Circular Piston - Revision history

Schuetz2 at 05:24, 12 June 2025

2025-06-12T05:24:12Z

← Older revision		Revision as of 05:24, 12 June 2025
Line 116:		Line 116:
	title = {Circular Piston},		title = {Circular Piston},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Circular_Piston}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Circular_Piston}</nowiki>,
	year = {20XX}		year = {20XX}
	}		}

Malhotra: infobox string

2023-11-30T09:27:49Z

infobox string

@@ Line 6: / Line 6: @@
 [[Category:Sparse]]
 [[Category:MIMO]]
 ==Description: Axi-Symmetric Infinite Element Model for Circular Piston==

Mlinaric: Edits, add categories

2023-08-29T17:26:15Z

Edits, add categories

← Older revision		Revision as of 17:26, 29 August 2023
Line 1:		Line 1:
	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]
			[[Category:linear]]
			[[Category:time invariant]]
	[[Category:second differential order]]		[[Category:second differential order]]
			[[Category:Sparse]]
			[[Category:MIMO]]

	==Description: Axi-Symmetric Infinite Element Model for Circular Piston==		==Description: Axi-Symmetric Infinite Element Model for Circular Piston==
Line 8:		Line 11:

	:<math>		:<math>
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = B,		M \ddot{x}(t) + E \dot{x}(t) + K x(t) = B,
	</math>		</math>

Line 14:		Line 17:
	This is thus a differential algebraic equation.		This is thus a differential algebraic equation.
	It is shown that it has index 1<ref name="coyette2003"/>.		It is shown that it has index 1<ref name="coyette2003"/>.
	The input of the system is <math>B</math>, the output is the state vector <math>x</math>.		The input of the system is <math>B</math> and the output is the state vector <math>x</math>.
	The motivation for using model reduction for this type of ~~problems~~ is the reduction of the computation time of a simulation.		The motivation for using model reduction for this type of problem is the reduction of the computation time of a simulation.

	This is an example from an acoustic radiation problem discussed in <ref name="pinsky1991"/>.		This is an example from an acoustic radiation problem discussed in <ref name="pinsky1991"/>.
Line 32:		Line 35:

	:<math>		:<math>
	a_r = \frac{-1}{\rho} \frac{\partial p(r,\theta)}{\partial r} \big\|_{r=a} = \begin{cases} a_0 \sin(\omega t) & 0<\theta<\theta_p \\ 0 & \theta>\theta_p \end{cases}		a_r
			= \frac{-1}{\rho} \frac{\partial p(r,\theta)}{\partial r} \big\|_{r=a}
			=
			\begin{cases}
			a_0 \sin(\omega t) & 0 < \theta < \theta_p \\
			0 & \theta > \theta_p
			\end{cases}
	</math>		</math>

Line 51:		Line 60:

	Download matrices in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/CircularPiston-dim1e3-piston.tar.gz CircularPiston-dim1e3-piston.tar.gz] (1.9 MB).		Download matrices in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/CircularPiston-dim1e3-piston.tar.gz CircularPiston-dim1e3-piston.tar.gz] (1.9 MB).

			Extracting will produce

			* <tt>piston.M</tt>
			* <tt>piston.E</tt>
			* <tt>piston.K</tt>
			* <tt>piston.B</tt>

			Note that for <tt>piston.B</tt>, loading with <tt>scipy.io.mmread</tt> will not work because the number of nonzeros is specified in the dense Matrix Market format.
			Replacing the line with "2025 1 2025" by "2025 1" will make it work.

	==Dimensions==		==Dimensions==
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	:<math>		:<math>
	\begin{align}		\begin{align}
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) &= B \\		M \ddot{x}(t) + E \dot{x}(t) + K x(t) &= B \\
	y(t) &= x(t)		y(t) &= x(t)
	\end{align}		\end{align}
	</math>		</math>
Line 65:		Line 84:
	System dimensions:		System dimensions:

	<math>M ~~\in \mathbb{R}^{2025 \times 2025}</math>~~,		<math>M, E, K \in \mathbb{R}^{2025 \times 2025}</math>,
	~~<math>~~E ~~\in \mathbb{R}^{2025 \times 2025}</math>~~,
	~~<math>~~K \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>B \in \mathbb{R}^{2025 \times 1}</math>.		<math>B \in \mathbb{R}^{2025 \times 1}</math>.

Aumann at 16:29, 18 November 2022

2022-11-18T16:29:37Z

← Older revision		Revision as of 16:29, 18 November 2022
Line 1:		Line 1:
	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]
			[[Category:second differential order]]

Lund: /* Dimensions */ add missing \\

2022-08-31T13:45:15Z

Dimensions: add missing \\

← Older revision		Revision as of 13:45, 31 August 2022
Line 57:		Line 57:
	:<math>		:<math>
	\begin{align}		\begin{align}
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) &= B		M\ddot{x}(t) + E\dot{x}(t) + Kx(t) &= B \\
	y(t) &= x(t)		y(t) &= x(t)
	\end{align}		\end{align}

Lund: /* Dimensions */ add output explicitly

2022-08-31T13:44:30Z

Dimensions: add output explicitly

← Older revision		Revision as of 13:44, 31 August 2022
Line 56:		Line 56:

	:<math>		:<math>
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = B		\begin{align}
			M\ddot{x}(t) + E\dot{x}(t) + Kx(t) &= B
			y(t) &= x(t)
			\end{align}
	</math>		</math>

Lund: change f to B

2022-08-31T13:35:11Z

change f to B

← Older revision		Revision as of 13:35, 31 August 2022
Line 7:		Line 7:

	:<math>		:<math>
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = f,		M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = B,
	</math>		</math>

Line 13:		Line 13:
	This is thus a differential algebraic equation.		This is thus a differential algebraic equation.
	It is shown that it has index 1<ref name="coyette2003"/>.		It is shown that it has index 1<ref name="coyette2003"/>.
	The input of the system is <math>f</math>, the output is the state vector <math>x</math>.		The input of the system is <math>B</math>, the output is the state vector <math>x</math>.
	The motivation for using model reduction for this type of problems is the reduction of the computation time of a simulation.		The motivation for using model reduction for this type of problems is the reduction of the computation time of a simulation.

Line 56:		Line 56:

	:<math>		:<math>
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = f		M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = B
	</math>		</math>

Line 64:		Line 64:
	<math>E \in \mathbb{R}^{2025 \times 2025}</math>,		<math>E \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>K \in \mathbb{R}^{2025 \times 2025}</math>,		<math>K \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>f \in \mathbb{R}^{2025 \times 1}</math>.		<math>B \in \mathbb{R}^{2025 \times 1}</math>.

	==Citation==		==Citation==

Lund: change b to f

2022-08-09T14:59:12Z

change b to f

← Older revision		Revision as of 14:59, 9 August 2022
Line 56:		Line 56:

	:<math>		:<math>
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = b		M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = f
	</math>		</math>

Line 64:		Line 64:
	<math>E \in \mathbb{R}^{2025 \times 2025}</math>,		<math>E \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>K \in \mathbb{R}^{2025 \times 2025}</math>,		<math>K \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>b \in \mathbb{R}^{2025 \times 1}</math>.		<math>f \in \mathbb{R}^{2025 \times 1}</math>.

	==Citation==		==Citation==

Himpe: load vector fixes

2022-04-23T16:03:27Z

load vector fixes

← Older revision		Revision as of 16:03, 23 April 2022
Line 56:		Line 56:

	:<math>		:<math>
	M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = B		M\ddot{x}(t) + E\dot{x}(t) + Kx(t) = b
	</math>		</math>

Line 64:		Line 64:
	<math>E \in \mathbb{R}^{2025 \times 2025}</math>,		<math>E \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>K \in \mathbb{R}^{2025 \times 2025}</math>,		<math>K \in \mathbb{R}^{2025 \times 2025}</math>,
	<math>B \in \mathbb{R}^{2025 \times 1}</math>.		<math>b \in \mathbb{R}^{2025 \times 1}</math>.

	==Citation==		==Citation==

Saak: /* Data */

2021-12-14T08:53:03Z

Data

← Older revision		Revision as of 08:53, 14 December 2021
Line 49:		Line 49:
	==Data==		==Data==

	Download matrices in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format [https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/CircularPiston-dim1e3-piston.tar.gz CircularPiston-dim1e3-piston.tar.gz] (1.9 MB).		Download matrices in the [http://math.nist.gov/MatrixMarket/ Matrix Market] format [https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/CircularPiston-dim1e3-piston.tar.gz CircularPiston-dim1e3-piston.tar.gz] (1.9 MB).

	==Dimensions==		==Dimensions==