unsigned int FEInterface::n_dofs(const unsigned int dim,
const FEType& fe_t,
const ElemType t)
{
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
if ( is_InfFE_elem(t) )
return ifem_n_dofs(dim, fe_t, t);
#endif
const Order o = fe_t.order;
fe_with_vec_switch(n_dofs(t, o));
libmesh_error();
return 0;
}
void InfFE<Dim,T_radial,T_map>::compute_shape_indices (const FEType & fet,
const ElemType inf_elem_type,
const unsigned int i,
unsigned int & base_shape,
unsigned int & radial_shape)
{
/*
* An example is provided: the numbers in comments refer to
* a fictitious InfHex18. The numbers are chosen as exemplary
* values. There is currently no base approximation that
* requires this many dof's at nodes, sides, faces and in the element.
*
* the order of the shape functions is heavily related with the
* order the dofs are assigned in \p DofMap::distributed_dofs().
* Due to the infinite elements with higher-order base approximation,
* some more effort is necessary.
*
* numbering scheme:
* 1. all vertices in the base, assign node->n_comp() dofs to each vertex
* 2. all vertices further out: innermost loop: radial shapes,
* then the base approximation shapes
* 3. all side nodes in the base, assign node->n_comp() dofs to each side node
* 4. all side nodes further out: innermost loop: radial shapes,
* then the base approximation shapes
* 5. (all) face nodes in the base, assign node->n_comp() dofs to each face node
* 6. (all) face nodes further out: innermost loop: radial shapes,
* then the base approximation shapes
* 7. element-associated dof in the base
* 8. element-associated dof further out
*/
const unsigned int radial_order = static_cast<unsigned int>(fet.radial_order.get_order()); // 4
const unsigned int radial_order_p_one = radial_order+1; // 5
const ElemType base_elem_type (Base::get_elem_type(inf_elem_type)); // QUAD9
// assume that the number of dof is the same for all vertices
unsigned int n_base_vertices = libMesh::invalid_uint; // 4
const unsigned int n_base_vertex_dof = FEInterface::n_dofs_at_node (Dim-1, fet, base_elem_type, 0);// 2
unsigned int n_base_side_nodes = libMesh::invalid_uint; // 4
unsigned int n_base_side_dof = libMesh::invalid_uint; // 3
unsigned int n_base_face_nodes = libMesh::invalid_uint; // 1
unsigned int n_base_face_dof = libMesh::invalid_uint; // 5
const unsigned int n_base_elem_dof = FEInterface::n_dofs_per_elem (Dim-1, fet, base_elem_type);// 9
switch (inf_elem_type)
{
case INFEDGE2:
{
n_base_vertices = 1;
n_base_side_nodes = 0;
n_base_face_nodes = 0;
n_base_side_dof = 0;
n_base_face_dof = 0;
break;
}
case INFQUAD4:
{
n_base_vertices = 2;
n_base_side_nodes = 0;
n_base_face_nodes = 0;
n_base_side_dof = 0;
n_base_face_dof = 0;
break;
}
case INFQUAD6:
{
n_base_vertices = 2;
n_base_side_nodes = 1;
n_base_face_nodes = 0;
n_base_side_dof = FEInterface::n_dofs_at_node (Dim-1, fet,base_elem_type, n_base_vertices);
n_base_face_dof = 0;
break;
}
case INFHEX8:
{
n_base_vertices = 4;
n_base_side_nodes = 0;
n_base_face_nodes = 0;
n_base_side_dof = 0;
n_base_face_dof = 0;
break;
}
case INFHEX16:
{
n_base_vertices = 4;
n_base_side_nodes = 4;
n_base_face_nodes = 0;
n_base_side_dof = FEInterface::n_dofs_at_node (Dim-1, fet,base_elem_type, n_base_vertices);
n_base_face_dof = 0;
break;
}
case INFHEX18:
{
n_base_vertices = 4;
n_base_side_nodes = 4;
n_base_face_nodes = 1;
n_base_side_dof = FEInterface::n_dofs_at_node (Dim-1, fet,base_elem_type, n_base_vertices);
n_base_face_dof = FEInterface::n_dofs_at_node (Dim-1, fet,base_elem_type, 8);
break;
}
case INFPRISM6:
{
n_base_vertices = 3;
n_base_side_nodes = 0;
n_base_face_nodes = 0;
n_base_side_dof = 0;
n_base_face_dof = 0;
break;
}
case INFPRISM12:
{
n_base_vertices = 3;
n_base_side_nodes = 3;
n_base_face_nodes = 0;
n_base_side_dof = FEInterface::n_dofs_at_node (Dim-1, fet,base_elem_type, n_base_vertices);
n_base_face_dof = 0;
break;
}
default:
libmesh_error_msg("Unrecognized inf_elem_type = " << inf_elem_type);
}
{
// these are the limits describing the intervals where the shape function lies
const unsigned int n_dof_at_base_vertices = n_base_vertices*n_base_vertex_dof; // 8
const unsigned int n_dof_at_all_vertices = n_dof_at_base_vertices*radial_order_p_one; // 40
const unsigned int n_dof_at_base_sides = n_base_side_nodes*n_base_side_dof; // 12
const unsigned int n_dof_at_all_sides = n_dof_at_base_sides*radial_order_p_one; // 60
const unsigned int n_dof_at_base_face = n_base_face_nodes*n_base_face_dof; // 5
const unsigned int n_dof_at_all_faces = n_dof_at_base_face*radial_order_p_one; // 25
// start locating the shape function
if (i < n_dof_at_base_vertices) // range of i: 0..7
{
// belongs to vertex in the base
radial_shape = 0;
base_shape = i;
}
else if (i < n_dof_at_all_vertices) // range of i: 8..39
{
/* belongs to vertex in the outer shell
*
* subtract the number of dof already counted,
* so that i_offset contains only the offset for the base
*/
const unsigned int i_offset = i - n_dof_at_base_vertices; // 0..31
// first the radial dof are counted, then the base dof
radial_shape = (i_offset % radial_order) + 1;
base_shape = i_offset / radial_order;
}
else if (i < n_dof_at_all_vertices+n_dof_at_base_sides) // range of i: 40..51
{
// belongs to base, is a side node
radial_shape = 0;
base_shape = i - radial_order * n_dof_at_base_vertices; // 8..19
}
else if (i < n_dof_at_all_vertices+n_dof_at_all_sides) // range of i: 52..99
{
// belongs to side node in the outer shell
const unsigned int i_offset = i - (n_dof_at_all_vertices
+ n_dof_at_base_sides); // 0..47
radial_shape = (i_offset % radial_order) + 1;
base_shape = (i_offset / radial_order) + n_dof_at_base_vertices;
}
else if (i < n_dof_at_all_vertices+n_dof_at_all_sides+n_dof_at_base_face) // range of i: 100..104
{
// belongs to the node in the base face
radial_shape = 0;
base_shape = i - radial_order*(n_dof_at_base_vertices
+ n_dof_at_base_sides); // 20..24
}
else if (i < n_dof_at_all_vertices+n_dof_at_all_sides+n_dof_at_all_faces) // range of i: 105..124
{
// belongs to the node in the outer face
const unsigned int i_offset = i - (n_dof_at_all_vertices
+ n_dof_at_all_sides
+ n_dof_at_base_face); // 0..19
radial_shape = (i_offset % radial_order) + 1;
base_shape = (i_offset / radial_order) + n_dof_at_base_vertices + n_dof_at_base_sides;
}
else if (i < n_dof_at_all_vertices+n_dof_at_all_sides+n_dof_at_all_faces+n_base_elem_dof) // range of i: 125..133
{
// belongs to the base and is an element associated shape
radial_shape = 0;
base_shape = i - (n_dof_at_all_vertices
+ n_dof_at_all_sides
+ n_dof_at_all_faces); // 0..8
}
else // range of i: 134..169
{
libmesh_assert_less (i, n_dofs(fet, inf_elem_type));
// belongs to the outer shell and is an element associated shape
const unsigned int i_offset = i - (n_dof_at_all_vertices
+ n_dof_at_all_sides
+ n_dof_at_all_faces
+ n_base_elem_dof); // 0..19
radial_shape = (i_offset % radial_order) + 1;
base_shape = (i_offset / radial_order) + n_dof_at_base_vertices + n_dof_at_base_sides + n_dof_at_base_face;
}
}
return;
}
void InfFE<Dim,T_radial,T_map>::compute_data(const FEType & fet,
const Elem * inf_elem,
FEComputeData & data)
{
libmesh_assert(inf_elem);
libmesh_assert_not_equal_to (Dim, 0);
const Order o_radial (fet.radial_order);
const Order radial_mapping_order (Radial::mapping_order());
const Point & p (data.p);
const Real v (p(Dim-1));
UniquePtr<const Elem> base_el (inf_elem->build_side_ptr(0));
/*
* compute \p interpolated_dist containing the mapping-interpolated
* distance of the base point to the origin. This is the same
* for all shape functions. Set \p interpolated_dist to 0, it
* is added to.
*/
Real interpolated_dist = 0.;
switch (Dim)
{
case 1:
{
libmesh_assert_equal_to (inf_elem->type(), INFEDGE2);
interpolated_dist = Point(inf_elem->point(0) - inf_elem->point(1)).size();
break;
}
case 2:
{
const unsigned int n_base_nodes = base_el->n_nodes();
const Point origin = inf_elem->origin();
const Order base_mapping_order (base_el->default_order());
const ElemType base_mapping_elem_type (base_el->type());
// interpolate the base nodes' distances
for (unsigned int n=0; n<n_base_nodes; n++)
interpolated_dist += Point(base_el->point(n) - origin).size()
* FE<1,LAGRANGE>::shape (base_mapping_elem_type, base_mapping_order, n, p);
break;
}
case 3:
{
const unsigned int n_base_nodes = base_el->n_nodes();
const Point origin = inf_elem->origin();
const Order base_mapping_order (base_el->default_order());
const ElemType base_mapping_elem_type (base_el->type());
// interpolate the base nodes' distances
for (unsigned int n=0; n<n_base_nodes; n++)
interpolated_dist += Point(base_el->point(n) - origin).size()
* FE<2,LAGRANGE>::shape (base_mapping_elem_type, base_mapping_order, n, p);
break;
}
default:
libmesh_error_msg("Unknown Dim = " << Dim);
}
#ifdef LIBMESH_USE_COMPLEX_NUMBERS
// assumption on time-harmonic behavior
const short int sign (-1);
// the wave number
const Real wavenumber = 2. * libMesh::pi * data.frequency / data.speed;
// the exponent for time-harmonic behavior
const Real exponent = sign /* +1. or -1. */
* wavenumber /* k */
* interpolated_dist /* together with next line: */
* InfFE<Dim,INFINITE_MAP,T_map>::eval(v, radial_mapping_order, 1); /* phase(s,t,v) */
const Number time_harmonic = Number(cos(exponent), sin(exponent)); /* e^(sign*i*k*phase(s,t,v)) */
/*
* compute \p shape for all dof in the element
*/
if (Dim > 1)
{
const unsigned int n_dof = n_dofs (fet, inf_elem->type());
data.shape.resize(n_dof);
for (unsigned int i=0; i<n_dof; i++)
{
// compute base and radial shape indices
unsigned int i_base, i_radial;
compute_shape_indices(fet, inf_elem->type(), i, i_base, i_radial);
data.shape[i] = (InfFE<Dim,T_radial,T_map>::Radial::decay(v) /* (1.-v)/2. in 3D */
* FEInterface::shape(Dim-1, fet, base_el.get(), i_base, p) /* S_n(s,t) */
* InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial)) /* L_n(v) */
* time_harmonic; /* e^(sign*i*k*phase(s,t,v) */
}
}
else
libmesh_error_msg("compute_data() for 1-dimensional InfFE not implemented.");
#else
const Real speed = data.speed;
/*
* This is quite weird: the phase is actually
* a measure how @e advanced the pressure is that
* we compute. In other words: the further away
* the node \p data.p is, the further we look into
* the future...
*/
data.phase = interpolated_dist /* phase(s,t,v)/c */
* InfFE<Dim,INFINITE_MAP,T_map>::eval(v, radial_mapping_order, 1) / speed;
if (Dim > 1)
{
const unsigned int n_dof = n_dofs (fet, inf_elem->type());
data.shape.resize(n_dof);
for (unsigned int i=0; i<n_dof; i++)
{
// compute base and radial shape indices
unsigned int i_base, i_radial;
compute_shape_indices(fet, inf_elem->type(), i, i_base, i_radial);
data.shape[i] = InfFE<Dim,T_radial,T_map>::Radial::decay(v) /* (1.-v)/2. in 3D */
* FEInterface::shape(Dim-1, fet, base_el.get(), i_base, p) /* S_n(s,t) */
* InfFE<Dim,T_radial,T_map>::eval(v, o_radial, i_radial); /* L_n(v) */
}
}
else
libmesh_error_msg("compute_data() for 1-dimensional InfFE not implemented.");
#endif
}
