libMesh::InfFERadial Class Reference

Infinite elements are in some sense directional, compared to conventional finite elements. More...

#include <inf_fe.h>

Static Public Member Functions
static Real	decay (const unsigned int dim, const Real v)
static Real	decay_deriv (const unsigned int dim, const Real)
static Real	D (const Real v)
static Real	Dxr_sq (const Real)
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
	InfFERadial ()
	Never use an object of this type. More...

Detailed Description

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 class. This class offers static methods for use in InfFE and InfFEMap

Author

Daniel Dreyer

Date

2003

Definition at line 53 of file inf_fe.h.

Constructor & Destructor Documentation

InfFERadial()

libMesh::InfFERadial::InfFERadial ( )

inlineprivate

Never use an object of this type.

Definition at line 60 of file inf_fe.h.

{}

Member Function Documentation

D()

static Real libMesh::InfFERadial::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. FIXME: This is only valid for 3D!! And also makes assumptions on the mapping

Definition at line 82 of file inf_fe.h.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::init_shape_functions().

{ return (1.-v)*(1.-v)/4.; }

D_deriv()

static Real libMesh::InfFERadial::D_deriv ( const Real  v )

inlinestatic

Returns

The first (local) radial derivative of the radial weight D. FIXME: this is valid only in 3D.

Definition at line 90 of file inf_fe.h.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::init_shape_functions().

{ return (v-1.)/2.; }

decay()

Real libMesh::InfFERadial::decay ( const unsigned int  dim, const Real  v  )

inlinestatic

Returns

The decay in the radial direction of the Dim dimensional infinite element.

Definition at line 1283 of file inf_fe.h.

References dim.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::compute_data(), libMesh::InfFE< Dim, T_radial, T_map >::init_radial_shape_functions(), libMesh::InfFE< Dim, T_radial, T_map >::shape(), and libMesh::InfFE< Dim, T_radial, T_map >::shape_deriv().

{
  switch (dim)
    {
    case 3:
      return (1.-v)/2.;

    case 2:
      // according to P. Bettess "Infinite Elements",
      // the 2D case is rather tricky:
      //  - the sqrt() requires special integration rules
      //    if not both trial- and test function are involved
      //  - the analytic solutions contain not only the sqrt, but
      //    also a polynomial with rather many terms, so convergence
      //    might be bad.
      return sqrt((1.-v)/2.);

    case 1:
      return 1.;

    default:
      libmesh_error_msg("Invalid dim = " << dim);
    }
}

decay_deriv()

Real libMesh::InfFERadial::decay_deriv ( const unsigned int  dim, const Real  v  )

inlinestatic

Returns

The first (local) derivative of the decay in radial direction of the infinite element.

Definition at line 1309 of file inf_fe.h.

References dim, and libMesh::libmesh_assert().

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::compute_data(), libMesh::InfFE< Dim, T_radial, T_map >::init_radial_shape_functions(), and libMesh::InfFE< Dim, T_radial, T_map >::shape_deriv().

{
  switch (dim)
    {
    case 3:
      return -0.5;

    case 2:
      // according to P. Bettess "Infinite Elements",
      // the 2D case is rather tricky:
      //  - the sqrt() requires special integration rules
      //    if not both trial- and test function are involved
      //  - the analytic solutions contain not only the sqrt, but
      //    also a polynomial with rather many terms, so convergence
      //    might be bad.

      libmesh_assert (-1.-1.e-5 <= v && v < 1.);
      return -0.25/sqrt(1.-v);

    case 1:
      return 0.;

    default:
      libmesh_error_msg("Invalid dim = " << dim);
    }
}

Dxr_sq()

static Real libMesh::InfFERadial::Dxr_sq ( const Real  )

inlinestatic

Definition at line 84 of file inf_fe.h.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::init_shape_functions().

{ return 1.; }

mapping_order()

static Order libMesh::InfFERadial::mapping_order ( )

inlinestatic

Returns

The Order of the mapping functions in the radial direction. Currently, this is always FIRST.

Definition at line 97 of file inf_fe.h.

References libMesh::FIRST.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::compute_data(), and libMesh::InfFEMap::map().

{ return FIRST; }

n_dofs()

static unsigned int libMesh::InfFERadial::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

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 113 of file inf_fe.h.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::compute_shape_functions(), libMesh::InfFE< Dim, T_radial, T_map >::init_radial_shape_functions(), libMesh::InfFE< Dim, T_radial, T_map >::init_shape_functions(), and libMesh::InfFE< Dim, T_radial, T_map >::n_dofs().

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

n_dofs_at_node()

unsigned int libMesh::InfFERadial::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 115 of file inf_fe_base_radial.C.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::n_dofs_at_node().

{
  libmesh_assert_less (n_onion, 2);

  if (n_onion == 0)
    /*
     * in the base, no matter what, we have 1 node associated
     * with radial direction
     */
    return 1;
  else
    /*
     * this works, since for Order o_radial=CONST=0, we still
     * have the (1-v)/2 mode, associated to the base
     */
    return static_cast<unsigned int>(o_radial);
}

n_dofs_per_elem()

static unsigned int libMesh::InfFERadial::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

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 136 of file inf_fe.h.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::n_dofs_per_elem().

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

---

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

• include/fe/inf_fe.h
• src/fe/inf_fe_base_radial.C