Gauss quadrature on triangle

effort8 · May 9, 2012, 09:50

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.

cfdnewbie · May 10, 2012, 06:43

Just map the triangle to a rectangle, and apply the 1d Gauss quadrature in a tensor product way!

praveen · May 10, 2012, 09:15

Here are some quadrature rules

http://people.sc.fsu.edu/~jburkardt/.../dunavant.html

Also, check any good book on fem.

Jonas Holdeman · May 10, 2012, 09:23

Look at http://people.sc.fsu.edu/~jburkardt/...rules_tri.html

effort8 · May 10, 2012, 09:33

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 ?

effort8 · May 10, 2012, 09:40

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.

Jonas Holdeman · May 10, 2012, 11:19

It is a simple scale and shift.
x=(1+q)/2, y=(1+r)/2, for q=+/- 1, r=+/- 1.

effort8 · May 11, 2012, 01:03

Hi, Jonas Holdeman
Thank-you for your answer.

Your answer is big help to me.

May 10, 2012, 06:43		#2
cfdnewbie 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! effort8 likes this.

May 10, 2012, 09:15		#3
praveen Super Moderator Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 342 Blog Entries: 6 Rep Power: 18	Here are some quadrature rules http://people.sc.fsu.edu/~jburkardt/.../dunavant.html Also, check any good book on fem. effort8 likes this.

May 10, 2012, 09:23		#4
Jonas Holdeman Senior Member Jonas T. Holdeman, Jr. Join Date: Mar 2009 Location: Knoxville, Tennessee Posts: 128 Rep Power: 18	Look at http://people.sc.fsu.edu/~jburkardt/...rules_tri.html effort8 likes this.

May 10, 2012, 09:33		#5
effort8 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.

May 10, 2012, 09:40		#6
effort8 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.

May 10, 2012, 11:19		#7
Jonas Holdeman 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. effort8 likes this.

May 11, 2012, 01:03		#8
effort8 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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