public void NewtonRaphson()
{
internalForcesTotalVector = discretization.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(BoundaryConditionsImposition.ReducedVector(internalForcesTotalVector, boundaryDof), forceVector);
residualNorm = VectorOperations.VectorNorm2(residual);
int iteration = 0;
while (residualNorm > tolerance && iteration < maxIterations)
{
Array.Clear(discretization.TotalStiffnessMatrix, 0, discretization.TotalStiffnessMatrix.Length);
discretization.CreateTotalStiffnessMatrix();
double[,] reducedStiffnessMatrix = BoundaryConditionsImposition.ReducedTotalStiff(discretization.TotalStiffnessMatrix, boundaryDof);
DirectSolver linearSolution = new DirectSolver(reducedStiffnessMatrix, residual);
linearSolution.SolveWithMethod("PCG");
deltaU = linearSolution.GetSolutionVector;
double[] reducedSolutionVector = BoundaryConditionsImposition.ReducedVector(solutionVector, boundaryDof);
reducedSolutionVector = VectorOperations.VectorVectorSubtraction(reducedSolutionVector, deltaU);
solutionVector = BoundaryConditionsImposition.CreateFullVectorFromReducedVector(reducedSolutionVector, boundaryDof);
discretization.UpdateValues(solutionVector);
Array.Clear(discretization.internalForcesTotalVector, 0, discretization.internalForcesTotalVector.Length);
internalForcesTotalVector = discretization.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(BoundaryConditionsImposition.ReducedVector(internalForcesTotalVector, boundaryDof), forceVector);
residualNorm = VectorOperations.VectorNorm2(residual);
iteration = iteration + 1;
}
}
private double [] PCG()
{
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.VectorScalarProduct(preconVector, alpha));
residual = VectorOperations.VectorVectorSubtraction(residual, VectorOperations.VectorScalarProduct(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.VectorScalarProduct(preconVector, beta)
);
}
return(solutionVector);
}
private double[] Jacobi()
{
double[] oldSolution = new double[forceVector.Length];
double[,] Diag = MatrixOperations.PutZerosInDiag(stiffnessMatrix);
MatrixOperations.InvertDiagMatrix(Diag);
double[,] zeroDiagStiff = MatrixOperations.GetDiagMatrix(stiffnessMatrix);
for (int i = 0; i < maxIterations; i++)
{
oldSolution = solutionVector;
solutionVector = VectorOperations.MatrixVectorProduct(
Diag,
VectorOperations.VectorVectorSubtraction(
forceVector,
VectorOperations.MatrixVectorProduct(zeroDiagStiff, solutionVector)
));
if (VectorOperations.VectorDotProduct(solutionVector, oldSolution) < tolerance)
{
break;
}
}
return(solutionVector);
}