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#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 {
// ------ P4 Hierarchical (just remove P1 node of the P2 finite element) --------
class TypeOfFE_P4Lagrange : public TypeOfFE { public:
static const int k=4;
static const int ndf = (k+2)*(k+1)/2;
static int Data[];
static double Pi_h_coef[];
static const int nn[15][4] ;
static const int aa[15][4] ;
static const int ff[15];
static const int il[15];
static const int jl[15];
static const int kl[15];
TypeOfFE_P4Lagrange(): TypeOfFE(3+3*3+3,1,Data,4,1,15+6,15,0)
{
static const R2 Pt[15] = {
R2( 0/4. , 0/4. ) ,
R2( 4/4. , 0/4. ) ,
R2( 0/4. , 4/4. ) ,
R2( 3/4. , 1/4. ) ,
R2( 2/4. , 2/4. ) ,
R2( 1/4. , 3/4. ) ,
R2( 0/4. , 3/4. ) ,
R2( 0/4. , 2/4. ) ,
R2( 0/4. , 1/4. ) ,
R2( 1/4. , 0/4. ) ,
R2( 2/4. , 0/4. ) ,
R2( 3/4. , 0/4. ) ,
R2( 1/4. , 2/4. ) ,
R2( 2/4. , 1/4. ) ,
R2( 1/4. , 1/4. ) }
;
// 3,4,5, 6,7,8, 9,10,11,
int other[15]= { 0,1,2, 5,4,3, 8,7,6, 11,10,9,12,13,14};
int kk=0;
for (int i=0;i<NbDoF;i++)
{
pij_alpha[kk++]= IPJ(i,i,0);
if(other[i]!=i)
pij_alpha[kk++]= IPJ(i,other[i],0);
P_Pi_h[i]=Pt[i];
}
assert(P_Pi_h.N()==NbDoF);
assert(pij_alpha.N()==kk);
}
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<15+6;++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};
/* 3,4
5,
6,7
8,9,
10,
11,12,
13,14,
15
16,17
*/
int iii[6]={3,6,8,11,13,16};
int jjj[6];
for(int i=0;i<6;++i)
{
jjj[i]= iii[i]+1; // si orient = -1
}
for(int i=0;i<6;++i)
if(ooo[i]==1) v[jjj[i]]=0;
else v[iii[i]]=0;
}
} ;
// on what nu df on node node of df
int TypeOfFE_P4Lagrange::Data[]={
0,1,2,3,3,3,4,4,4,5,5,5,6,6,6, // the support number of the node of the df
0,0,0,0,1,2,0,1,2,0,1,2,0,1,2, // the number of the df on the node
0,1,2,3,3,3,4,4,4,5,5,5,6,6,6, // the node of the df
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, // the df come from which FE (generaly 0)
0,1,2,3,4,5,6,7,8,9,10,11,12,13,14, // which are de df on sub FE
0, // for each compontant $j=0,N-1$ it give the sub FE associated
0,15 };
void TypeOfFE_P4Lagrange::FB(const bool * whatd,const Mesh & ,const Triangle & K,const R2 & P,RNMK_ & val) const
{
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[15];
for(int i=0;i<15;++i)
p[i]=i;
if(K.EdgeOrientation(0) <0) Exchange(p[3],p[5]);// 3,4
if(K.EdgeOrientation(1) <0) Exchange(p[6],p[8]);// 5,6
if(K.EdgeOrientation(2) <0) Exchange(p[9],p[11]);// 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])
{
R2 D[]={K.H(0)*k, K.H(1)*k,K.H(2)*k };
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_P4.hpp"
// link with FreeFem++
static TypeOfFE_P4Lagrange P4LagrangeP4;
// a static variable to add the finite element to freefem++
static AddNewFE P4Lagrange("P4",&P4LagrangeP4);
} // FEM2d namespace
// --- fin --
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