# Galeri::FiniteElements::HexQuadrature Class Reference

Quadrature formula on hexahedra. More...

`#include <Galeri_HexQuadrature.h>`

Inheritance 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.

## 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.

Definition at line 52 of file Galeri_HexQuadrature.h.

## 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.

Definition at line 62 of file Galeri_HexQuadrature.h.

 Galeri::FiniteElements::HexQuadrature::~HexQuadrature ( ) ` [inline]`

Definition at line 182 of file Galeri_HexQuadrature.h.

## Member Function Documentation

 void Galeri::FiniteElements::HexQuadrature::ComputeJacobian ( const int QuadrNode, const double * x, const double * y, const double * z ) const` [inline, virtual]`

Computes the Jacobian at the specified quadrature node.

Definition at line 185 of file Galeri_HexQuadrature.h.

 void Galeri::FiniteElements::HexQuadrature::ComputeQuadrNodes ( const int QuadrNode, const double * x, const double * y, const double * z, double & xq, double & yq, double & zq ) const` [inline, virtual]`

Maps the quadrature nodes from the reference element to the actual one.

Definition at line 270 of file Galeri_HexQuadrature.h.

 void Galeri::FiniteElements::HexQuadrature::ComputeDerivatives ( const int QuadrNode ) const` [inline, virtual]`

Computes the derivatives at the specified quadrature node.

Definition at line 290 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::QuadrWeight ( const int QuadrNode ) const` [inline, virtual]`

Computes the weight at the specified quadrature node.

Definition at line 306 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::DetJacobian ( const int QuadrNode ) const` [inline, virtual]`

Computes the determinant of the Jacobian matrix at the quadrature node.

Definition at line 311 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::Phi ( const int i ) const` [inline, virtual]`

Returns the value of the i-th basis function on the reference element.

Definition at line 316 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::PhiX ( const int i ) const` [inline, virtual]`

Returns the value of the x-derivative i-th basis function on the reference element.

Definition at line 321 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::PhiY ( const int i ) const` [inline, virtual]`

Returns the value of the y-derivative i-th basis function on the reference element.

Definition at line 326 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::PhiZ ( const int i ) const` [inline, virtual]`

Returns the value of the z-derivative i-th basis function on the reference element.

Definition at line 331 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::Psi ( const int i ) const` [inline, virtual]`

Returns the value of the i-th test function on the reference element.

Definition at line 336 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::PsiX ( const int i ) const` [inline, virtual]`

Returns the value of the z-derivative i-th test function on the reference element.

Definition at line 341 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::PsiY ( const int i ) const` [inline, virtual]`

Returns the value of the y-derivative i-th test function on the reference element.

Definition at line 346 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::PsiZ ( const int i ) const` [inline, virtual]`

Returns the value of the z-derivative i-th test function on the reference element.

Definition at line 351 of file Galeri_HexQuadrature.h.

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

Returns the number of quadrature node per element.

Definition at line 356 of file Galeri_HexQuadrature.h.

 int Galeri::FiniteElements::HexQuadrature::NumPhiFunctions ( ) const` [inline, virtual]`

Returns the number of basis function on the reference element.

Definition at line 361 of file Galeri_HexQuadrature.h.

 int Galeri::FiniteElements::HexQuadrature::NumPsiFunctions ( ) const` [inline, virtual]`

Returns the number of test function on the reference element.

Definition at line 366 of file Galeri_HexQuadrature.h.

## Member Data Documentation

 int Galeri::FiniteElements::HexQuadrature::NumQuadrNodes_` [protected]`

Definition at line 373 of file Galeri_HexQuadrature.h.

 int Galeri::FiniteElements::HexQuadrature::NumDimensions_` [protected]`

Definition at line 374 of file Galeri_HexQuadrature.h.

 int Galeri::FiniteElements::HexQuadrature::NumLocalNodes_` [protected]`

Definition at line 375 of file Galeri_HexQuadrature.h.

 double Galeri::FiniteElements::HexQuadrature::det_J_` [mutable, protected]`

Definition at line 377 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseMatrix Galeri::FiniteElements::HexQuadrature::J_` [mutable, protected]`

Definition at line 379 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseMatrix Galeri::FiniteElements::HexQuadrature::basis_rs_` [mutable, protected]`

Definition at line 381 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseMatrix Galeri::FiniteElements::HexQuadrature::basis_dr_` [mutable, protected]`

Definition at line 382 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseMatrix Galeri::FiniteElements::HexQuadrature::basis_ds_` [mutable, protected]`

Definition at line 383 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseMatrix Galeri::FiniteElements::HexQuadrature::basis_dt_` [mutable, protected]`

Definition at line 384 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_xy_` [mutable, protected]`

Definition at line 386 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_dx_` [mutable, protected]`

Definition at line 387 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_dy_` [mutable, protected]`

Definition at line 388 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_dz_` [mutable, protected]`

Definition at line 389 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_rs_temp_` [mutable, protected]`

Definition at line 391 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_dr_temp_` [mutable, protected]`

Definition at line 392 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_ds_temp_` [mutable, protected]`

Definition at line 393 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::basis_dt_temp_` [mutable, protected]`

Definition at line 394 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::Weight_` [mutable, protected]`

Definition at line 396 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::qr_` [mutable, protected]`

Definition at line 398 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::qs_` [mutable, protected]`

Definition at line 399 of file Galeri_HexQuadrature.h.

 Epetra_SerialDenseVector Galeri::FiniteElements::HexQuadrature::qt_` [mutable, protected]`

Definition at line 400 of file Galeri_HexQuadrature.h.

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