CFD Online Discussion Forums

CFD Online Discussion Forums (http://www.cfd-online.com/Forums/)
-   Main CFD Forum (http://www.cfd-online.com/Forums/main/)
-   -   Gauss quadrature on triangle (http://www.cfd-online.com/Forums/main/101631-gauss-quadrature-triangle.html)

effort8 May 9, 2012 09:50

Gauss quadrature on triangle
 
1 Attachment(s)
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.


All times are GMT -4. The time now is 05:44.