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{{expert-subject|mathematics|date=February 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
'''Interval boundary element method''' is classical [[boundary element method]] with the interval parameters.<BR>
Boundary element method is based on the following integral equation


<math> c\cdot u=\int\limits_{\partial \Omega}\left(G\frac{\partial u}{\partial n} - \frac{\partial G}{\partial n}u\right)dS </math>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


The exact interval solution on the boundary can be defined in the following way:
Registered users will be able to choose between the following three rendering modes:  


<math> \tilde{u}(x)=\{u(x,p):c(p)\cdot u(p)=\int\limits_{\partial \Omega}\left(G(p)\frac{\partial u(p)}{\partial n} - \frac{\partial G(p)}{\partial n}u(p)\right)dS, p\in\hat{p} \}</math>
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


In practice we are interested in the smallest interval which contain the exact solution set
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


<math> \hat{u}(x)=hull \ \tilde {u}(x)=hull \{u(x,p):c(p)\cdot u(p)=\int\limits_{\partial \Omega}\left(G(p)\frac{\partial u(p)}{\partial n} - \frac{\partial G(p)}{\partial n}u(p)\right)dS, p\in\hat{p} \}</math>
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


In similar way it is possible to calculate the interval solution inside the boundary <math> \Omega </math>.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


==References==
==Demos==
* T. Burczyński and J. Skrzypczyk, The fuzzy boundary element method: a new solution concept, Proceedings of XII Polish conference on computer methods in mechanics, Warsaw-Zegrze, Poland (1995), pp. 65–66.
* T. Burczynski, J. Skrzypczyk J. The fuzzy boundary element method: a new methodology. Series Civil Eng, Vol. 83. Gliwice: Sci Fasc of Silesian Tech Univ; 1995, pp. 25–42.
* J. Skrzypczyk, A Note on Interval Fredholm Integral Equations. Zeszyty Naukowe Politechniki Śląskiej, Seria Budownictwo, Z.85, pp.75-83, 1998
* T. Burczynski, J. Skrzypczyk, Fuzzy aspects of the boundary element method, Engineering Analysis with Boundary Elements, Vol.19, No.3, pp.209-216, 1997
* H. Witek, Boundary element method in analysis of civil engineering structures with uncertain parameters. Ph.D. Dissertation, Silesian University of Technology, Faculty of Civil Engineering, Poland, 2005
* B.F. Zalewski, R.L. Mullen, R.L. Muhanna, “Boundary Element Analysis of Systems Using Interval Methods”, Proceedings of the NSF Workshop on Modeling Errors and Uncertainty in Engineering Computations, Georgia Tech Savannah, February 2006.
* B.F. Zalewski and R.L. Mullen, "Interval Bounds on the Local Discretization Error in Boundary Element Analysis for Domains with Singular Flux", SAE 2008 Reliability and Robust Design in Automotive Engineering, SP-2170, Pages 237-246, 2008.
* B.F. Zalewski and R.L. Mullen, "Discretization Error in Boundary Element Analysis using Interval Methods", SAE 2007 International Transactions Journal of Passenger Cars: Mechanical Systems, Volume 116, Issue 6, Pages 1353-1361, 2008.
* B.F. Zalewski and R.L. Mullen, "Point-wise Discretization Errors in Boundary Element Method for Elasticity Problem", Third NSF Workshop on Reliable Engineering Computing, Pages 429-457, February 2008.
* B.F. Zalewski, “Uncertainties in the Solutions to Boundary Element Method: An Interval Approach”, Case Western Reserve University, Ph.D. Dissertation, © 2008.
* B.F. Zalewski and R.L. Mullen, “Local Discretization Error Bounds Using Interval Boundary Element Method”, International Journal for Numerical Methods in Engineering, Volume 78, Issue 4, April 2009, Pages 403-428.
* A. Piasecka Belkhayat, Interval boundary element method for 2D transient diffusion problem, Engineering Analysis with Boundary Elements, Volume 32, Issue 5, May 2008, Pages 424-430
* B.F. Zalewski, R.L. Mullena, and R.L. Muhanna, "Interval Boundary Element Method in the Presence of Uncertain Boundary Conditions, Integration Errors, and Truncation Errors", Engineering Analysis with Boundary Elements, Volume 33, Issue 4, April 2009, Pages 508-513. [http://dx.doi.org/10.1016/j.enganabound.2008.08.006]
* B.F. Zalewski, R.L. Mullen, and R.L. Muhanna, “Fuzzy Boundary Element Method for Geometric Uncertainty in Elasticity Problem”, SAE 2009 International Journal of Materials and Manufacturing, Volume 2, Issue 1, Pages 310-316, 2009.
* B.F. Zalewski and R.L. Mullen, “Worst Case Bounds on the Point-wise Discretization Error in Boundary Element Method for the Elasticity Problem”, Computer Methods in Applied Mechanics and Engineering, Volume 198, Issue 37-40, Pages 2996-3005, 2009.
* B.F. Zalewski and R.L. Mullen, “Worst Case Point-wise Discretization Error Bounds for Systems with Geometrically Induced Singular Flux Solutions Using Interval Boundary Element Method”, ASCE Journal of Engineering Mechanics, Volume 136, Issue 6, Pages 710-720, 2010.
* B.F. Zalewski, "Fuzzy Boundary Element Method for Material Uncertainty in Steady State Heat Conduction", SAE 2010 International Journal of Materials and Manufacturing, Volume 3, Issue 1, Pages 372-379, 2010.
* B.F. Zalewski and W.B. Dial, "Fuzzy Boundary Element Method with Uncertain Shear Modulus in Linear Plane Strain Elasticity", SAE 2011 International Journal of Materials and Manufacturing, Volume 4, Issue 1, Pages 947-956, 2011.
* A. Piasecka-Belkhayat, "Interval Boundary Element Method for Transient Diffusion Problem in Two-Layered Domain", Journal of Theoretical and Applied Mechanics, Volume 49, Issue 1, Pages 265-276, 2011.
* A. Piasecka-Belkhayat, "Interval Boundary Element Method for 2D Transient Diffusion Problem Using the Directed Interval Arithmetic", Engineering Analysis with Boundary Elements, Volume 35, Issue 3, Pages 259-263, 2011.


==See also==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
[[Interval finite element]]


[[Category:Numerical differential equations]]
 
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.
 
==Test pages ==
 
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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