gsOverIntegrateRule< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsOverIntegrateRule< T >

Class that defines a mixed quadrature rule with different rules for the interior and the boundaries.

This class is defined using two other quadrature rules (only works for gsGaussRule or gsLobattoRule) for the interior and for the boundary. Depending on the location of the considered element, it will either use the interior rule or the boundary rule. In this way, one can for example use full (exact) integration on the boundary points and reduced integration in the interior.

Inheritance diagram for gsOverIntegrateRule< T >:

Collaboration diagram for gsOverIntegrateRule< T >:

Public Member Functions
index_t	dim () const
	Dimension of the rule.
	gsOverIntegrateRule ()
	Default empty constructor.
	gsOverIntegrateRule (const gsBasis< T > &basis, const std::vector< gsQuadRule< T > > &quadInterior, const std::vector< gsQuadRule< T > > &quadBoundary)
	Constructor. More...
void	mapTo (const gsVector< T > &lower, const gsVector< T > &upper, gsMatrix< T > &nodes, gsVector< T > &weights) const
	Maps the points in the d-dimensional cube with points lower and upper. More...
virtual void	mapTo (T startVal, T endVal, gsMatrix< T > &nodes, gsVector< T > &weights) const
	Maps a univariate quadrature rule (i.e., points and weights) from the reference interval to an arbitrary interval.
void	mapToAll (const std::vector< T > &breaks, gsMatrix< T > &nodes, gsVector< T > &weights) const
	Maps a univariate quadrature rule (i.e., points and weights) from the reference interval to a number of intervals, implied by the breaks.
index_t	numNodes () const
	Number of nodes in the currently kept rule.
const gsMatrix< T > &	referenceNodes () const
	Returns reference nodes for the currently kept rule. More...
const gsVector< T > &	referenceWeights () const
	Returns reference weights for the currently kept rule. More...
virtual void	setNodes (gsVector< index_t > const &, unsigned=0)
	Initialize quadrature rule with numNodes number of quadrature points per integration variable. More...
void	setNodes (index_t numNodes, unsigned digits=0)
	Initialize a univariate quadrature rule with numNodes quadrature points. More...

Static Public Member Functions
static uPtr	make (const gsBasis< T > &basis, const std::vector< gsQuadRule< T > > &quadInterior, const std::vector< gsQuadRule< T > > &quadBoundary)
	Construct a smart-pointer to the rule. More...

Protected Member Functions
void	computeTensorProductRule (const std::vector< gsVector< T > > &nodes, const std::vector< gsVector< T > > &weights)
	Computes the tensor product rule from coordinate-wise 1D nodes and weights.

Protected Attributes
gsMatrix< T >	m_nodes
	Reference quadrature nodes (on the interval [-1,1]).
gsVector< T >	m_weights
	Reference quadrature weights (corresponding to interval [-1,1]).

Constructor & Destructor Documentation

gsOverIntegrateRule ( const gsBasis< T > &  basis, const std::vector< gsQuadRule< T > > &  quadInterior, const std::vector< gsQuadRule< T > > &  quadBoundary  )

inline

Constructor.

Parameters

[in]	basis	The basis
[in]	quadInterior	vector with the univariate INTERIOR quadrature rules for each dimension of the basis.
[in]	quadBoundary	vector with the univariate BOUNDARY quadrature rules for each dimension of the basis.

Note

: Only works for QuadRules that do not re-implement mapTo (slicing occurs)

Member Function Documentation

static uPtr make ( const gsBasis< T > &  basis, const std::vector< gsQuadRule< T > > &  quadInterior, const std::vector< gsQuadRule< T > > &  quadBoundary  )

inlinestatic

Construct a smart-pointer to the rule.

Parameters

[in]	basis	The basis
[in]	quadInterior	The rule used for the interior
[in]	quadBoundary	The rule used for the boundary

Note

: Only works for QuadRules that do not re-implement mapTo (slicing occurs)

void mapTo ( const gsVector< T > &  lower, const gsVector< T > &  upper, gsMatrix< T > &  nodes, gsVector< T > &  weights  ) const

inlinevirtual

Maps the points in the d-dimensional cube with points lower and upper.

Parameters

[in]	lower	The lower corner
[in]	upper	The upper corner
	nodes	Quadrature points
	weights	Quadrature weights

Reimplemented from gsQuadRule< T >.

const gsMatrix<T>& referenceNodes ( ) const

inlineinherited

Returns reference nodes for the currently kept rule.

Returns

v Vector of length d = dim(), where each entry v_i of v is again a vector. v_i contains the reference quadrature points for the i-th coordinate direction.

const gsVector<T>& referenceWeights ( ) const

inlineinherited

Returns reference weights for the currently kept rule.

Returns

v Vector of length d = dim(), where each entry v_i of v is again a vector. v_i contains the reference quadrature weights for the i-th coordinate direction.

virtual void setNodes ( gsVector< index_t > const &  , unsigned  = 0  )

inlinevirtualinherited

Initialize quadrature rule with numNodes number of quadrature points per integration variable.

The call of this function initializes the quadrature rule for further use, i.e., the quadrature points and weights on the reference cube are set up and stored. The dimension d of the reference cube is specified by the length of the vector numNodes.

Example: numNodes = [2,5] corresponds to quadrature in 2D where two quadrature points are used for the first coordinate and five quadrature points for the second coordinate. In this case, 2*5 = 10 quadrature nodes and weights are set up.

---

Parameters
numNodes vector of length digits containing numbers of nodes to be used (per integration variable).
digits accuracy of nodes and weights. If 0, the quadrature rule will use precomputed tables if possible. If greater then 0, it will force to compute it everytime.

Reimplemented in gsGaussRule< T >, gsNewtonCotesRule< T >, and gsLobattoRule< T >.

void setNodes ( index_t  numNodes, unsigned  digits = 0  )

inlineinherited

Initialize a univariate quadrature rule with numNodes quadrature points.

Parameters

numNodes	quadrature point
digits	accuracy of nodes and weights. If 0, the quadrature rule will use precomputed tables if possible. If greater then 0, it will force to compute it everytime.