Init Windscreen |
Added dimension section and fixes |
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==Description== | ==Description== | ||
<figure id="fig1">[[File:Windscreen1.gif|490px|thumb|right|Figure 1]]</figure> | <figure id="fig1">[[File:Windscreen1.gif|490px|thumb|right|Figure 1]]</figure> | ||
<figure id=" | <figure id="fig2">[[File:Windscreen2.png|490px|thumb|right|Figure 2]]</figure> | ||
This is an example for a model in the frequency domain of the form | This is an example for a model in the frequency domain of the form | ||
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The test problem is a structural model of a car windscreen. | The test problem is a structural model of a car windscreen. | ||
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 | The mesh is shown in <xr id="fig1"/>. | ||
The material is glass with the following properties: | The material is glass with the following properties: | ||
The 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 Poisson ratio is <math>0.23</math>. The natural damping is <math>10\%</math>, i.e. <math>\gamma=0.1</math>. | The 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 Poisson ratio is <math>0.23</math>. The natural damping is <math>10\%</math>, i.e. <math>\gamma=0.1</math>. | ||
The structural boundaries are free (free-free boundary conditions). | The structural boundaries are free (free-free boundary conditions). | ||
The windscreen is subjected to a point force applied on a corner. | The windscreen is subjected to a point force applied on a corner. | ||
The goal of the model reduction is the fast evaluation of y. | The goal of the model reduction is the fast evaluation of <math>y</math>. | ||
Model reduction is used as a fast linear solver for a sequence of parametrized linear systems. | Model reduction is used as a fast linear solver for a sequence of parametrized linear systems. | ||
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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"/> and <xr id="fig2"/> show the mesh of the car windscreen and frequency response function. | |||
==Origin== | ==Origin== | ||
This benchmark is part of the '''Oberwolfach Benchmark Collection'''<ref name="korvink2005"/>. | This benchmark is part of the '''Oberwolfach Benchmark Collection'''<ref name="korvink2005"/>; No. 38886. | ||
==Data== | ==Data== | ||
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The archive contains files <tt>windscreen.K</tt>, <tt>windscreen.M</tt> and <tt>windscreen.B</tt> representing <math>Kd</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>Kd</math>, <math>M</math> and <math>f</math> accordingly. | ||
==Dimensions== | |||
System structure: | |||
:<math> | |||
\begin{align} | |||
K x - \omega^2 M x &= B \\ | |||
y &= B^\intercal x | |||
\end{align} | |||
</math> | |||
System dimensions: | |||
<math>K \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>. | |||
==References== | ==References== | ||
Revision as of 11:38, 1 March 2018
Note: This page has not been verified by our editors.
Description
This is an example for a model in the frequency domain of the form
where represents a unit point load in one unknown of the state vector. is a symmetric positive-definite matrix and where is symmetric positive semi-definite.
The test problem is a structural model of a car windscreen. This is a 3D problem discretized with nodes and linear hexahedral elements (3 layers of elements). The mesh is shown in xx--CrossReference--dft--fig1--xx. The material is glass with the following properties: The Young modulus is , the density is , and the Poisson ratio is . The natural damping is , i.e. . The structural boundaries are free (free-free boundary conditions). The windscreen is subjected to a point force applied on a corner. The goal of the model reduction is the fast evaluation of . Model reduction is used as a fast linear solver for a sequence of parametrized linear systems.
The discretized problem has dimension . The goal is to estimate for . In order to generate the plots the frequency range was discretized as with .
xx--CrossReference--dft--fig1--xx and xx--CrossReference--dft--fig2--xx show the mesh of the car windscreen and frequency response function.
Origin
This benchmark is part of the Oberwolfach Benchmark Collection[1]; No. 38886.
Data
Download matrices in the Matrix Market format:
- windscreen.tar.gz (21.5 MB)
The archive contains files windscreen.K, windscreen.M and windscreen.B representing , and accordingly.
Dimensions
System structure:
System dimensions:
, , .
References
- ↑ J.G. Korvink, E.B. Rudnyi, Oberwolfach Benchmark Collection, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.