# Galeri::FiniteElements::AbstractQuadrature Class Reference

Interfaces for quadrature over elements. More...

`#include <Galeri_AbstractQuadrature.h>`

Inheritance diagram for Galeri::FiniteElements::AbstractQuadrature:
[legend]

List of all members.

## Public Member Functions

virtual ~AbstractQuadrature ()
Destructor.

virtual int NumQuadrNodes () const =0
Returns the number of quadrature node per element.
virtual int NumPhiFunctions () const =0
Returns the number of basis function on the reference element.
virtual int NumPsiFunctions () const =0
Returns the number of test function on the reference element.

virtual void ComputeJacobian (const int QuadrNode, const double *x, const double *y, const double *z) const =0
Computes the Jacobian at the specified quadrature node.
virtual void ComputeQuadrNodes (const int QuadrNode, const double *x, const double *y, const double *z, double &xq, double &yq, double &zq) const =0
Maps the quadrature nodes from the reference element to the actual one.
virtual void ComputeDerivatives (const int QuadrNode) const =0
Computes the derivatives at the specified quadrature node.
virtual double QuadrWeight (const int QuadrNode) const =0
Computes the weight at the specified quadrature node.
virtual double DetJacobian (const int QuadrNode) const =0
Computes the determinant of the Jacobian matrix at the quadrature node.

virtual double Phi (const int i) const =0
Returns the value of the i-th basis function on the reference element.
virtual double PhiX (const int i) const =0
Returns the value of the x-derivative i-th basis function on the reference element.
virtual double PhiY (const int i) const =0
Returns the value of the y-derivative i-th basis function on the reference element.
virtual double PhiZ (const int i) const =0
Returns the value of the z-derivative i-th basis function on the reference element.
virtual double Psi (const int i) const =0
Returns the value of the i-th test function on the reference element.
virtual double PsiX (const int i) const =0
Returns the value of the z-derivative i-th test function on the reference element.
virtual double PsiY (const int i) const =0
Returns the value of the y-derivative i-th test function on the reference element.
virtual double PsiZ (const int i) const =0
Returns the value of the z-derivative i-th test function on the reference element.

virtual ~AbstractQuadrature ()
Destructor.

virtual int NumQuadrNodes () const =0
Returns the number of quadrature node per element.
virtual int NumPhiFunctions () const =0
Returns the number of basis function on the reference element.
virtual int NumPsiFunctions () const =0
Returns the number of test function on the reference element.

virtual void ComputeJacobian (const int QuadrNode, const double *x, const double *y, const double *z) const =0
Computes the Jacobian at the specified quadrature node.
virtual void ComputeQuadrNodes (const int QuadrNode, const double *x, const double *y, const double *z, double &xq, double &yq, double &zq) const =0
Maps the quadrature nodes from the reference element to the actual one.
virtual void ComputeDerivatives (const int QuadrNode) const =0
Computes the derivatives at the specified quadrature node.
virtual double QuadrWeight (const int QuadrNode) const =0
Computes the weight at the specified quadrature node.
virtual double DetJacobian (const int QuadrNode) const =0
Computes the determinant of the Jacobian matrix at the quadrature node.

virtual double Phi (const int i) const =0
Returns the value of the i-th basis function on the reference element.
virtual double PhiX (const int i) const =0
Returns the value of the x-derivative i-th basis function on the reference element.
virtual double PhiY (const int i) const =0
Returns the value of the y-derivative i-th basis function on the reference element.
virtual double PhiZ (const int i) const =0
Returns the value of the z-derivative i-th basis function on the reference element.
virtual double Psi (const int i) const =0
Returns the value of the i-th test function on the reference element.
virtual double PsiX (const int i) const =0
Returns the value of the z-derivative i-th test function on the reference element.
virtual double PsiY (const int i) const =0
Returns the value of the y-derivative i-th test function on the reference element.
virtual double PsiZ (const int i) const =0
Returns the value of the z-derivative i-th test function on the reference element.

## Detailed Description

Interfaces for quadrature over elements.

AbstractQuadrature is a pure virtual class that defines a set of abstract interfaces to basis and test functions (and their derivatives), and also furnishes all the tools required to numerically integrate over an element.

Date:
Last updated on Apr-05.

The documentation for this class was generated from the following files:
• FiniteElements/Galeri_AbstractQuadrature.h
• fem/Galeri_AbstractQuadrature.h
Generated on Wed Apr 13 10:08:44 2011 for Galeri by  1.6.3