#include <boundadapted.hpp>

Detailed Description

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>
class Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >

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

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

Author: Gilles Steiner

See Also: boundadapted.hpp

Inheritance diagram for Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >:

Public Types
typedef BoundaryAdaptedTraits < Dim, Degree, T, StoragePolicy >	traits_type

Typedefs
typedef BoundaryAdapted< 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 traits_type::convex_type	convex_type

typedef traits_type::reference_convex_type	reference_convex_type

typedef traits_type::diff_pointset_type	diff_pointset_type

typedef traits_type::storage_policy	storage_policy

typedef traits_type::vector_type	vector_type

typedef traits_type::matrix_type	matrix_type

typedef traits_type::vector_matrix_type	vector_matrix_type

typedef traits_type::vector_vector_matrix_type	vector_vector_matrix_type

typedef traits_type::matrix_node_type	matrix_node_type

typedef traits_type::points_type	points_type

typedef traits_type::node_type	node_type

typedef Principal< Degree, T, StoragePolicy >	principal_type

Public Member Functions
template<typename AE >
BoundaryAdapted< Dim, Degree, T, StoragePolicy > ::vector_matrix_type	derivate (ublas::matrix_expression< AE > const &__pts, mpl::int_< 2 >)

template<typename AE >
BoundaryAdapted< Dim, Degree, T, StoragePolicy > ::vector_matrix_type	derivate (ublas::matrix_expression< AE > const &__pts, mpl::int_< 3 >)

points_type const &	points () const

points_type const &	points (int f) const

Constructors, destructor
	BoundaryAdapted ()

	BoundaryAdapted (BoundaryAdapted const &d)

	~BoundaryAdapted ()

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

Static Public Attributes
static const bool	is_normalized = traits_type::is_normalized

static const uint16_type	nConvexOrderDiff = traits_type::nConvexOrderDiff

static const uint16_type	nDim = traits_type::nDim

static const uint16_type	nOrder = traits_type::nOrder

static const uint16_type	numFaces = traits_type::numFaces

static const uint16_type	numVertices = traits_type::numVertices

Methods
matrix_type	coeff () const

static matrix_type	evaluate (points_type const &__pts)

template<typename AE >
static vector_matrix_type	derivate (ublas::matrix_expression< AE > const &__pts)

Additional Inherited Members
Private Types inherited from Feel::Basis< BoundaryAdaptedTag< Dim, Degree >, T >
typedef T	value_type

typedef ublas::matrix < value_type, ublas::row_major >	matrix_type

Private Member Functions inherited from Feel::Basis< BoundaryAdaptedTag< Dim, Degree >, T >
	Basis (PrimalBasis const &p)

	Basis (Basis const &b)

virtual	~Basis ()

Static Private Member Functions inherited from Feel::Basis< BoundaryAdaptedTag< Dim, Degree >, T >
static matrix_type const &	d (uint16_type i)
	derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice More...

static matrix_type const &	derivate (uint16_type i)
	derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice More...

static void	initDerivation (PrimalBasis const &basis)

Member Function Documentation

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

self_type const& Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::basis ( ) const

inline

Returns: self as a basis

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

uint_type Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::degree ( ) const

inline

Returns: the maximum degree of the BoundaryAdapted polynomial to be constructed

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

template<typename AE >

BoundaryAdapted<Dim, Degree, T, StoragePolicy>::vector_matrix_type Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::derivate	(	ublas::matrix_expression< AE > const &	__pts,
		mpl::int_< 3 >
	)

We must save the Jacobian matrix $Jac(i,j) = \frac{\partial\eta_j}{\partial \xi_i}$ for all points and all cases. We choose to build $Jac \in \mathcal M_{9 \times pts().size2()}$ such that ublas::row(Jac,3*(j-1)+i-1) = $\frac{\partial\eta_j}{\partial \xi_i}$

$d\eta_1/d\xi_i$

-2/( + )

2(1+)/( + )^2

$d\eta_2/d\xi_i$

0

2/(1-)

2(1+)/(1-)^2

$d\eta_3/d\xi_i$

0

1

Usefull intermediate matrix to simplify the construction

Adding Jacobian contribution

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

static matrix_type Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::evaluate ( points_type const & __pts)

inlinestatic

evaluate the BoundaryAdapted polynomials at a set of points __pts

__pts is a set of points

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

std::string Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::familyName ( ) const

inline

Returns: the familyName()

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

points_type const& Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::points ( ) const

inline

Access to the points of the reference convex associated

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>

points_type const& Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >::points ( int f) const

inline

Access to the points associated with the face f

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

boundadapted.hpp

Detailed Description

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy> class Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >

Public Types

Public Member Functions

Static Public Attributes

Methods

Additional Inherited Members

Member Function Documentation

template<uint16_type Dim, uint16_type Degree, typename T, template< class > class StoragePolicy>
class Feel::BoundaryAdapted< Dim, Degree, T, StoragePolicy >