Rheolef  7.2
an efficient C++ finite element environment
basis_fem_RTk.h
Go to the documentation of this file.
1 #ifndef _RHEOLEF_BASIS_FEM_RTK_H
2 #define _RHEOLEF_BASIS_FEM_RTK_H
23 /*Class:sherwin
24 NAME: @code{RTk} - The Raviart-Thomas vector-valued polynomial basis
25 @cindex polynomial basis
26 @clindex space
27 @clindex basis
28 SYNOPSIS:
29  space Vh(omega,"RT0");
30 DESCRIPTION:
31  @noindent
32  This @code{basis} is described
33  in Raviart and Thomas (Mathematical aspects of finite element methods, Springer, 1977).
34  It is indicated in the @code{space} (see @ref{space class})
35  by a string starting with
36  the two letters @code{"RT"},
37  followed by digits indicating the polynomial order.
38 
39 OPTIONS:
40  This basis recognizes the equispaced/warburton node option
41  for degrees of freedom located on sides.
42  See @ref{basis_option class}.
43 
44 AUTHOR: Pierre.Saramito@imag.fr
45 DATE: 12 september 2017
46 End:
47 */
48 #include "rheolef/basis.h"
49 #include "rheolef/quadrature.h"
50 namespace rheolef {
51 
52 template<class T>
53 class basis_fem_RTk: public basis_rep<T> {
54 public:
55 
56 // typedefs:
57 
58  typedef basis_rep<T> base;
61  typedef typename base::valued_type valued_type;
62 
63 // allocators:
64 
65  basis_fem_RTk (size_type k, const basis_option& sopt);
67 
68 // accessors:
69 
70  size_type degree() const { return _b_pre_kp1.degree(); }
71  std::string family_name() const { return "RT"; }
72  size_type family_index() const { return degree()-1; }
73  bool is_nodal() const { return false; }
75  const std::string& valued() const { return space_constant::valued_name (valued_tag()); }
76 
77  const Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1>&
78  hat_node (reference_element hat_K) const;
79 
80  const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>&
81  vdm (reference_element hat_K) const;
82 
83  const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>&
84  inv_vdm (reference_element hat_K) const;
85 
86 // evaluation of all basis functions at hat_x:
87 
88  void evaluate (
89  reference_element hat_K,
90  const point_basic<T>& hat_x,
91  Eigen::Matrix<value_type,Eigen::Dynamic,1>& value) const;
92 
93  void grad_evaluate (
94  reference_element hat_K,
95  const point_basic<T>& hat_x,
96  Eigen::Matrix<tensor_basic<T>,Eigen::Dynamic,1>& value) const;
97 
98 // internals:
99 
100  void _initialize_cstor_sizes() const;
101  void _initialize_data (reference_element hat_K) const;
102  void _compute_dofs (
103  reference_element hat_K,
104  const Eigen::Matrix<value_type,Eigen::Dynamic,1>& f_xnod,
105  Eigen::Matrix<T,Eigen::Dynamic,1>& dof) const;
106 
107 protected:
108 
109 // data:
110  // valued: initialized by _initialize_data:
112 
113  mutable std::array<
114  Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1>,
116 
117  mutable std::array<Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>,
119 
121 
122  mutable std::array<
123  Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>,
125 
126  mutable std::array<
127  std::array<
128  Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>
129  ,3>,
131 };
132 
133 } // namespace rheolef
134 #endif // _RHEOLEF_BASIS_FEM_RTK_H
basis_rep< T > base
Definition: basis_fem_RTk.h:58
std::array< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >, reference_element::max_variant > _inv_vdm
std::array< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >, reference_element::max_variant > _bar_a
std::array< std::array< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >,3 >, reference_element::max_variant > _bkm1_node_internal_d
valued_type valued_tag() const
Definition: basis_fem_RTk.h:74
void grad_evaluate(reference_element hat_K, const point_basic< T > &hat_x, Eigen::Matrix< tensor_basic< T >, Eigen::Dynamic, 1 > &value) const
void _compute_dofs(reference_element hat_K, const Eigen::Matrix< value_type, Eigen::Dynamic, 1 > &f_xnod, Eigen::Matrix< T, Eigen::Dynamic, 1 > &dof) const
point_basic< T > value_type
Definition: basis_fem_RTk.h:60
void evaluate(reference_element hat_K, const point_basic< T > &hat_x, Eigen::Matrix< value_type, Eigen::Dynamic, 1 > &value) const
const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & vdm(reference_element hat_K) const
std::array< Eigen::Matrix< point_basic< T >, Eigen::Dynamic, 1 >, reference_element::max_variant > _hat_node
reference_element::size_type size_type
Definition: basis_fem_RTk.h:59
const std::string & valued() const
Definition: basis_fem_RTk.h:75
size_type degree() const
Definition: basis_fem_RTk.h:70
void _initialize_cstor_sizes() const
basis_raw_basic< T > _b_pre_kp1
basis_fem_RTk(size_type k, const basis_option &sopt)
std::array< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >, reference_element::max_variant > _vdm
size_type family_index() const
Definition: basis_fem_RTk.h:72
const Eigen::Matrix< point_basic< T >, Eigen::Dynamic, 1 > & hat_node(reference_element hat_K) const
base::valued_type valued_type
Definition: basis_fem_RTk.h:61
std::string family_name() const
Definition: basis_fem_RTk.h:71
quadrature< T > _quad
const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & inv_vdm(reference_element hat_K) const
void _initialize_data(reference_element hat_K) const
see the basis_option page for the full documentation
Definition: basis_option.h:93
reference_element::size_type size_type
Definition: basis.h:214
see the reference_element page for the full documentation
static const variant_type max_variant
std::vector< int >::size_type size_type
rheolef::std value
const std::string & valued_name(valued_type valued_tag)
This file is part of Rheolef.