Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy > Class Template Reference

TensorisedBoundaryAdapted Basis on simplex products. More...

#include <tensorisedboundadapted.hpp>

List of all members.

Classes
struct	Convex
Public Member Functions
points_type	points ()
points_type const &	points (int f) const
Constructors, destructor
	TensorisedBoundaryAdapted ()
	TensorisedBoundaryAdapted (TensorisedBoundaryAdapted const &d)
	~TensorisedBoundaryAdapted ()
Operator overloads
self_type const &	operator= (self_type const &d)
matrix_type	operator() (node_type const &pt) const
matrix_type	operator() (points_type const &pts) const
Accessors
uint_type	degree () const
self_type const &	basis () const
std::string	familyName () const
Methods
matrix_type	coeff () const
matrix_type	evaluate (points_type const &__pts) const
template<typename AE >
vector_matrix_type	derivate (ublas::matrix_expression< AE > const &__pts) const
matrix_type const &	d (uint16_type i)
	derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice
matrix_type const &	derivate (uint16_type i)
	derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice
Static Public Attributes
static const uint16_type	nDim = Dim
static const uint16_type	nOrder = Degree
static const uint16_type	nConvexOrder = nDim+nOrder+1
Typedefs
typedef TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >	self_type
typedef self_type	basis_type
typedef T	value_type
typedef int16_type	int_type
typedef uint16_type	uint_type
typedef Hypercube< nDim, nConvexOrder, nDim >	convex_type
typedef Reference< convex_type, nDim, nConvexOrder, nDim, T >	reference_convex_type
typedef reference_convex_type::points_type	points_type
typedef StoragePolicy< value_type >	storage_policy
typedef storage_policy::vector_type	vector_type
typedef storage_policy::matrix_type	matrix_type
typedef storage_policy::vector_matrix_type	vector_matrix_type
typedef storage_policy::vector_vector_matrix_type	vector_vector_matrix_type
typedef storage_policy::matrix_node_type	matrix_node_type
typedef storage_policy::node_type	node_type
static const uint16_type	numVertices = reference_convex_type::numVertices
static const uint16_type	numFaces = reference_convex_type::numFaces

---

Detailed Description

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>
class Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >

TensorisedBoundaryAdapted Basis on simplex products.

This class represents the Boundary Adapted Basis made from Jacobi polynomials up to degree Degree on a simplex in dimension Dim.

The Boundary adapted basis is constructed to preserve a part of the Jacobi polynomials' orthogonality. However we need to modify the basis in order to manage easily the boundary condtions.

Author:

Gilles Steiner

See also:

dubiner.hpp

---

Member Function Documentation

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

self_type const& Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::basis

(

)

const [inline]

Returns:

self as a basis

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

matrix_type const& Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::d

(

uint16_type

i

)

[inline]

derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice

• i index of the derivative (0 : x, 1 : y, 2 : z )

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

uint_type Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::degree

(

)

const [inline]

Returns:

the maximum degree of the TensorisedBoundaryAdapted polynomial to be constructed

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

matrix_type const& Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::derivate

(

uint16_type

i

)

[inline]

derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice

• i index of the derivative (0 : x, 1 : y, 2 : z )

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

matrix_type Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::evaluate

(

points_type const &

__pts

)

const [inline]

evaluate the TensorisedBoundaryAdapted polynomials at a set of points __pts

• __pts is a set of points

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

std::string Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::familyName

(

)

const [inline]

Returns:

the family name of the finite element

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

points_type Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::points

(

)

[inline]

Access to the points of the reference convex associated

template<uint16_type Dim, uint16_type Degree, typename T = double, template< class > class StoragePolicy = StorageUBlas>

points_type const& Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy >::points

(

int

f

)

const [inline]

Access to the points associated with the face f