Feel++  0.92.0
Public Member Functions | Static Public Attributes
Feel::Principal< Degree, T, StoragePolicy > Class Template Reference

Principal modified functions. More...

#include <principal.hpp>

List of all members.

Public Types

Typedefs
typedef Principal< Degree, T,
StoragePolicy > 
self_type
typedef T value_type
typedef StoragePolicy< value_type > storage_policy
typedef storage_policy::matrix_type matrix_type
typedef
storage_policy::vector_matrix_type 
vector_matrix_type
typedef
storage_policy::matrix_node_type 
matrix_node_type
typedef storage_policy::node_type node_type
typedef
storage_policy::vector_vector_matrix_type 
vector_vector_matrix_type
typedef storage_policy::vector_type vector_type

Public Member Functions

self_type const & operator= (self_type const &d)
matrix_type derivate_1 (vector_type const &__pts) const
vector_matrix_type derivate_2 (vector_type const &__pts) const
vector_vector_matrix_type derivate_3 (vector_type const &__pts) const
Constructors, destructor
 Principal ()
 Principal (value_type a, value_type b)
 ~Principal ()
Accessors
uint16_type degree () const
Methods
value_type a () const
value_type b () const
matrix_type evaluate_1 (vector_type const &__pts) const
vector_matrix_type evaluate_2 (vector_type const &__pts) const
vector_vector_matrix_type evaluate_3 (vector_type const &__pts) const

Static Public Attributes

static const uint16_type nOrder = Degree

Detailed Description

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

Principal modified functions.

This class is a useful class to construct multidimensionnal boundary adapted expansions basis. It is constructed following the section 3.2.3.1 of the book from Sherwin and Karniadakis "Spectral/hp element methods for computational fluid dynamics".

Author:
Gilles Steiner
See also:
dubiner.hpp

Member Function Documentation

template<uint16_type Degree, typename T , template< class > class StoragePolicy>
Principal< Degree, T, StoragePolicy >::matrix_type Feel::Principal< Degree, T, StoragePolicy >::evaluate_1 ( vector_type const &  __pts) const

evaluate the Principal functions at a set of points __pts

  • __pts is a set of points in one dimension One order principal function $ \psi_i(z) $
template<uint16_type Degree, typename T , template< class > class StoragePolicy>
Principal< Degree, T, StoragePolicy >::vector_matrix_type Feel::Principal< Degree, T, StoragePolicy >::evaluate_2 ( vector_type const &  __pts) const

Second order principal function $ \psi_{ij}(z) $

template<uint16_type Degree, typename T , template< class > class StoragePolicy>
Principal< Degree, T, StoragePolicy >::vector_vector_matrix_type Feel::Principal< Degree, T, StoragePolicy >::evaluate_3 ( vector_type const &  __pts) const

Third order principal function $ \psi_{ijk}(z) $