private double[] PCG(double[,] stiffnessMatrix, double[] forceVector)
{
double[] solutionVector = new double[forceVector.Length];
double[,] preconditioner = new double[stiffnessMatrix.GetLength(0), stiffnessMatrix.GetLength(1)];
for (int i = 0; i < preconditioner.GetLength(0); i++)
{
preconditioner[i, i] = 1 / stiffnessMatrix[i, i];
}
double[] residual = VectorOperations.VectorVectorSubtraction(
forceVector,
VectorOperations.MatrixVectorProduct(stiffnessMatrix, solutionVector)
);
double[] preconVector = VectorOperations.MatrixVectorProduct(preconditioner, residual);
for (int iter = 0; iter < maxIterations; iter++)
{
double[] u = VectorOperations.MatrixVectorProduct(stiffnessMatrix, preconVector);
double residualDotOld = VectorOperations.VectorDotProduct(residual, preconVector);
double alpha = residualDotOld / VectorOperations.VectorDotProduct(preconVector, u);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, VectorOperations.VectorScalarProductNew(preconVector, alpha));
residual = VectorOperations.VectorVectorSubtraction(residual, VectorOperations.VectorScalarProductNew(u, alpha));
if (VectorOperations.VectorDotProduct(residual, residual) < tolerance)
{
break;
}
double residualDotNew = VectorOperations.VectorDotProduct(residual, VectorOperations.MatrixVectorProduct(preconditioner, residual));
double beta = residualDotNew / residualDotOld;
preconVector = VectorOperations.VectorVectorAddition(
VectorOperations.MatrixVectorProduct(preconditioner, residual),
VectorOperations.VectorScalarProductNew(preconVector, beta)
);
}
return(solutionVector);
}
private Tuple <double[], double, double[], double[], double> MasterSegmentGeometry(double[,] daMatrix, double[,] da2Matrix)
{
double Xm1 = Nodes[1].XCoordinate + DisplacementVector[0];
double Ym1 = Nodes[1].YCoordinate + DisplacementVector[1];
double Xm2 = Nodes[2].XCoordinate + DisplacementVector[2];
double Ym2 = Nodes[2].YCoordinate + DisplacementVector[3];
double Xm3 = Nodes[3].XCoordinate + DisplacementVector[4];
double Ym3 = Nodes[3].YCoordinate + DisplacementVector[5];
double Xs = Nodes[4].XCoordinate + DisplacementVector[6];
double Ys = Nodes[4].YCoordinate + DisplacementVector[7];
double[] xupd = new double[] { -Xm1, -Ym1, -Xm2, -Ym2, -Xm3, -Ym3, -Xs, -Ys };
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double[] surfaceVectorDerivative = VectorOperations.MatrixVectorProduct(da2Matrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[] { -surfaceVector[1], surfaceVector[0] };
double scalarCoef = 1.0 / (Math.Sqrt(detm));
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
double[] tangentVector = VectorOperations.VectorScalarProductNew(surfaceVector, scalarCoef);
double scalarCoef2 = Math.Pow(m11, 2.0);
double curvatureTensor = scalarCoef2 * VectorOperations.VectorDotProduct(surfaceVectorDerivative, normalUnitVec);
return(new Tuple <double[], double, double[], double[], double>(surfaceVector, m11, normalUnitVec, tangentVector, curvatureTensor));
}
private double CalculatePenetration(double[] normalVector, double[,] aMatrix, double[] xUpdated)
{
double ksi3 = VectorOperations.VectorDotProduct(
xUpdated, VectorOperations.MatrixVectorProduct(
MatrixOperations.Transpose(aMatrix), normalVector));
return(ksi3);
}
private double[,] MetricTensor(List <double[]> dRho)
{
double[,] m = new double[2, 2];
m[0, 0] = VectorOperations.VectorDotProduct(dRho[0], dRho[0]);
m[0, 1] = VectorOperations.VectorDotProduct(dRho[0], dRho[1]);
m[1, 0] = VectorOperations.VectorDotProduct(dRho[1], dRho[0]);
m[1, 1] = VectorOperations.VectorDotProduct(dRho[1], dRho[1]);
return(m);
}
private double CalculatePenetration(double[,] aMatrix, double[] n)
{
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] xupd = NodalXUpdated();
double normalGap = VectorOperations.VectorDotProduct(xupd, AT_n);
return(normalGap);
}
private double[] BiCGSTAB(double[,] stiffnessMatrix, double[] forceVector)
{
double[] solutionVector = new double[forceVector.Length];
double[] xVector = new double[forceVector.Length];
double[] pVector = new double[forceVector.Length];
double[] vVector = new double[forceVector.Length];
double[,] K = stiffnessMatrix;
double[] bVector = forceVector;
double[] rVector = VectorOperations.VectorVectorSubtraction(bVector, VectorOperations.MatrixVectorProduct(K, xVector));
double[] r0hatVector = rVector;
double rho0 = 1.0;
double w = 1.0;
double a = 1.0;
double rho1 = VectorOperations.VectorDotProduct(r0hatVector, rVector);
double b;
double[] sVector;
double[] tVector;
int iters = 100;
double converged;
for (int i = 0; i < iters; i++)
{
b = (rho1 / rho0) * (a / w);
pVector = VectorOperations.VectorVectorAddition(rVector,
VectorOperations.VectorScalarProductNew(
VectorOperations.VectorVectorSubtraction(pVector,
VectorOperations.VectorScalarProductNew(vVector, w)), b));
vVector = VectorOperations.MatrixVectorProduct(K, pVector);
a = rho1 / VectorOperations.VectorDotProduct(r0hatVector, vVector);
sVector = VectorOperations.VectorVectorSubtraction(rVector,
VectorOperations.VectorScalarProductNew(vVector, a));
tVector = VectorOperations.MatrixVectorProduct(K, sVector);
w = VectorOperations.VectorDotProduct(tVector, sVector) / VectorOperations.VectorDotProduct(tVector, tVector);
rho0 = rho1;
rho1 = -w *VectorOperations.VectorDotProduct(r0hatVector, tVector);
xVector = VectorOperations.VectorVectorAddition(xVector,
VectorOperations.VectorScalarProductNew(pVector, a));
xVector = VectorOperations.VectorVectorAddition(xVector,
VectorOperations.VectorScalarProductNew(sVector, w));
rVector = VectorOperations.VectorVectorSubtraction(sVector,
VectorOperations.VectorScalarProductNew(tVector, w));
converged = VectorOperations.VectorNorm2(rVector);
if (i == iters | converged < 0.00000001)
{
break;
}
}
solutionVector = xVector;
return(solutionVector);
}
private double CalculateDeltaKsi(double[] masterSlaveRelativeVector, double[] surfaceVector, double[] surfaceVectorDerivative)
{
double scalar1 = VectorOperations.VectorDotProduct(surfaceVector, masterSlaveRelativeVector);
double scalar2 = VectorOperations.VectorDotProduct(surfaceVectorDerivative, masterSlaveRelativeVector) -
VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double deltaKsi = -scalar1 / scalar2;
return(deltaKsi);
}
private double[] Calculate_f(List <double[]> dRho, double[,] aMatrix, double[] xUpdated)
{
double[] f = new double[2];
f[0] = VectorOperations.VectorDotProduct(
dRho[0], VectorOperations.MatrixVectorProduct(
aMatrix, xUpdated));
f[1] = VectorOperations.VectorDotProduct(
dRho[1], VectorOperations.MatrixVectorProduct(
aMatrix, xUpdated));
return(f);
}
private double CalculateTangentialTraction()
{
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[] displacementVector = DisplacementVector;
double[] tangentUnitvector = CalculateTangentUnitVector();
double[] aT_t = VectorOperations.MatrixVectorProduct(AT, tangentUnitvector);
double tangentGap = VectorOperations.VectorDotProduct(displacementVector, aT_t);
double tangentialTraction = -PenaltyFactor * tangentGap;
return(tangentialTraction);
}
private double Calculate_e(double[,] aMatrix, double[] xUpdated)
{
double[] dRho12 = new double[] {
0.25 * (xUpdated[0] - xUpdated[3] + xUpdated[6] - xUpdated[9]),
0.25 * (xUpdated[1] - xUpdated[4] + xUpdated[7] - xUpdated[10]),
0.25 * (xUpdated[2] - xUpdated[5] + xUpdated[8] - xUpdated[11])
};
double e = VectorOperations.VectorDotProduct(
dRho12, VectorOperations.MatrixVectorProduct(
aMatrix, xUpdated));
return(e);
}
private double CalculateNormalGap(double[,] aMatrix, double[] n)
{
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] xupd = new double[] {
Nodes[1].XCoordinate + DisplacementVector[0],
Nodes[1].YCoordinate + DisplacementVector[1],
Nodes[2].XCoordinate + DisplacementVector[2],
Nodes[2].YCoordinate + DisplacementVector[3],
Nodes[3].XCoordinate + DisplacementVector[4],
Nodes[3].YCoordinate + DisplacementVector[5]
};
double normalGap = VectorOperations.VectorDotProduct(xupd, AT_n);
return(normalGap);
}
private double CalculateNormalGap()
{
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[] n = CalculateNormalUnitVector();
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] xupd = new double[] {
Nodes[1].XCoordinate + DisplacementVector[0],
Nodes[1].YCoordinate + DisplacementVector[1],
Nodes[2].XCoordinate + DisplacementVector[2],
Nodes[2].YCoordinate + DisplacementVector[3]
};
double normalGap = VectorOperations.VectorDotProduct(xupd, AT_n);
return(normalGap);
}
private double CalculatePenetration(double ksi1, double ksi2)
{
double[] xUpdated = xUpdatedVector();
List <double[]> dRho = SurfaceVectors(ksi1, ksi2);
double[,] m = MetricTensor(dRho);
double[] n = NormalVector(m, dRho);
Tuple <double[, ], double[, ], double[, ]> aMatrices = CalculatePositionMatrix(ksi1, ksi2);
double[,] a = aMatrices.Item1;
double[,] aT = MatrixOperations.Transpose(a);
double ksi3 = VectorOperations.VectorDotProduct(
xUpdated, VectorOperations.MatrixVectorProduct(
aT, n));
return(ksi3);
}
private Tuple <double[], double, double[], double[], double> SlaveSegmentGeometry(double[,] daMatrix, double[,] da2Matrix)
{
double[] xupd = NodalXUpdated();
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double[] surfaceVectorDerivative = VectorOperations.MatrixVectorProduct(da2Matrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[] { -surfaceVector[1], surfaceVector[0] };
double scalarCoef = 1.0 / (Math.Sqrt(detm));
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
double[] tangentVector = VectorOperations.VectorScalarProductNew(surfaceVector, scalarCoef);
double scalarCoef2 = Math.Pow(m11, 2.0);
double curvatureTensor = scalarCoef2 * VectorOperations.VectorDotProduct(surfaceVectorDerivative, normalUnitVec);
return(new Tuple <double[], double, double[], double[], double>(surfaceVector, detm, normalUnitVec, tangentVector, curvatureTensor));
}
private Tuple <double[], double, double[]> SurfaceGeometry(double[,] daMatrix)
{
double Xm1 = Nodes[1].XCoordinate + DisplacementVector[0];
double Ym1 = Nodes[1].YCoordinate + DisplacementVector[1];
double Xm2 = Nodes[2].XCoordinate + DisplacementVector[2];
double Ym2 = Nodes[2].YCoordinate + DisplacementVector[3];
double Xs = Nodes[3].XCoordinate + DisplacementVector[4];
double Ys = Nodes[3].YCoordinate + DisplacementVector[5];
double[] xupd = new double[] { -Xm1, -Ym1, -Xm2, -Ym2, -Xs, -Ys };
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[] { Ym2 - Ym1, Xm1 - Xm2 };
double scalarCoef = -1.0 / (2.0 * Math.Sqrt(detm));
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
return(new Tuple <double[], double, double[]>(surfaceVector, m11, normalUnitVec));
}
private Tuple <double[], double, double[], double[], double> MasterSegmentGeometry(double[,] daMatrix, double[,] da2Matrix)
{
double[] xupd = VectorOperations.VectorScalarProduct(NodalXUpdated(), -1);
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double[] surfaceVectorDerivative = VectorOperations.MatrixVectorProduct(da2Matrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[2];
double scalarCoef = new double();
double scalarCoef2 = Math.Pow(m11, 2.0);
double[] tangentVector = new double[2];
double curvatureTensor = new double();
if (Properties.MasterSegmentPolynomialDegree == 1)
{
double Xm1 = Nodes[1].XCoordinate + DisplacementVector[0];
double Ym1 = Nodes[1].YCoordinate + DisplacementVector[1];
double Xm2 = Nodes[2].XCoordinate + DisplacementVector[2];
double Ym2 = Nodes[2].YCoordinate + DisplacementVector[3];
vector[0] = Ym2 - Ym1;
vector[1] = Xm1 - Xm2;
scalarCoef = -1.0 / (2.0 * Math.Sqrt(detm));
}
else
{
vector[0] = -surfaceVector[1];
vector[1] = surfaceVector[0];
scalarCoef = 1.0 / (Math.Sqrt(detm));
tangentVector = VectorOperations.VectorScalarProductNew(surfaceVector, scalarCoef);
}
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
curvatureTensor = scalarCoef2 * VectorOperations.VectorDotProduct(surfaceVectorDerivative, normalUnitVec);
return(new Tuple <double[], double, double[], double[], double>(surfaceVector, m11, normalUnitVec, tangentVector, curvatureTensor));
}
