with <math>7564</math> nodes and <math>5400</math> linear hexahedral elements (3 layers of <math>60 \times 30</math> elements).		This is a 3D problem discretized with <math>7564</math> nodes and <math>5400</math> linear hexahedral elements (3 layers of <math>60 \times 30</math> elements).
	The mesh is shown in ~~<xr id="fig1"/>~~.		The mesh is shown in Fig. 1.
	The material is glass with the following properties:		The material is glass with the following properties:
	The [[wikipedia:Young's_modulus\|Young modulus]] is <math>7\times10^{10}\mathrm{N}/\mathrm{m}^2</math>, the density is <math>2490 \mathrm{kg}/\mathrm{m}^3</math>, and the [[wikipedia:Poisson's_ratio\|Poisson ratio]] is <math>0.23</math>. The natural damping is <math>10\%</math>, i.e. <math>\gamma=0.1</math>.		The [[wikipedia:Young's_modulus\|Young modulus]] is <math>7\times10^{10}\mathrm{N}/\mathrm{m}^2</math>, the density is <math>2490 \mathrm{kg}/\mathrm{m}^3</math>, and the [[wikipedia:Poisson's_ratio\|Poisson ratio]] is <math>0.23</math>. The natural damping is <math>10\%</math>, i.e. <math>\gamma=0.1</math>.

Saak: /* Data */

2021-12-14T09:05:29Z

Data

← Older revision		Revision as of 09:05, 14 December 2021
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	Download matrices in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format:		Download matrices in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format:

	* [https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Windscreen-dim1e4-windscreen.tar.gz Windscreen-dim1e4-windscreen.tar.gz] (21.5 MB)		* [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Windscreen-dim1e4-windscreen.tar.gz Windscreen-dim1e4-windscreen.tar.gz] (21.5 MB)

	The archive contains files <tt>windscreen.K</tt>, <tt>windscreen.M</tt> and <tt>windscreen.B</tt> representing <math>K_d</math>, <math>-M</math> and <math>f</math> accordingly.		The archive contains files <tt>windscreen.K</tt>, <tt>windscreen.M</tt> and <tt>windscreen.B</tt> representing <math>K_d</math>, <math>-M</math> and <math>f</math> accordingly.

Himpe: Fix CrossRefs

2021-08-27T07:53:28Z

Fix CrossRefs

← Older revision		Revision as of 07:53, 27 August 2021
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	\{0.5j,j=1,\ldots,m\}</math> with <math>m=400</math>.		\{0.5j,j=1,\ldots,m\}</math> with <math>m=400</math>.

	~~<xr id="fig1"/>~~ shows the mesh of the car windscreen and ~~<xr id="fig2"/>~~ the frequency response <math>\vert \Re(y(\omega)) \vert</math>.		Fig. 1 shows the mesh of the car windscreen and Fig. 2 the frequency response <math>\vert \Re(y(\omega)) \vert</math>.

	==Origin==		==Origin==