# Galeri::FiniteElements::TetQuadrature Class Reference

Quadrature formula on tetrahedra. More...

`#include <Galeri_TetQuadrature.h>`

Inheritance diagram for Galeri::FiniteElements::TetQuadrature:
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List of all members.

## Public Member Functions

TetQuadrature (const int NumQuadrNodes)
Constructor.
~TetQuadrature ()
void ComputeJacobian (const int QuadrNode, const double *x, const double *y, const double *z) 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.
double QuadrWeight (const int QuadrNode) const
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 NumQuadrNodes_
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 tetrahedra.

Definition at line 54 of file Galeri_TetQuadrature.h.

## Constructor & Destructor Documentation

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

Constructor.

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

Definition at line 64 of file Galeri_TetQuadrature.h.

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

Definition at line 131 of file Galeri_TetQuadrature.h.

## Member Function Documentation

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

Computes the Jacobian at the specified quadrature node.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 134 of file Galeri_TetQuadrature.h.

 void Galeri::FiniteElements::TetQuadrature::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.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 186 of file Galeri_TetQuadrature.h.

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

Computes the derivatives at the specified quadrature node.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 206 of file Galeri_TetQuadrature.h.

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

Computes the weight at the specified quadrature node.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 222 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 227 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 232 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 237 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 242 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 247 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 252 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 257 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 262 of file Galeri_TetQuadrature.h.

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

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

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 267 of file Galeri_TetQuadrature.h.

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

Returns the number of quadrature node per element.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 272 of file Galeri_TetQuadrature.h.

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

Returns the number of basis function on the reference element.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 277 of file Galeri_TetQuadrature.h.

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

Returns the number of test function on the reference element.

Implements Galeri::FiniteElements::AbstractQuadrature.

Definition at line 282 of file Galeri_TetQuadrature.h.

## Member Data Documentation

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

Definition at line 289 of file Galeri_TetQuadrature.h.

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

Definition at line 290 of file Galeri_TetQuadrature.h.

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

Definition at line 291 of file Galeri_TetQuadrature.h.

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

Definition at line 293 of file Galeri_TetQuadrature.h.

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

Definition at line 295 of file Galeri_TetQuadrature.h.

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

Definition at line 297 of file Galeri_TetQuadrature.h.

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

Definition at line 298 of file Galeri_TetQuadrature.h.

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

Definition at line 299 of file Galeri_TetQuadrature.h.

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

Definition at line 300 of file Galeri_TetQuadrature.h.

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

Definition at line 302 of file Galeri_TetQuadrature.h.

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

Definition at line 303 of file Galeri_TetQuadrature.h.

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

Definition at line 304 of file Galeri_TetQuadrature.h.

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

Definition at line 305 of file Galeri_TetQuadrature.h.

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

Definition at line 307 of file Galeri_TetQuadrature.h.

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

Definition at line 308 of file Galeri_TetQuadrature.h.

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

Definition at line 309 of file Galeri_TetQuadrature.h.

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

Definition at line 310 of file Galeri_TetQuadrature.h.

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

Definition at line 312 of file Galeri_TetQuadrature.h.

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

Definition at line 314 of file Galeri_TetQuadrature.h.

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

Definition at line 315 of file Galeri_TetQuadrature.h.

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

Definition at line 316 of file Galeri_TetQuadrature.h.

The documentation for this class was generated from the following file:
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