petsc-master 2020-01-15
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# Compute_Lagrange_Basis_3D_Internal

Evaluate bases and derivatives at quadrature points for a HEX8 or TET4 element.

### Synopsis

```#include "petscdt.h"
#include "petscdmmoab.h"
PetscErrorCode Compute_Lagrange_Basis_3D_Internal ( const PetscInt nverts, const PetscReal *coords, const PetscInt npts, const PetscReal *quad, PetscReal *phypts,
PetscReal *jxw, PetscReal *phi, PetscReal *dphidx, PetscReal *dphidy, PetscReal *dphidz,
PetscReal *jacobian, PetscReal *ijacobian, PetscReal *volume)
```
The routine is given the coordinates of the vertices of a hexahedra or tetrahedra.

The routine evaluates the basis functions associated with each quadrature point provided, and their derivatives with respect to X, Y and Z.

### Notes

Example Physical Element (HEX8)

```      8------7
/|     /|        t  s
5------6 |        | /
| |    | |        |/
| 4----|-3        0-------r
|/     |/
1------2
```

### Input Parameter

 PetscInt nverts - the number of element vertices PetscReal coords[3*nverts] - the physical coordinates of the vertices (in canonical numbering) PetscInt npts - the number of evaluation points (quadrature points) PetscReal quad[3*npts] - the evaluation points (quadrature points) in the reference space

### Output Parameter

 PetscReal phypts[3*npts] - the evaluation points (quadrature points) transformed to the physical space PetscReal jxw[npts] - the jacobian determinant * quadrature weight necessary for assembling discrete contributions PetscReal phi[npts] - the bases evaluated at the specified quadrature points PetscReal dphidx[npts] - the derivative of the bases wrt X-direction evaluated at the specified quadrature points PetscReal dphidy[npts] - the derivative of the bases wrt Y-direction evaluated at the specified quadrature points PetscReal dphidz[npts] - the derivative of the bases wrt Z-direction evaluated at the specified quadrature points