libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial Class Reference

#include <inf_fe.h>

Static Public Member Functions

static Real decay (const Real v)
 
static Real decay_deriv (const Real)
 
static Real D (const Real v)
 
static Real D_deriv (const Real v)
 
static Order mapping_order ()
 
static unsigned int n_dofs (const Order o_radial)
 
static unsigned int n_dofs_at_node (const Order o_radial, const unsigned int n_onion)
 
static unsigned int n_dofs_per_elem (const Order o_radial)
 

Private Member Functions

 Radial ()
 

Detailed Description

template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
class libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial

Infinite elements are in some sense directional, compared to conventional finite elements. All methods related to the radial part, which extends perpendicular from the base, are collected in this nested class. This class offers static methods, which are only available to InfFE members.

Author
Daniel Dreyer
Date
2003

Definition at line 97 of file inf_fe.h.

Constructor & Destructor Documentation

template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::Radial ( )
inlineprivate

Never use an object of this type.

Definition at line 104 of file inf_fe.h.

104 {}

Member Function Documentation

template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
static Real libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::D ( const Real  v)
inlinestatic
Returns
the radial weight D, used as an additional weight for the test function, evaluated at local radial coordinate v.

Definition at line 124 of file inf_fe.h.

124 { return (1.-v)*(1.-v)/4.; }
template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
static Real libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::D_deriv ( const Real  v)
inlinestatic
Returns
the first (local) radial derivative of the radial weight D.

Definition at line 129 of file inf_fe.h.

129 { return (v-1.)/2.; }
template<unsigned int Dim, FEFamily T_radial, InfMapType T_map>
Real libMesh::InfFE< Dim, T_radial, T_map >::Radial::decay ( const Real  v)
inlinestatic
Returns
the decay in radial direction of the Dim dimensional infinite element.

Definition at line 846 of file inf_fe.h.

Referenced by libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::compute_data(), and libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::shape().

847 {
848  switch (Dim)
849  //TODO:[DD] What decay do i have in 2D and 1D?
850  {
851  case 3:
852  return (1.-v)/2.;
853 
854  case 2:
855  return 0.;
856 
857  case 1:
858  return 0.;
859 
860  default:
861  libmesh_error();
862  return 0.;
863  }
864 }
template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
static Real libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::decay_deriv ( const Real  )
inlinestatic
Returns
the first (local) derivative of the decay in radial direction of the infinite element.

Definition at line 118 of file inf_fe.h.

118 { return -.5; }
template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
static Order libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::mapping_order ( )
inlinestatic
Returns
the Order of the mapping functions in radial direction. Currently, this is always FIRST.

Definition at line 135 of file inf_fe.h.

References libMeshEnums::FIRST.

135 { return FIRST; }
template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
static unsigned int libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::n_dofs ( const Order  o_radial)
inlinestatic
Returns
the number of shape functions in radial direction associated with this infinite element. Either way, if the modes are stored as nodal dofs (n_dofs_at_node) or as element dofs (n_dofs_per_elem), in each case we have the same number of modes in radial direction. Note that for the case of 1D infinite elements, in the base the dof-per-node scheme is used.

From the formulation of the infinite elements, we have 1 mode, when o_radial=CONST. Therefore, we have a total of o_radial+1 modes in radial direction.

Definition at line 149 of file inf_fe.h.

150  { return static_cast<unsigned int>(o_radial)+1; }
template<unsigned int Dim, FEFamily T_radial, InfMapType T_map>
unsigned int libMesh::InfFE< Dim, T_radial, T_map >::Radial::n_dofs_at_node ( const Order  o_radial,
const unsigned int  n_onion 
)
static
Returns
the number of dofs in radial direction on "onion slice" n (either 0 or 1) for an infinite element of type inf_elem_type and radial order o_radial.

Currently, the first radial mode is associated with the nodes in the base. All higher radial modes are associated with the physically existing nodes further out.

Definition at line 128 of file inf_fe_base_radial.C.

130 {
131  libmesh_assert_less (n_onion, 2);
132 
133  if (n_onion == 0)
134  /*
135  * in the base, no matter what, we have 1 node associated
136  * with radial direction
137  */
138  return 1;
139  else
140  /*
141  * this works, since for Order o_radial=CONST=0, we still
142  * have the (1-v)/2 mode, associated to the base
143  */
144  return static_cast<unsigned int>(o_radial);
145 }
template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
static unsigned int libMesh::InfFE< friend_Dim, friend_T_radial, friend_T_map >::Radial::n_dofs_per_elem ( const Order  o_radial)
inlinestatic
Returns
the number of modes in radial direction interior to the element, not associated with any interior nodes. Note that these modes are a discontinuous approximation, therefore we have no special formulation for coupling in the base, like in the case of associating (possibly) multiple dofs per (outer) node.

Definition at line 171 of file inf_fe.h.

172  { return static_cast<unsigned int>(o_radial)+1; }

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

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Last modified: February 07 2014 16:57:22 UTC

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