Logo  0.95.0-final
Finite Element Embedded Library and Language in C++
Feel++ Feel++ on Github Feel++ community
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Groups Pages
Feel::TensorisedBoundaryAdapted< Dim, Degree, T, StoragePolicy > Class Template Reference

#include <tensorisedboundadapted.hpp>

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

Public Member Functions

template<typename AE >
TensorisedBoundaryAdapted< Dim,
Degree, T, StoragePolicy >
::vector_matrix_type 
derivate (ublas::matrix_expression< AE > const &__pts, mpl::int_< 2 >) const
 
template<typename AE >
TensorisedBoundaryAdapted< Dim,
Degree, T, StoragePolicy >
::vector_matrix_type 
derivate (ublas::matrix_expression< AE > const &__pts, mpl::int_< 3 >) const
 
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 More...
 
matrix_type const & derivate (uint16_type i)
 derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice More...
 

Static Public Attributes

static const uint16_type nConvexOrder = nDim+nOrder+1
 
static const uint16_type nDim = Dim
 
static const uint16_type nOrder = Degree
 

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
 

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


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

Generated on Fri Oct 25 2013 14:24:32 for Feel++ by doxygen 1.8.4