public QuadratureRule_ND Make_QuadratureRule_Triangle_Gaussian_Order_3()
{
QuadratureRule_ND QR = Initialize_2D_QuadratureRule(4);
double Xi_0 = 1.0D / 3.0D;
QR.wi[0] = -27.0D / 48.0D;
QR.Xi[0].Values[0] = Xi_0;
QR.Xi[0].Values[1] = Xi_0;
double Wi = 25.0D / 48.0D;
QR.wi[1] = Wi;
QR.Xi[1].Values[0] = 0.6D;
QR.Xi[1].Values[1] = 0.2D;
QR.wi[2] = Wi;
QR.Xi[2].Values[0] = 0.2D;
QR.Xi[2].Values[1] = 0.6D;
QR.wi[3] = Wi;
QR.Xi[3].Values[0] = 0.2D;
QR.Xi[3].Values[1] = 0.2D;
return(QR);
}
public QuadratureRule_ND Make_QuadratureRule_Tetrahedron_Gaussian_Order_2()
{
QuadratureRule_ND QR = Initialize_3D_QuadratureRule(4);
double Wi = 1.0D / 4.0D;
double t = 1.0D / Math.Sqrt(5.0D);
double A = (1.0D - t) / 4.0D;
double B = (1.0D + 3.0D * t) / 4.0D;
QR.wi[0] = Wi;
QR.Xi[0].Values[0] = A;
QR.Xi[0].Values[1] = A;
QR.Xi[0].Values[2] = A;
QR.wi[1] = Wi;
QR.Xi[1].Values[0] = A;
QR.Xi[1].Values[1] = A;
QR.Xi[1].Values[2] = B;
QR.wi[2] = Wi;
QR.Xi[2].Values[0] = B;
QR.Xi[2].Values[1] = A;
QR.Xi[2].Values[2] = A;
QR.wi[3] = Wi;
QR.Xi[3].Values[0] = A;
QR.Xi[3].Values[1] = B;
QR.Xi[3].Values[2] = A;
return(QR);
}
/// <summary>
/// Developed by: Mehrdad Negahban
/// Date: 11/12/2012
///
/// Purpose: Construct Quadrature points and weights for different number of integration points
/// Comments: Gaussian
///
/// Date modified:
/// Modified by:
/// Comments:
/// </summary>
public static QuadratureRule_ND Make_QuadratureRule_Rectangular_Gaussian_LxMxNPoints(int L_NIP, int M_NIP, int N_NIP)
{
QuadratureRule QR_L = GaussianQuadratureRule.MakeGaussianQuadrature(L_NIP);
QuadratureRule QR_M = GaussianQuadratureRule.MakeGaussianQuadrature(M_NIP);
QuadratureRule QR_N = GaussianQuadratureRule.MakeGaussianQuadrature(N_NIP);
QuadratureRule_ND QR_ND = new QuadratureRule_ND();
QR_ND.NIP = L_NIP * M_NIP * N_NIP;
QR_ND.wi = new double[QR_ND.NIP];
QR_ND.Xi = new Vector[QR_ND.NIP];
int Index = 0;
for (int i = 0; i < L_NIP; i++)
{
for (int j = 0; j < M_NIP; j++)
{
for (int k = 0; k < N_NIP; k++)
{
QR_ND.wi[Index] = QR_L.wi[i] * QR_M.wi[j] * QR_N.wi[k];
QR_ND.Xi[i] = new Vector(3);
QR_ND.Xi[i].Values[0] = QR_L.Xi[i];
QR_ND.Xi[i].Values[1] = QR_M.Xi[j];
QR_ND.Xi[i].Values[2] = QR_N.Xi[k];
}
}
}
return(QR_ND);
}
public QuadratureRule_ND Make_QuadratureRule_Triangle_Gaussian_Order_1()
{
QuadratureRule_ND QR = Initialize_2D_QuadratureRule(1);
QR.wi[0] = 1.0D;
double Xi = 1.0D / 3.0D;
QR.Xi[0].Values[0] = Xi;
QR.Xi[0].Values[1] = Xi;
return(QR);
}
public QuadratureRule_ND Make_QuadratureRule_Tetrahedron_Gaussian_Order_1()
{
QuadratureRule_ND QR = Initialize_3D_QuadratureRule(1);
QR.wi[0] = 1.0D;
double Xi = 1.0D / 4.0D;
QR.Xi[0].Values[0] = Xi;
QR.Xi[0].Values[1] = Xi;
QR.Xi[0].Values[2] = Xi;
return(QR);
}
public QuadratureRule_ND Initialize_3D_QuadratureRule(int NumberOfIntegrationPoints)
{
QuadratureRule_ND QR = new QuadratureRule_ND();
QR.NIP = NumberOfIntegrationPoints;
QR.wi = new double[NumberOfIntegrationPoints];
QR.Xi = new Vector[NumberOfIntegrationPoints];
for (int i = 0; i < NumberOfIntegrationPoints; i++)
{
QR.Xi[i] = new Vector(2);
}
return(QR);
}
/// <summary>
/// Developed by: Mehrdad Negahban
/// Date: 11/12/2012
///
/// Purpose: Construct Quadrature points and weights for different number of integration points
/// Comments: Gaussian
///
/// Date modified:
/// Modified by:
/// Comments:
/// </summary>
public static QuadratureRule_ND Make_QuadratureRule_Gaussian_NPoint(int NIP)
{
QuadratureRule QR = GaussianQuadratureRule.MakeGaussianQuadrature(NIP);
QuadratureRule_ND QR_ND = new QuadratureRule_ND();
QR_ND.NIP = NIP;
QR_ND.wi = QR.wi;
QR_ND.Xi = new Vector[NIP];
for (int i = 0; i < NIP; i++)
{
QR_ND.Xi[i] = new Vector(1);
QR_ND.Xi[i].Values[0] = QR.Xi[i];
}
return(QR_ND);
}
public QuadratureRule_ND Make_QuadratureRule_Triangle_Gaussian_Order_5()
{
QuadratureRule_ND QR = Initialize_2D_QuadratureRule(7);
double Xi_0 = 1.0D / 3.0D;
QR.wi[0] = 0.225;
QR.Xi[0].Values[0] = Xi_0;
QR.Xi[0].Values[1] = Xi_0;
double Wi_1 = (155.0D - Math.Sqrt(15.0D)) / 1200.0D;
double Wi_2 = (155.0D - Math.Sqrt(15.0D)) / 1200.0D;
double t_1 = (1.0D + Math.Sqrt(15.0D)) / 7.0D;
double A_1 = (1.0D + 2.0D * t_1) / 3.0D;
double B_1 = (1.0D - t_1) / 3.0D;
QR.wi[1] = Wi_1;
QR.Xi[1].Values[0] = A_1;
QR.Xi[1].Values[1] = B_1;
QR.wi[2] = Wi_1;
QR.Xi[2].Values[0] = B_1;
QR.Xi[2].Values[1] = A_1;
QR.wi[3] = Wi_1;
QR.Xi[3].Values[0] = B_1;
QR.Xi[3].Values[1] = B_1;
double t_2 = (1.0D - Math.Sqrt(15.0D)) / 7.0D;
double A_2 = (1.0D + 2.0D * t_2) / 3.0D;
double B_2 = (1.0D - t_2) / 3.0D;
QR.wi[4] = Wi_2;
QR.Xi[4].Values[0] = A_2;
QR.Xi[4].Values[1] = B_2;
QR.wi[5] = Wi_2;
QR.Xi[5].Values[0] = B_2;
QR.Xi[5].Values[1] = A_2;
QR.wi[6] = Wi_2;
QR.Xi[6].Values[0] = B_2;
QR.Xi[6].Values[1] = B_2;
return(QR);
}
public QuadratureRule_ND Make_QuadratureRule_Triangle_Gaussian_Order_2()
{
QuadratureRule_ND QR = Initialize_2D_QuadratureRule(3);
double Wi = 1.0D / 3.0D;
QR.wi[0] = Wi;
QR.Xi[0].Values[0] = 0.5D;
QR.Xi[0].Values[1] = 0.5D;
QR.wi[1] = Wi;
QR.Xi[1].Values[0] = 0.0D;
QR.Xi[1].Values[1] = 0.5D;
QR.wi[2] = Wi;
QR.Xi[2].Values[0] = 0.5D;
QR.Xi[2].Values[1] = 0.0D;
return(QR);
}
public QuadratureRule_ND Make_QuadratureRule_Tetrahedron_Gaussian_Order_3()
{
QuadratureRule_ND QR = Initialize_3D_QuadratureRule(5);
double Xi_0 = 1.0D / 4.0D;
QR.wi[0] = -4.0D / 5.0D;
QR.Xi[0].Values[0] = Xi_0;
QR.Xi[0].Values[1] = Xi_0;
QR.Xi[0].Values[2] = Xi_0;
double Wi = 9.0D / 20.0D;
double A = 1.0D / 3.0D;
double B = 1.0D / 6.0D;
QR.wi[1] = Wi;
QR.Xi[1].Values[0] = A;
QR.Xi[1].Values[1] = B;
QR.Xi[1].Values[2] = B;
QR.wi[2] = Wi;
QR.Xi[2].Values[0] = B;
QR.Xi[2].Values[1] = A;
QR.Xi[2].Values[2] = B;
QR.wi[3] = Wi;
QR.Xi[3].Values[0] = B;
QR.Xi[3].Values[1] = B;
QR.Xi[3].Values[2] = A;
QR.wi[4] = Wi;
QR.Xi[4].Values[0] = B;
QR.Xi[4].Values[1] = B;
QR.Xi[4].Values[2] = B;
return(QR);
}
/// <summary>
/// Developed by: Mehrdad Negahban
/// Date: 11/12/2012
///
/// Purpose: Construct Quadrature points and weights for different number of integration points
/// Comments: Gaussian
///
/// Date modified:
/// Modified by:
/// Comments:
/// </summary>
public static QuadratureRule_ND Make_QuadratureRule_Rectangular_Gaussian_MxNPoints(int M_NIP, int N_NIP)
{
QuadratureRule QR_M = GaussianQuadratureRule.MakeGaussianQuadrature(M_NIP);
QuadratureRule QR_N = GaussianQuadratureRule.MakeGaussianQuadrature(N_NIP);
QuadratureRule_ND QR_ND = new QuadratureRule_ND();
QR_ND.NIP = M_NIP * N_NIP;
QR_ND.wi = new double[QR_ND.NIP];
QR_ND.Xi = new Vector[QR_ND.NIP];
int Index = 0;
for (int i = 0; i < M_NIP; i++)
{
for (int j = 0; j < N_NIP; j++)
{
QR_ND.wi[Index] = QR_M.wi[i] * QR_N.wi[j];
QR_ND.Xi[Index] = new Vector(2);
QR_ND.Xi[Index].Values[0] = QR_M.Xi[i];
QR_ND.Xi[Index].Values[1] = QR_N.Xi[j];
Index++;
}
}
return(QR_ND);
}
public Integrator_ND_Quadrature(QuadratureRule_ND qRule)
{
QRule = qRule;
}