# 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 Parameters#

• PetscInt nverts - the number of element vertices

• PetscReal coords[3nverts] -* the physical coordinates of the vertices (in canonical numbering)

• PetscInt npts - the number of evaluation points (quadrature points)

• PetscReal quad[3npts] -* the evaluation points (quadrature points) in the reference space

## Output Parameters#

• PetscReal phypts[3npts] -* 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

• jacobian - jacobian

• ijacobian - ijacobian

• volume - volume