petsc-3.13.6 2020-09-29
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# Compute_Lagrange_Basis_2D_Internal

Evaluate bases and derivatives at quadrature points for a QUAD4 or TRI3 element.

### Synopsis

    #include "petscdt.h"
    #include "petscdmmoab.h"
    PetscErrorCode Compute_Lagrange_Basis_2D_Internal ( const PetscInt nverts, const PetscReal *coords, const PetscInt npts, const PetscReal *quad, PetscReal *phypts,
        PetscReal *jxw, PetscReal *phi, PetscReal *dphidx, PetscReal *dphidy,
        PetscReal *jacobian, PetscReal *ijacobian, PetscReal *volume)

The routine is given the coordinates of the vertices of a quadrangle or triangle.

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

### Notes

Example Physical Element (QUAD4)

        4------3        s
        |      |        |
        |      |        |
        |      |        |
        1------2        0-------r

### 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

### Level

advanced

### Location

src/dm/impls/moab/dmmbfem.cxx
Index of all DMMOAB routines
Table of Contents for all manual pages
Index of all manual pages