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/****************************************************************************/
/* This file is part of FreeFem++. */
/* */
/* FreeFem++ is free software: you can redistribute it and/or modify */
/* it under the terms of the GNU Lesser General Public License as */
/* published by the Free Software Foundation, either version 3 of */
/* the License, or (at your option) any later version. */
/* */
/* FreeFem++ 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 Lesser General Public License for more details. */
/* */
/* You should have received a copy of the GNU Lesser General Public License */
/* along with FreeFem++. If not, see <http://www.gnu.org/licenses/>. */
/****************************************************************************/
// SUMMARY : ...
// LICENSE : LGPLv3
// ORG : LJLL Universite Pierre et Marie Curie, Paris, FRANCE
// AUTHORS : ...
// E-MAIL : ...
// *INDENT-OFF* //
//ff-c++-LIBRARY-dep:
//ff-c++-cpp-dep:
// *INDENT-ON* //
#include "ff++.hpp"
#include "AddNewFE.h"
// Attention probleme de numerotation des inconnues
// -------------------------------------------------
// dans freefem, il y a un noeud par objets sommet, arete, element.
// et donc la numerotation des dl dans l'element depend
// de l'orientation des aretes
//
/// ---------------------------------------------------------------
namespace Fem2D {
// ------ P3dc
class TypeOfFE_P3dcLagrange: public TypeOfFE {
public:
static const int k = 3;
static const int ndf = (k + 2) * (k + 1) / 2;
static int Data [];
static double Pi_h_coef [];
static const int nn[10][3];
static const int aa[10][3];
static const int ff[10];
static const int il[10];
static const int jl[10];
static const int kl[10];
static const R2 G;
static const R cshrink;
static const R cshrink1;
// (1 -1/3)*
static R2 Shrink (const R2 &P) {return (P - G) * cshrink + G;}
static R2 Shrink1 (const R2 &P) {return (P - G) * cshrink1 + G;}
TypeOfFE_P3dcLagrange (): TypeOfFE(3 + 2 * 3 + 1, 1, Data, 4, 1, 10, 10, Pi_h_coef) {
static const R2 Pt[10] = {
R2(0 / 3., 0 / 3.),
R2(3 / 3., 0 / 3.),
R2(0 / 3., 3 / 3.),
R2(2 / 3., 1 / 3.),
R2(1 / 3., 2 / 3.),
R2(0 / 3., 2 / 3.),
R2(0 / 3., 1 / 3.),
R2(1 / 3., 0 / 3.),
R2(2 / 3., 0 / 3.),
R2(1 / 3., 1 / 3.)};
// 3,4,5,6,7,8
for (int i = 0; i < NbDoF; i++) {
pij_alpha[i] = IPJ(i, i, 0);
P_Pi_h[i] = Shrink(Pt[i]);
}
}
void FB (const bool *whatd, const Mesh &Th, const Triangle &K, const R2 &P, RNMK_ &val) const;
/* void Pi_h_alpha(const baseFElement & K,KN_<double> & v) const
* {
* for (int i=0;i<10;++i)
* v[i]=1;
* int e0=K.EdgeOrientation(0);
* int e1=K.EdgeOrientation(1);
* int e2=K.EdgeOrientation(2);
* int ooo[6]={e0,e0,e1,e1,e2,e2};
* int iii[6];
* int jjj[6];
* for(int i=0;i<6;++i)
* {
* iii[i]= 3+2*i; // si orient = 1
* jjj[i]= 4+2*i; // si orient = -1
* }
* for(int i=0;i<6;++i)
* if(ooo[i]==1) v[jjj[i]]=0;
* else v[iii[i]]=0;
*
* }*/
};
const R2 TypeOfFE_P3dcLagrange::G(1. / 3., 1. / 3.);
const R TypeOfFE_P3dcLagrange::cshrink = 1 - 1e-2;
const R TypeOfFE_P3dcLagrange::cshrink1 = 1. / TypeOfFE_P3dcLagrange::cshrink;
// on what nu df on node node of df
int TypeOfFE_P3dcLagrange::Data [] = {
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, // the support number of the node of the df
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, // the number of the df on the node
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // the node of the df
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // the df come from which FE (generaly 0)
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, // which are de df on sub FE
0, // for each compontant $j=0,N-1$ it give the sub FE associated
0, 10};
double TypeOfFE_P3dcLagrange::Pi_h_coef [] = {1., 1., 1., 1., 1., 1., 1., 1., 1., 1.};
void TypeOfFE_P3dcLagrange::FB (const bool *whatd, const Mesh &, const Triangle &K, const R2 &P1, RNMK_ &val) const {
R2 P = Shrink1(P1);
R2 A(K[0]), B(K[1]), C(K[2]);
R l0 = 1 - P.x - P.y, l1 = P.x, l2 = P.y;
R L[3] = {l0 *k, l1 *k, l2 *k};
throwassert(val.N() >= 10);
throwassert(val.M() == 1);
// Attention il faut renumeroter les fonction de bases
// car dans freefem++, il y a un node par sommet, arete or element
// et la numerotation naturelle mais 2 noud pas arete
// donc p est la perumation
// echange de numerotation si les arete sont dans le mauvais sens
int p[10];
for (int i = 0; i < 10; ++i) {
p[i] = i;
}
/*
* if(K.EdgeOrientation(0) <0) Exchange(p[3],p[4]);// 3,4
* if(K.EdgeOrientation(1) <0) Exchange(p[5],p[6]);// 5,6
* if(K.EdgeOrientation(2) <0) Exchange(p[7],p[8]);// 7,8
*/
// cout << KN_<int>(p,10) <<endl;
val = 0;
/*
* // les fonction de base du Pk Lagrange sont
* //
* //
*/
// --
if (whatd[op_id]) {
RN_ f0(val('.', 0, op_id));
for (int df = 0; df < ndf; df++) {
int pdf = p[df];
R f = 1. / ff[df];
for (int i = 0; i < k; ++i) {
f *= L[nn[df][i]] - aa[df][i];
// cout << L[nn[df][i]]-aa[df][i]<< " ";
}
f0[pdf] = f;
// cout << pdf<< " " << df << " f " <<f <<endl;
}
// cout <<" L " << L[0] << " " << L[1] << " " << L[2] << endl;
// cout << ndf << " nbf = "<< f0 <<endl;
}
if (whatd[op_dx] || whatd[op_dy] || whatd[op_dxx] || whatd[op_dyy] || whatd[op_dxy]) {
R ks = k * cshrink1;
R2 D [] = {K.H(0) * ks, K.H(1) * ks, K.H(2) * ks};
if (whatd[op_dx] || whatd[op_dy]) {
for (int df = 0; df < ndf; df++) {
int pdf = p[df];
R fx = 0., fy = 0., f = 1. / ff[df];
for (int i = 0; i < k; ++i) {
int n = nn[df][i];
R Ln = L[n] - aa[df][i];
fx = fx * Ln + f * D[n].x;
fy = fy * Ln + f * D[n].y;
f = f * Ln;
}
if (whatd[op_dx]) {val(pdf, 0, op_dx) = fx;}
if (whatd[op_dy]) {val(pdf, 0, op_dy) = fy;}
}
}
if (whatd[op_dyy] || whatd[op_dxy] || whatd[op_dxx]) {
for (int df = 0; df < ndf; df++) {
int pdf = p[df];
R fx = 0., fy = 0., f = 1. / ff[df];
R fxx = 0., fyy = 0., fxy = 0.;
for (int i = 0; i < k; ++i) {
int n = nn[df][i];
R Ln = L[n] - aa[df][i];
fxx = fxx * Ln + 2. * fx * D[n].x;
fyy = fyy * Ln + 2. * fy * D[n].y;
fxy = fxy * Ln + fx * D[n].y + fy * D[n].x;
fx = fx * Ln + f * D[n].x;
fy = fy * Ln + f * D[n].y;
f = f * Ln;
}
if (whatd[op_dxx]) {val(pdf, 0, op_dxx) = fxx;}
if (whatd[op_dyy]) {val(pdf, 0, op_dyy) = fyy;}
if (whatd[op_dxy]) {val(pdf, 0, op_dxy) = fxy;}
}
}
}
}
#include "Element_P3dc.hpp"
// link with FreeFem++
static TypeOfFE_P3dcLagrange P3dcLagrangeP3dc;
// a static variable to add the finite element to freefem++
static AddNewFE P3dcLagrange("P3dc", &P3dcLagrangeP3dc);
} // FEM2d namespace
// --- fin --
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