QIterated< dim > Class Template Reference
[Quadrature formulas]

Inheritance diagram for QIterated< dim >:

Inheritance graph
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List of all members.

Classes

class  ExcInvalidQuadratureFormula

Public Member Functions

 QIterated (const Quadrature< 1 > &base_quadrature, const unsigned int n_copies)

Static Private Member Functions

static bool uses_both_endpoints (const Quadrature< 1 > &base_quadrature)


Detailed Description

template<int dim>
class QIterated< dim >

Quadrature formula constructed by iteration of another quadrature formula in each direction. In more than one space dimension, the resulting quadrature formula is constructed in the usual way by building the tensor product of the respective iterated quadrature formula in one space dimension.

In one space dimension, the given base formula is copied and scaled onto a given number of subintervals of length 1/n_copies. If the quadrature formula uses both end points of the unit interval, then in the interior of the iterated quadrature formula there would be quadrature points which are used twice; we merge them into one with a weight which is the sum of the weights of the left- and the rightmost quadrature point.

Since all dimensions higher than one are built up by tensor products of one dimensional and dim-1 dimensional quadrature formulæ, the argument given to the constructor needs to be a quadrature formula in one space dimension, rather than in dim dimensions.

The aim of this class is to provide a low order formula, where the error constant can be tuned by increasing the number of quadrature points. This is useful in integrating non-differentiable functions on cells.

Author:
Wolfgang Bangerth 1999

Constructor & Destructor Documentation

template<int dim>
QIterated< dim >::QIterated ( const Quadrature< 1 > &  base_quadrature,
const unsigned int  n_copies 
)

Constructor. Iterate the given quadrature formula n_copies times in each direction.


Member Function Documentation

template<int dim>
static bool QIterated< dim >::uses_both_endpoints ( const Quadrature< 1 > &  base_quadrature  )  [static, private]

Check whether the given quadrature formula has quadrature points at the left and right end points of the interval.


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

deal.II documentation generated on Sat Aug 15 16:52:15 2009 by doxygen 1.5.9