BF_C_T_P4_2D.h

// ***********************************************************************
// P4 element, conforming, 2D
// ***********************************************************************

// base function values
static void C_T_P4_2D_Funct(double xi, double eta, double *values)
{
  double t3, t5, t7, t9, t11, t13, t15, t17, t18, t19, t20, t21, t22, t23;
  double t24, t25, t26, t27, t30, t34, t35, t36, t40, t43, t48, t50, t60;
  double t61, t68, t70, t75;

  t3 = xi*xi;
  t5 = xi*eta;
  t7 = eta*eta;
  t9 = t3*xi;
  t11 = t3*eta;
  t13 = xi*t7;
  t15 = t7*eta;
  t17 = t3*t3;
  t18 = 32.0/3.0*t17;
  t19 = t9*eta;
  t20 = 128.0/3.0*t19;
  t21 = t3*t7;
  t22 = 64.0*t21;
  t23 = xi*t15;
  t24 = 128.0/3.0*t23;
  t25 = t7*t7;
  t26 = 32.0/3.0*t25;
  t27 = 1.0-25.0/3.0*xi-25.0/3.0*eta+70.0/3.0*t3+140.0/3.0*t5+70.0/3.0*t7-80.0/3.0*t9-80.0*t11-80.0*t13-80.0/3.0*t15+t18+t20+t22+t24+t26;
  t30 = 208.0/3.0*t5;
  t34 = 128.0/3.0*t17;
  t35 = 128.0*t19;
  t36 = 128.0*t21;
  t40 = 28.0*t5;
  t43 = 16.0*t13;
  t48 = 16.0/3.0*t5;
  t50 = 32.0*t11;
  t60 = 128.0*t23;
  t61 = 128.0/3.0*t25;
  t68 = 32.0*t5;
  t70 = 32.0*t13;
  t75 = 16.0*t11;

  values[0] = t27;
  values[1] = 16.0*xi-208.0/3.0*t3-t30+96.0*t9+192.0*t11+96.0*t13-t34-t35-t36-t24;
  values[2] = -12.0*xi+76.0*t3+t40-128.0*t9-144.0*t11-t43+64.0*t17+t35+t22;
  values[3] = 16.0/3.0*xi-112.0/3.0*t3-t48+224.0/3.0*t9+t50-t34-t20;
  values[4] = -xi+22.0/3.0*t3-16.0*t9+t18;
  values[5] = 16.0*eta-t30-208.0/3.0*t7+96.0*t11+192.0*t13+96.0*t15-t20-t36-t60-t61;
  values[6] = 96.0*t5-224.0*t11-224.0*t13+t35+256.0*t21+t60;
  values[7] = -t68+160.0*t11+t70-t35-t36;
  values[8] = t48-t50+t20;
  values[9] = -12.0*eta+t40+76.0*t7-t75-144.0*t13-128.0*t15+t22+t60+64.0*t25;
  values[10] = -t68+t50+160.0*t13-t36-t60;
  values[11] = 4.0*t5-t75-t43+t22;
  values[12] = 16.0/3.0*eta-t48-112.0/3.0*t7+t70+224.0/3.0*t15-t24-t61;
  values[13] = t48-t70+t24;
  values[14] = -eta+22.0/3.0*t7-16.0*t15+t26;
}

// values of the derivatives in xi direction
static void C_T_P4_2D_DeriveXi(double xi, double eta, double *values)
{
  double t3, t5, t7, t9, t10, t11, t12, t13, t14, t15, t16, t19, t23, t24;
  double t25, t28, t31, t35, t37, t44, t51, t53, t56, t63;

  t3 = xi*xi;
  t5 = xi*eta;
  t7 = eta*eta;
  t9 = t3*xi;
  t10 = 128.0/3.0*t9;
  t11 = t3*eta;
  t12 = 128.0*t11;
  t13 = xi*t7;
  t14 = 128.0*t13;
  t15 = t7*eta;
  t16 = 128.0/3.0*t15;
  t19 = 208.0/3.0*eta;
  t23 = 512.0/3.0*t9;
  t24 = 384.0*t11;
  t25 = 256.0*t13;
  t28 = 28.0*eta;
  t31 = 16.0*t7;
  t35 = 16.0/3.0*eta;
  t37 = 64.0*t5;
  t44 = 128.0*t15;
  t51 = 32.0*eta;
  t53 = 32.0*t7;
  t56 = 32.0*t5;
  t63 = -t35+t53-t16;

  values[0] = -25.0/3.0+140.0/3.0*xi+140.0/3.0*eta-80.0*t3-160.0*t5-80.0*t7+t10+t12+t14+t16;
  values[1] = 16.0-416.0/3.0*xi-t19+288.0*t3+384.0*t5+96.0*t7-t23-t24-t25-t16;
  values[2] = -12.0+152.0*xi+t28-384.0*t3-288.0*t5-t31+256.0*t9+t24+t14;
  values[3] = 16.0/3.0-224.0/3.0*xi-t35+224.0*t3+t37-t23-t12;
  values[4] = -1.0+44.0/3.0*xi-48.0*t3+t10;
  values[5] = -t19+192.0*t5+192.0*t7-t12-t25-t44;
  values[6] = 96.0*eta-448.0*t5-224.0*t7+t24+512.0*t13+t44;
  values[7] = -t51+320.0*t5+t53-t24-t25;
  values[8] = t35-t37+t12;
  values[9] = t28-t56-144.0*t7+t14+t44;
  values[10] = -t51+t37+160.0*t7-t25-t44;
  values[11] = 4.0*eta-t56-t31+t14;
  values[12] = t63;
  values[13] = -t63;
  values[14] = 0.0;
}

// values of the derivatives in eta direction
static void C_T_P4_2D_DeriveEta(double xi, double eta, double *values)
{
  double t3, t5, t7, t9, t10, t11, t12, t13, t14, t15, t16, t18, t21, t22;
  double t24, t26, t28, t29, t30, t35, t36, t43, t45, t48;

  t3 = xi*xi;
  t5 = xi*eta;
  t7 = eta*eta;
  t9 = t3*xi;
  t10 = 128.0/3.0*t9;
  t11 = t3*eta;
  t12 = 128.0*t11;
  t13 = xi*t7;
  t14 = 128.0*t13;
  t15 = t7*eta;
  t16 = 128.0/3.0*t15;
  t18 = 208.0/3.0*xi;
  t21 = 128.0*t9;
  t22 = 256.0*t11;
  t24 = 28.0*xi;
  t26 = 32.0*t5;
  t28 = 16.0/3.0*xi;
  t29 = 32.0*t3;
  t30 = -t28+t29-t10;
  t35 = 384.0*t13;
  t36 = 512.0/3.0*t15;
  t43 = 32.0*xi;
  t45 = 64.0*t5;
  t48 = 16.0*t3;

  values[0] = -25.0/3.0+140.0/3.0*xi+140.0/3.0*eta-80.0*t3-160.0*t5-80.0*t7+t10+t12+t14+t16;
  values[1] = -t18+192.0*t3+192.0*t5-t21-t22-t14;
  values[2] = t24-144.0*t3-t26+t21+t12;
  values[3] = t30;
  values[4] = 0.0;
  values[5] = 16.0-t18-416.0/3.0*eta+96.0*t3+384.0*t5+288.0*t7-t10-t22-t35-t36;
  values[6] = 96.0*xi-224.0*t3-448.0*t5+t21+512.0*t11+t35;
  values[7] = -t43+160.0*t3+t45-t21-t22;
  values[8] = -t30;
  values[9] = -12.0+t24+152.0*eta-t48-288.0*t5-384.0*t7+t12+t35+256.0*t15;
  values[10] = -t43+t29+320.0*t5-t22-t35;
  values[11] = 4.0*xi-t48-t26+t12;
  values[12] = 16.0/3.0-t28-224.0/3.0*eta+t45+224.0*t7-t14-t36;
  values[13] = t28-t45+t14;
  values[14] = -1.0+44.0/3.0*eta-48.0*t7+t16;
}

// values of the derivatives in xi-xi direction
static void C_T_P4_2D_DeriveXiXi(double xi, double eta, double *values)
{
  double t3, t4, t5, t6, t7, t8, t12, t13, t14, t21, t34;

  t3 = xi*xi;
  t4 = 128.0*t3;
  t5 = xi*eta;
  t6 = 256.0*t5;
  t7 = eta*eta;
  t8 = 128.0*t7;
  t12 = 512.0*t3;
  t13 = 768.0*t5;
  t14 = 256.0*t7;
  t21 = 64.0*eta;
  t34 = -32.0*eta+t8;

  values[0] = 140.0/3.0-160.0*xi-160.0*eta+t4+t6+t8;
  values[1] = -416.0/3.0+576.0*xi+384.0*eta-t12-t13-t14;
  values[2] = 152.0-768.0*xi-288.0*eta+768.0*t3+t13+t8;
  values[3] = -224.0/3.0+448.0*xi+t21-t12-t6;
  values[4] = 44.0/3.0-96.0*xi+t4;
  values[5] = 192.0*eta-t6-t14;
  values[6] = -448.0*eta+t13+512.0*t7;
  values[7] = 320.0*eta-t13-t14;
  values[8] = -t21+t6;
  values[9] = t34;
  values[10] = t21-t14;
  values[11] = t34;
  values[12] = 0.0;
  values[13] = 0.0;
  values[14] = 0.0;
}

// values of the derivatives in xi-eta direction
static void C_T_P4_2D_DeriveXiEta(double xi, double eta, double *values)
{
  double t3, t4, t5, t6, t7, t8, t12, t13, t16, t18, t19, t22, t29, t31;
  double t37;

  t3 = xi*xi;
  t4 = 128.0*t3;
  t5 = xi*eta;
  t6 = 256.0*t5;
  t7 = eta*eta;
  t8 = 128.0*t7;
  t12 = 384.0*t3;
  t13 = 512.0*t5;
  t16 = 32.0*eta;
  t18 = 64.0*xi;
  t19 = -16.0/3.0+t18-t4;
  t22 = 384.0*t7;
  t29 = 64.0*eta;
  t31 = 32.0*xi;
  t37 = -16.0/3.0+t29-t8;

  values[0] = 140.0/3.0-160.0*xi-160.0*eta+t4+t6+t8;
  values[1] = -208.0/3.0+384.0*xi+192.0*eta-t12-t13-t8;
  values[2] = 28.0-288.0*xi-t16+t12+t6;
  values[3] = t19;
  values[4] = 0.0;
  values[5] = -208.0/3.0+192.0*xi+384.0*eta-t4-t13-t22;
  values[6] = 96.0-448.0*xi-448.0*eta+t12+1024.0*t5+t22;
  values[7] = -32.0+320.0*xi+t29-t12-t13;
  values[8] = -t19;
  values[9] = 28.0-t31-288.0*eta+t6+t22;
  values[10] = -32.0+t18+320.0*eta-t13-t22;
  values[11] = 4.0-t31-t16+t6;
  values[12] = t37;
  values[13] = -t37;
  values[14] = 0.0;
}

// values of the derivatives in eta-eta direction
static void C_T_P4_2D_DeriveEtaEta(double xi, double eta, double *values)
{
  double t3, t4, t5, t6, t7, t8, t11, t14, t17, t18, t23;

  t3 = xi*xi;
  t4 = 128.0*t3;
  t5 = xi*eta;
  t6 = 256.0*t5;
  t7 = eta*eta;
  t8 = 128.0*t7;
  t11 = 256.0*t3;
  t14 = -32.0*xi+t4;
  t17 = 768.0*t5;
  t18 = 512.0*t7;
  t23 = 64.0*xi;

  values[0] = 140.0/3.0-160.0*xi-160.0*eta+t4+t6+t8;
  values[1] = 192.0*xi-t11-t6;
  values[2] = t14;
  values[3] = 0.0;
  values[4] = 0.0;
  values[5] = -416.0/3.0+384.0*xi+576.0*eta-t11-t17-t18;
  values[6] = -448.0*xi+512.0*t3+t17;
  values[7] = t23-t11;
  values[8] = 0.0;
  values[9] = 152.0-288.0*xi-768.0*eta+t4+t17+768.0*t7;
  values[10] = 320.0*xi-t11-t17;
  values[11] = t14;
  values[12] = -224.0/3.0+t23+448.0*eta-t6-t18;
  values[13] = -t23+t6;
  values[14] = 44.0/3.0-96.0*eta+t8;
}
  
// ***********************************************************************

TBaseFunct2D *BF_C_T_P4_2D_Obj = new TBaseFunct2D
        (15, BF_C_T_P4_2D, BFUnitTriangle, 
         C_T_P4_2D_Funct, C_T_P4_2D_DeriveXi,
         C_T_P4_2D_DeriveEta, C_T_P4_2D_DeriveXiXi,
         C_T_P4_2D_DeriveXiEta, C_T_P4_2D_DeriveEtaEta, 4, 4,
         0, NULL);