BF_N_T_BDM1_2D.h

// ***********************************************************************
// P1 BDM vector element, nonconforming , 2D
// History:  12.09.2013 implementation (Markus Wolff)
// ***********************************************************************

// base function values
// vector function, orthonormal to edges, 
// functions 1 and 2 are orthogonal to edge 1
// functions 3 and 4 are orthogonal to edge 2
// functions 5 and 6 are orthogonal to edge 3

// coefficient matrix
// NOTE: If you want to use other evaluation points for degress of freedom on
// the edges of a cell, you also have to change the evaluation points in NF_N_T_BDM1_2D.h
// using equidistant points on edges
/*
static double N_T_BDM1_2D_CM[36] = {
-0,0,0,0,1,-2,
-2,1,0,0,0,0,
-1,2,2,-1,-1,2,
3,-3,0,0,0,0,
0,0,0,0,-3,3,
2,-1,-1,2,2,-1
};*/

// using Gauss-Points on edges
/*
static double N_T_BDM1_2D_CM[36] = {
-0,0,0,0,0.3660254,-1.3660254,
-1.3660254,0.3660254,0,0,0,0,
-0.3660254,1.3660254,1.3660254,-0.3660254,-0.3660254,1.3660254,
1.7320508,-1.7320508,0,0,0,0,
0,0,0,0,-1.7320508,1.7320508,
1.3660254,-0.3660254,-0.3660254,1.3660254,1.3660254,-0.3660254
};*/

// using Tschebyscheff-points on edges
static double N_T_BDM1_2D_CM[36] = {
-0,0,0,0,0.20710678,-1.2071068,
-1.2071068,0.20710678,-0,0,0,-0,
-0.20710678,1.2071068,1.2071068,-0.20710678,-0.20710678,1.2071068,
1.4142136,-1.4142136,0,-0,-0,0,
0,0,0,0,-1.4142136,1.4142136,
1.2071068,-0.20710678,-0.20710678,1.2071068,1.2071068,-0.20710678
};

static void N_T_BDM1_2D_Funct(double xi, double eta, double *values)
{
  int nBF = 6; // number of basis functions
  // monomials x-component and y-component
  double mon_x[]={1,0,xi,0 ,eta,0 };
  double mon_y[]={0,1,0 ,xi,0  ,eta};
  
  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
  for(int i=0; i<nBF; i++)
  {
    for(int j=0; j<nBF; j++)
    {
      values[i    ] += N_T_BDM1_2D_CM[i+j*nBF]*mon_x[j];
      values[i+nBF] += N_T_BDM1_2D_CM[i+j*nBF]*mon_y[j];
    }
  }
}

// values of the derivatives in xi direction
static void N_T_BDM1_2D_DeriveXi(double xi, double eta, double *values)
{
  int nBF = 6; // number of basis functions
  // monomials x-component and y-component
  double mon_x[]={0,0,1,0,0,0};
  double mon_y[]={0,0,0,1,0,0};
  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
  for(int i=0; i<nBF; i++)
  {
    for(int j=0; j<nBF; j++)
    {
      values[i    ] += N_T_BDM1_2D_CM[i+j*nBF]*mon_x[j];
      values[i+nBF] += N_T_BDM1_2D_CM[i+j*nBF]*mon_y[j];
    }
  }
}

// values of the derivatives in eta direction
static void N_T_BDM1_2D_DeriveEta(double xi, double eta, double *values)
{
  int nBF = 6; // number of basis functions
  // monomials x-component and y-component
  double mon_x[]={0,0,0,0,1,0};
  double mon_y[]={0,0,0,0,0,1};
  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
  for(int i=0; i<nBF; i++)
  {
    for(int j=0; j<nBF; j++)
    {
      values[i    ] += N_T_BDM1_2D_CM[i+j*nBF]*mon_x[j];
      values[i+nBF] += N_T_BDM1_2D_CM[i+j*nBF]*mon_y[j];
    }
  }
}

// values of derivatives in xi-xi direction
static void N_T_BDM1_2D_DeriveXiXi(double xi, double eta, double *values)
{
/*
  int nBF = 6; // number of basis functions
  // monomials x-component and y-component
  double mon_x[]={0,0,0,0,0,0};
  double mon_y[]={0,0,0,0,0,0};
  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
  for(int i=0; i<nBF; i++)
  {
    for(int j=0; j<nBF; j++)
    {
      values[i    ] += N_T_BDM1_2D_CM[i+j*nBF]*mon_x[j];
      values[i+nBF] += N_T_BDM1_2D_CM[i+j*nBF]*mon_y[j];
    }
  }
  */
// first component
  values[0]= 0;
  values[1]= 0;
  values[2]= 0;
  values[3]= 0;
  values[4]= 0;
  values[5]= 0;

  // second component
  values[6]= 0;
  values[7]= 0;
  values[8]= 0;
  values[9]= 0;
  values[10]= 0;
  values[11]= 0;
}

// values of derivatives in eta-eta direction
static void N_T_BDM1_2D_DeriveEtaEta(double xi, double eta, double *values)
{
/*
  int nBF = 6; // number of basis functions
  // monomials x-component and y-component
  double mon_x[]={0,0,0,0,0,0};
  double mon_y[]={0,0,0,0,0,0};
  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
  for(int i=0; i<nBF; i++)
  {
    for(int j=0; j<nBF; j++)
    {
      values[i    ] += N_T_BDM1_2D_CM[i+j*nBF]*mon_x[j];
      values[i+nBF] += N_T_BDM1_2D_CM[i+j*nBF]*mon_y[j];
    }
  }
  */
// first component
    values[0]= 0;
    values[1]= 0;
    values[2]= 0;
    values[3]= 0;
    values[4]= 0;
    values[5]= 0;

// second component
    values[6]= 0;
    values[7]= 0;
    values[8]= 0;
    values[9]= 0;
    values[10]= 0;
    values[11]= 0;
}

// values of derivatives in xi-eta direction
static void N_T_BDM1_2D_DeriveXiEta(double xi, double eta, double *values)
{
    /*
  int nBF = 6; // number of basis functions
  // monomials x-component and y-component
  double mon_x[]={0,0,0,0,0,0,0,1};
  double mon_y[]={0,0,0,0,0,0,1,0};
  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
  for(int i=0; i<nBF; i++)
  {
    for(int j=0; j<nBF; j++)
    {
      values[i    ] += N_T_BDM1_2D_CM[i+j*nBF]*mon_x[j];
      values[i+nBF] += N_T_BDM1_2D_CM[i+j*nBF]*mon_y[j];
    }
  }
  */
// first component
    values[0]= 0;
    values[1]= 0;
    values[2]= 0;
    values[3]= 0;
    values[4]= 0;
    values[5]= 0;

    // second component
    values[6]= 0;
    values[7]= 0;
    values[8]= 0;
    values[9]= 0;
    values[10]= 0;
    values[11]= 0;
}

// ***********************************************************************
//TODO die zahlen am ende
/*
  int polynomialdegree,
  int accuracy,
  int n_bf2change,
  int **bf2change,
  int baseVectDim
 */
TBaseFunct2D *BF_N_T_BDM1_2D_Obj = new TBaseFunct2D
        (6, BF_N_T_BDM1_2D, BFUnitTriangle,
         N_T_BDM1_2D_Funct, N_T_BDM1_2D_DeriveXi,
         N_T_BDM1_2D_DeriveEta, N_T_BDM1_2D_DeriveXiXi,
         N_T_BDM1_2D_DeriveXiEta, N_T_BDM1_2D_DeriveEtaEta, 2, 1,
         0, NULL, 2);