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Quadrature formula on hexahedra. More...

`#include <Galeri_HexQuadrature.h>`

Inheritance diagram for Galeri::FiniteElements::HexQuadrature:
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Collaboration diagram for Galeri::FiniteElements::HexQuadrature:
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List of all members.

## Public Member Functions

Constructor.
void ComputeJacobian (const int QuadrNode, const double *x_hex, const double *y_hex, const double *z_hex) const
Computes the Jacobian at the specified quadrature node.
void ComputeQuadrNodes (const int ii, const double *x, const double *y, const double *z, double &xq, double &yq, double &zq) const
Maps the quadrature nodes from the reference element to the actual one.
void ComputeDerivatives (const int QuadrNode) const
Computes the derivatives at the specified quadrature node.
Computes the weight at the specified quadrature node.
double DetJacobian (const int QuadrNode) const
Computes the determinant of the Jacobian matrix at the quadrature node.
double Phi (const int i) const
Returns the value of the i-th basis function on the reference element.
double PhiX (const int i) const
Returns the value of the x-derivative i-th basis function on the reference element.
double PhiY (const int i) const
Returns the value of the y-derivative i-th basis function on the reference element.
double PhiZ (const int i) const
Returns the value of the z-derivative i-th basis function on the reference element.
double Psi (const int i) const
Returns the value of the i-th test function on the reference element.
double PsiX (const int i) const
Returns the value of the z-derivative i-th test function on the reference element.
double PsiY (const int i) const
Returns the value of the y-derivative i-th test function on the reference element.
double PsiZ (const int i) const
Returns the value of the z-derivative i-th test function on the reference element.
int NumQuadrNodes () const
Returns the number of quadrature node per element.
int NumPhiFunctions () const
Returns the number of basis function on the reference element.
int NumPsiFunctions () const
Returns the number of test function on the reference element.
Constructor.
void ComputeJacobian (const int QuadrNode, const double *x_hex, const double *y_hex, const double *z_hex) const
Computes the Jacobian at the specified quadrature node.
void ComputeQuadrNodes (const int ii, const double *x, const double *y, const double *z, double &xq, double &yq, double &zq) const
Maps the quadrature nodes from the reference element to the actual one.
void ComputeDerivatives (const int QuadrNode) const
Computes the derivatives at the specified quadrature node.
Computes the weight at the specified quadrature node.
double DetJacobian (const int QuadrNode) const
Computes the determinant of the Jacobian matrix at the quadrature node.
double Phi (const int i) const
Returns the value of the i-th basis function on the reference element.
double PhiX (const int i) const
Returns the value of the x-derivative i-th basis function on the reference element.
double PhiY (const int i) const
Returns the value of the y-derivative i-th basis function on the reference element.
double PhiZ (const int i) const
Returns the value of the z-derivative i-th basis function on the reference element.
double Psi (const int i) const
Returns the value of the i-th test function on the reference element.
double PsiX (const int i) const
Returns the value of the z-derivative i-th test function on the reference element.
double PsiY (const int i) const
Returns the value of the y-derivative i-th test function on the reference element.
double PsiZ (const int i) const
Returns the value of the z-derivative i-th test function on the reference element.
int NumQuadrNodes () const
Returns the number of quadrature node per element.
int NumPhiFunctions () const
Returns the number of basis function on the reference element.
int NumPsiFunctions () const
Returns the number of test function on the reference element.

## Protected Attributes

int NumDimensions_
int NumLocalNodes_
double det_J_
Epetra_SerialDenseMatrix J_
Epetra_SerialDenseMatrix basis_rs_
Epetra_SerialDenseMatrix basis_dr_
Epetra_SerialDenseMatrix basis_ds_
Epetra_SerialDenseMatrix basis_dt_
Epetra_SerialDenseVector basis_xy_
Epetra_SerialDenseVector basis_dx_
Epetra_SerialDenseVector basis_dy_
Epetra_SerialDenseVector basis_dz_
Epetra_SerialDenseVector basis_rs_temp_
Epetra_SerialDenseVector basis_dr_temp_
Epetra_SerialDenseVector basis_ds_temp_
Epetra_SerialDenseVector basis_dt_temp_
Epetra_SerialDenseVector Weight_
Epetra_SerialDenseVector qr_
Epetra_SerialDenseVector qs_
Epetra_SerialDenseVector qt_

## Detailed Description

Quadrature formula on hexahedra.

## Constructor & Destructor Documentation

 Galeri::FiniteElements::HexQuadrature::HexQuadrature ( const int NumQuadrNodes ) ` [inline]`

Constructor.

Parameters:
 NumQuadrNodes - (In) Number of quadrature nodes per element. Valid choices are: 1.

 Galeri::FiniteElements::HexQuadrature::HexQuadrature ( const int NumQuadrNodes ) ` [inline]`

Constructor.

Parameters:
 NumQuadrNodes - (In) Number of quadrature nodes per element. Valid choices are: 1.