#include <legendre.hpp>

Detailed Description

template<uint16_type Dim, uint16_type RealDim, uint16_type Degree, typename NormalizationPolicy, typename T, template< class > class StoragePolicy>
class Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >

Legendre polynomial orthonormal basis.

This class represents the Legendre polynomials up to degree Degree on a simplex in dimension Dim.

The legendre polynomials in 1D, the segment $[-1;1]$ are defined using Jacobi polynomials as follows: $\phi_i(x) = P_i^{0,0}(x)$ where $P_i^{0,0}(x)$ is the i-th Jacobi polynomial evaluated at $x \in [-1;1]$ with weights $(0,0)$ .

Author: Christophe Prud'homme

See Also: G.E. Karniadakis and S.J. Sherwin, ''Spectral/hp Element Methods for CFD,'' Oxford University Press, March 1999.

Public Types
typedef Discontinuous	continuity_type

typedef LegendreTraits< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >	traits_type

Typedefs
typedef Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >	self_type

typedef self_type	basis_type

typedef traits_type::value_type	value_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::matrix_type	matrix_type

typedef traits_type::vector_matrix_type	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

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

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

Constructors, destructor
	Legendre ()

	Legendre (Legendre const &d)

	~Legendre ()

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
size_type	size () const

uint16_type	degree () const

self_type const &	basis () const

bool	isNormalized () const

std::string	familyName () const

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

static const bool	is_product = true

static const bool	isContinuous = false

static const bool	isTransformationEquivalent = true

static const uint16_type	nConvexOrder = nOrder+2

static const uint16_type	nDim = Dim

static const uint16_type	nOrder = Degree

static const uint16_type	nRealDim = RealDim

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)

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...