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May 9, 2012, 09:50 |
Gauss quadrature on triangle
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#1 |
New Member
DJChoi
Join Date: Jan 2012
Posts: 8
Rep Power: 14 |
Hello?
I want to do Gauss quadrature over triangle as attachted file. I would like to know how to find the points and weights for Gauss quadrature. Thanks. |
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May 10, 2012, 06:43 |
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#2 |
Senior Member
cfdnewbie
Join Date: Mar 2010
Posts: 557
Rep Power: 20 |
Just map the triangle to a rectangle, and apply the 1d Gauss quadrature in a tensor product way!
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May 10, 2012, 09:15 |
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#3 |
Super Moderator
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Here are some quadrature rules
http://people.sc.fsu.edu/~jburkardt/.../dunavant.html Also, check any good book on fem. |
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May 10, 2012, 09:23 |
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#4 |
Senior Member
Jonas T. Holdeman, Jr.
Join Date: Mar 2009
Location: Knoxville, Tennessee
Posts: 128
Rep Power: 18 |
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May 10, 2012, 09:33 |
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#5 |
New Member
DJChoi
Join Date: Jan 2012
Posts: 8
Rep Power: 14 |
Hi, cfdnewbie.
Thank you for your answer. I know the mapping the triangle to a rectangle. And I can apply the 1d Gauss quadrature. But I don't know how to apply the 1d Gauss quadrature in a tensor product way. Would you tell me the way how to do that, please ? Or, would you recommend any book written that way, please ? Last edited by effort8; May 10, 2012 at 09:54. |
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May 10, 2012, 09:40 |
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#6 |
New Member
DJChoi
Join Date: Jan 2012
Posts: 8
Rep Power: 14 |
Hi, praveen. Hi, Jonas Holdeman praveen.
Thank-you for useful information about website. One more question. Would you tell me the transformation mapping from "(-1,-1),(1,-1),(-1,1)" to "(0,0), (1,0), (0,1)" ? I would like to know the transformation mapping equation. Last edited by effort8; May 10, 2012 at 09:57. |
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May 10, 2012, 11:19 |
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#7 |
Senior Member
Jonas T. Holdeman, Jr.
Join Date: Mar 2009
Location: Knoxville, Tennessee
Posts: 128
Rep Power: 18 |
It is a simple scale and shift.
x=(1+q)/2, y=(1+r)/2, for q=+/- 1, r=+/- 1. |
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May 11, 2012, 01:03 |
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#8 |
New Member
DJChoi
Join Date: Jan 2012
Posts: 8
Rep Power: 14 |
Hi, Jonas Holdeman
Thank-you for your answer. Your answer is big help to me. |
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