private Matrix GetLocalDerivativeMatrix(IFiniteElement element, double ksi, double eta)
{
Matrix LocalDerivativeMatrix = new Matrix(8, 4);
Matrix gradNksieta = new Matrix(2, 4);
gradNksieta[0, 0] = (eta - 1) * 0.25;
gradNksieta[1, 0] = (ksi - 1) * 0.25;
gradNksieta[0, 1] = (1 - eta) * 0.25;
gradNksieta[1, 1] = (-ksi - 1) * 0.25;
gradNksieta[0, 2] = (eta + 1) * 0.25;
gradNksieta[1, 2] = (ksi + 1) * 0.25;
gradNksieta[0, 3] = (-eta - 1) * 0.25;
gradNksieta[1, 3] = (1 - ksi) * 0.25;
JacobianRectangular J = new JacobianRectangular();
J.Element = element;
Matrix gradN = J.GetInverseJacobian(ksi, eta) * gradNksieta;
LocalDerivativeMatrix[0, 0] = LocalDerivativeMatrix[1, 3] = gradN[0, 0];
LocalDerivativeMatrix[2, 0] = LocalDerivativeMatrix[3, 3] = gradN[0, 1];
LocalDerivativeMatrix[4, 0] = LocalDerivativeMatrix[5, 3] = gradN[0, 2];
LocalDerivativeMatrix[6, 0] = LocalDerivativeMatrix[7, 3] = gradN[0, 3];
LocalDerivativeMatrix[1, 1] = LocalDerivativeMatrix[0, 2] = gradN[1, 0];
LocalDerivativeMatrix[3, 1] = LocalDerivativeMatrix[2, 2] = gradN[1, 1];
LocalDerivativeMatrix[5, 1] = LocalDerivativeMatrix[4, 2] = gradN[1, 2];
LocalDerivativeMatrix[7, 1] = LocalDerivativeMatrix[6, 2] = gradN[1, 3];
return LocalDerivativeMatrix;
}
private Matrix LocalStiffnessMatrixFunction(double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
JacobianRectangular J = new JacobianRectangular();
J.Element = elementCurrent;
return derivativeMatrix * ConstMatrix * Matrix.Transpose(derivativeMatrix) * J.GetJacobianDeterminant(ksi, eta);
}
private Matrix LocalMassMatrixFunction(double ksi, double eta)
{
Matrix baseFunctionsMatrix = GetLocalBaseFunctionsMatrix(ksi, eta);
JacobianRectangular J = new JacobianRectangular();
J.Element = elementCurrent;
return baseFunctionsMatrix * Matrix.Transpose(baseFunctionsMatrix) * J.GetJacobianDeterminant(ksi, eta);
}
protected Matrix LocalNonlinearMatrixFunction(double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
Matrix derivativeUMatrix = GetLocalUDerivativeMatrix(previousU, elementCurrent, ksi, eta);
JacobianRectangular J = new JacobianRectangular();
J.Element = elementCurrent;
return derivativeMatrix * derivativeUMatrix * Matrix.Transpose(derivativeMatrix) * J.GetJacobianDeterminant(ksi, eta);
}
private Matrix LocalVectorFunction(double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
JacobianRectangular J = new JacobianRectangular();
J.Element = elementCurrent;
Matrix VariableVectorOnElement = GetVariableVectorOnElement(elementCurrent, ksi, eta);
return derivativeMatrix * VariableVectorOnElement * J.GetJacobianDeterminant(ksi, eta);
}
