## Re: [Libmesh-users] quadrature rule for Tet4 or Tet10

 Re: [Libmesh-users] quadrature rule for Tet4 or Tet10 From: John Peterson - 2010-09-20 18:03:49 ```On Mon, Sep 20, 2010 at 9:48 AM, yunfei zhu wrote: > > I noted  one of the comments in quadrature_gauss_3D.C,  the tetrahedral > quadrature rules are taken from pg. 222 of "The finite element method" vol.1 > ed.5 by Zienkiewicz & Taylor, > so I checked the details in the book. I find that for each of the quadrature > point, there are 4 tetrahedral coordinates and the sum of the weights are > equal to 1. Those are probably barycentric coordinates, one of which is not independent, i.e. (x,y,z,1-x-y-z). We have simply converted those to (x,y,z). I don't have the book in front of me at the moment, so I'm not totally sure, but you can see more about the barycentric coordinates in fe_lagrange_shape_3D.C, around line 78. -- John ```

 [Libmesh-users] quadrature rule for Tet4 or Tet10 From: yunfei zhu - 2010-09-20 14:48:18 ```Hi I am trying to recover the stress base on the Tet4/10 elements. The quadrature rule for element tet4 seems quite confusing, could anyone give me an explanation? For example, If the quadrature order is SECOND, the quadrature points have only 3 Tetrahedral coordinates, and the sum of all the weights are far less than 1. I noted one of the comments in quadrature_gauss_3D.C, the tetrahedral quadrature rules are taken from pg. 222 of "The finite element method" vol.1 ed.5 by Zienkiewicz & Taylor, so I checked the details in the book. I find that for each of the quadrature point, there are 4 tetrahedral coordinates and the sum of the weights are equal to 1. Thanks in advance for help. Best wishes, yunfei ```
 Re: [Libmesh-users] quadrature rule for Tet4 or Tet10 From: Kirk, Benjamin (JSC-EG311) - 2010-09-20 15:00:24 ```On 9/20/10 9:48 AM, "yunfei zhu" wrote: > and the sum of > all the weights are far less than 1. The weights should sum to the volume of the element in your reference coordinate system, which for us I believe is 1/6. ```
 Re: [Libmesh-users] quadrature rule for Tet4 or Tet10 From: John Peterson - 2010-09-20 18:03:49 ```On Mon, Sep 20, 2010 at 9:48 AM, yunfei zhu wrote: > > I noted  one of the comments in quadrature_gauss_3D.C,  the tetrahedral > quadrature rules are taken from pg. 222 of "The finite element method" vol.1 > ed.5 by Zienkiewicz & Taylor, > so I checked the details in the book. I find that for each of the quadrature > point, there are 4 tetrahedral coordinates and the sum of the weights are > equal to 1. Those are probably barycentric coordinates, one of which is not independent, i.e. (x,y,z,1-x-y-z). We have simply converted those to (x,y,z). I don't have the book in front of me at the moment, so I'm not totally sure, but you can see more about the barycentric coordinates in fe_lagrange_shape_3D.C, around line 78. -- John ```