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///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
#include "P2_numbering.h"
namespace rheolef {
using namespace std;
/* For mopre info: Dhatt et Touzot 2eme ed p110
* WARNING:
* The node numbering correspond to the basis numbering.
* The node numbering convention is different from Dhatt et Touzot:
* we use P. L. Georges et H. Borouchaki
* "Triangulation de Delaunay et maillages",
* Hermes, 1997
* - first the vertices
* - then the middle of the edges
*
* WARNING2: the transformation is still linear
*/
/*
* global numbering statement: uses symbolic values (do not uses as variable !):
*
* K_idx : the current element index in the mesh
* K.face(i) : the i-th element face index in the mesh
* K.edge(i) : the i-th element edge index in the mesh
* K[i] : the i-th element vertice index in the mesh
* mesh_n_geo (dim) : total number of vertices(dim=0), edges(1), faces(2), volume(3)
* in the mesh
* mesh_n_element (type) : total number of element of type 'p', 't', 'q', 'T', 'P', 'H'
* in the mesh
*/
std::string
numbering_P2::name() const
{
return "P2";
}
numbering_P2::size_type
numbering_P2::idof (
const size_type* mesh_n_geo,
const size_type* mesh_n_element,
const geo_element& K,
size_type loc_idof) const
{
// all vertices-based dof are numbered first
// then all edge-based dof
// and then all dof based on interior nodes (e.g. quadrangles)
// for mixed triangle-quadrangle mesh : assume triangle are numbered first
switch (K.variant()) {
case reference_element::p:
return K.index();
case reference_element::e:
if (loc_idof < 2) {
return K [loc_idof];
} else {
return mesh_n_geo[0] + K.index();
}
case reference_element::t: {
if (loc_idof < 3) {
return K [loc_idof];
}
size_type nv = mesh_n_geo[0];
size_type loc_iedg = loc_idof - 3;
size_type iedg = K.edge(loc_iedg);
return nv + iedg;
}
case reference_element::q: {
if (loc_idof < 4) {
return K [loc_idof];
}
if (loc_idof < 8) {
return mesh_n_geo[0] + K.edge(loc_idof - 4);
}
size_type iqua = K.index() - mesh_n_element[reference_element::t];
return mesh_n_geo[0] + mesh_n_geo[1] + iqua;
}
case reference_element::T:
if (loc_idof < 4) {
return K [loc_idof];
} else {
return mesh_n_geo[0] + K.edge(loc_idof - 4);
}
case reference_element::P: {
if (loc_idof < 6) { // 6 vertex dofs
return K [loc_idof];
}
size_type nv = mesh_n_geo[0];
if (loc_idof < 6+9) { // 9 edge face dofs
return nv + K.edge(loc_idof - 6);
}
// 3 quad face dofs
size_type nedg = mesh_n_geo[1];
size_type ntri = mesh_n_element[reference_element::t];
size_type iqua = K.face(loc_idof - 6 - 9) - ntri;
return nv + nedg + iqua;
}
case reference_element::H: {
if (loc_idof < 8) { // 8 vertex dofs
return K [loc_idof];
}
size_type nv = mesh_n_geo[0];
if (loc_idof < 8+12) { // 12 edge face dofs
return nv + K.edge(loc_idof - 8);
}
size_type nedg = mesh_n_geo[1];
size_type ntri = mesh_n_element[reference_element::t];
if (loc_idof < 8+12+6) { // 6 face dofs
size_type iqua = K.face(loc_idof - 8 - 12) - ntri;
return nv + nedg + iqua;
}
// else: 1 volume dof
assert_macro (loc_idof < 27, "invalid loc_idof="<<loc_idof);
size_type nqua = mesh_n_element[reference_element::q];
size_type ntet = mesh_n_element[reference_element::T];
size_type npri = mesh_n_element[reference_element::P];
size_type ihex = K.index() - ntet - npri;
return nv + nedg + nqua + ihex;
}
default:
error_macro ("unsupported P2 element on `" << K.name() << "'");
return 0;
}
}
void
numbering_P2::idof (
const size_type* mesh_n_geo,
const size_type* mesh_n_element,
const geo_element& K,
vector<size_type>& idof) const
{
for (size_type loc_idof = 0; loc_idof < K.size(); loc_idof++)
idof[loc_idof]
= numbering_P2::idof (mesh_n_geo, mesh_n_element, K, loc_idof);
}
numbering_P2::size_type
numbering_P2::ndof (
size_type mesh_map_dimension,
const size_type* mesh_n_geo,
const size_type* mesh_n_element) const
{
switch (mesh_map_dimension) {
case 0:
return mesh_n_geo[0];
case 1:
return mesh_n_geo[0] + mesh_n_geo[1];
case 2:
// number of vertices + nb of edges in the mesh
// + number of quadrangle (extra interior node)
return mesh_n_geo[0]
+ mesh_n_geo[1]
+ mesh_n_element[reference_element::q];
case 3: {
// number of vertices + nb of edges in the mesh
// + number of quadrangle (extra interior node)
// + number of hexaedra (extra interior node)
return mesh_n_geo[0]
+ mesh_n_geo[1]
+ mesh_n_element[reference_element::q]
+ mesh_n_element[reference_element::H];
}
default:
fatal_macro ("unsupported P2 approximation in `" << mesh_map_dimension << "'");
return 0;
}
}
bool
numbering_P2::is_continuous () const
{
return true;
}
} // namespace rheolef
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