public void Multiply(Vector lhs, Vector rhs)
{
rhs.Clear(); //TODO: perhaps this should be done outside.
foreach (var keyFactor in matrixManagers)
{
int id = keyFactor.Key;
IFeti1SubdomainMatrixManager matrixManager = keyFactor.Value;
SignedBooleanMatrixColMajor B = lagrangeEnumerator.BooleanMatrices[id];
Vector FBx = matrixManager.MultiplyInverseKffTimes(B.Multiply(lhs, true));
Vector BFBx = B.Multiply(FBx, false);
rhs.AddIntoThis(BFBx);
}
}
//TODO: This can be moved to a base class. Only the S matrix is different for these preconditioners.
// Other ones might be different though.
public void SolveLinearSystem(Vector rhs, Vector lhs)
{
lhs.Clear(); //TODO: this should be avoided
foreach (int s in subdomainIDs)
{
IFetiSubdomainMatrixManager matrixManager = matrixManagers[s];
IMappingMatrix Bpb = preconditioningBoundarySignedBooleanMatrices[s];
// inv(F) * y = Bpb * Kbb * Bpb^T * y
Vector temp = Bpb.Multiply(rhs, true);
temp = matrixManager.MultiplyKbbTimes(temp);
Vector subdomainContribution = Bpb.Multiply(temp);
lhs.AddIntoThis(subdomainContribution);
}
}
public void MultiplyFIrr(Vector lhs, Vector rhs)
{
Preconditions.CheckMultiplicationDimensions(Order, lhs.Length);
Preconditions.CheckSystemSolutionDimensions(Order, rhs.Length);
// FIrr[s] * x = sum_over_s( Br[s] * (inv(Krr[s]) * (Br[s]^T * x)) )
rhs.Clear();
foreach (int s in Br.Keys)
{
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
Vector temp = Br[s].Multiply(lhs, true);
temp = matrices.MultiplyInverseKrrTimes(temp);
temp = Br[s].Multiply(temp);
rhs.AddIntoThis(temp);
}
}
public (Vector lagrangeMultipliers, Vector cornerDisplacements) SolveInterfaceProblem(FetiDPFlexibilityMatrix flexibility,
IFetiPreconditioner preconditioner, IFetiDPCoarseProblemSolver coarseProblemSolver,
Vector globalFcStar, Vector dr, double globalForcesNorm, SolverLogger logger)
{
int systemOrder = flexibility.Order;
// Matrix, preconditioner & rhs
var pcgMatrix = new InterfaceProblemMatrix(flexibility, coarseProblemSolver);
var pcgPreconditioner = new InterfaceProblemPreconditioner(preconditioner);
Vector pcgRhs = CreateInterfaceProblemRhs(flexibility, coarseProblemSolver, globalFcStar, dr);
// Solve the interface problem using PCG algorithm
var pcgBuilder = new PcgAlgorithm.Builder();
pcgBuilder.MaxIterationsProvider = maxIterationsProvider;
pcgBuilder.ResidualTolerance = pcgConvergenceTolerance;
pcgBuilder.Convergence = pcgConvergenceStrategyFactory.CreateConvergenceStrategy(globalForcesNorm);
PcgAlgorithm pcg = pcgBuilder.Build(); //TODO: perhaps use the pcg from the previous analysis if it has reorthogonalization.
var lagranges = Vector.CreateZero(systemOrder);
IterativeStatistics stats = pcg.Solve(pcgMatrix, pcgPreconditioner, pcgRhs, lagranges, true,
() => Vector.CreateZero(systemOrder));
// Log statistics about PCG execution
if (!stats.HasConverged)
{
throw new IterativeSolverNotConvergedException(FetiDPSolver.name + " did not converge to a solution. PCG"
+ $" algorithm run for {stats.NumIterationsRequired} iterations and the residual norm ratio was"
+ $" {stats.ResidualNormRatioEstimation}");
}
logger.LogIterativeAlgorithm(stats.NumIterationsRequired, stats.ResidualNormRatioEstimation);
// Calculate corner displacements: uc = inv(KccStar) * (fcStar + FIrc^T * lagranges)
Vector uc = flexibility.MultiplyTransposedFIrc(lagranges);
uc.AddIntoThis(globalFcStar);
uc = coarseProblemSolver.MultiplyInverseCoarseProblemMatrixTimes(uc);
return(lagranges, uc);
}
private double[,] CalculateBendingDeformationMatrix(double[] surfaceBasisVector3, ShapeTSplines2DFromBezierExtraction tsplines, int j,
double[] surfaceBasisVector2, double[] surfaceBasisVectorDerivative1, double[] surfaceBasisVector1, double J1,
double[] surfaceBasisVectorDerivative2, double[] surfaceBasisVectorDerivative12, ControlPoint[] elementControlPoints)
{
var Bbending = new double[3, elementControlPoints.Length * 3];
var s1 = Vector.CreateFromArray(surfaceBasisVector1);
var s2 = Vector.CreateFromArray(surfaceBasisVector2);
var s3 = Vector.CreateFromArray(surfaceBasisVector3);
var s11 = Vector.CreateFromArray(surfaceBasisVectorDerivative1);
var s22 = Vector.CreateFromArray(surfaceBasisVectorDerivative2);
var s12 = Vector.CreateFromArray(surfaceBasisVectorDerivative12);
for (int column = 0; column < elementControlPoints.Length * 3; column += 3)
{
#region BI1
var BI1 = s3.CrossProduct(s3);
BI1.ScaleIntoThis(tsplines.TSplineDerivativeValuesHeta[column / 3, j]);
var auxVector = s2.CrossProduct(s3);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesKsi[column / 3, j]);
BI1.AddIntoThis(auxVector);
BI1.ScaleIntoThis(s3.DotProduct(s11));
auxVector = s1.CrossProduct(s11);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesHeta[column / 3, j]);
BI1.AddIntoThis(auxVector);
BI1.ScaleIntoThis(1 / J1);
auxVector[0] = surfaceBasisVector3[0];
auxVector[1] = surfaceBasisVector3[1];
auxVector[2] = surfaceBasisVector3[2];
auxVector.ScaleIntoThis(-tsplines.TSplineSecondDerivativesValueKsi[column / 3, j]);
BI1.AddIntoThis(auxVector);
#endregion BI1
#region BI2
IVector BI2 = s3.CrossProduct(s3);
BI2.ScaleIntoThis(tsplines.TSplineDerivativeValuesHeta[column / 3, j]);
auxVector = s2.CrossProduct(s3);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesKsi[column / 3, j]);
BI2.AddIntoThis(auxVector);
BI2.ScaleIntoThis(s3.DotProduct(s22));
auxVector = s1.CrossProduct(s22);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesHeta[column / 3, j]);
BI2.AddIntoThis(auxVector);
auxVector = s22.CrossProduct(s2);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesKsi[column / 3, j]);
BI2.AddIntoThis(auxVector);
BI2.ScaleIntoThis(1 / J1);
auxVector[0] = surfaceBasisVector3[0];
auxVector[1] = surfaceBasisVector3[1];
auxVector[2] = surfaceBasisVector3[2];
auxVector.ScaleIntoThis(-tsplines.TSplineSecondDerivativesValueHeta[column / 3, j]);
BI2.AddIntoThis(auxVector);
#endregion BI2
#region BI3
Vector BI3 = s3.CrossProduct(s3);
BI3.ScaleIntoThis(tsplines.TSplineDerivativeValuesHeta[column / 3, j]);
auxVector = s2.CrossProduct(s3);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesKsi[column / 3, j]);
BI3.AddIntoThis(auxVector);
BI3.ScaleIntoThis(s3.DotProduct(s12));
auxVector = s1.CrossProduct(s12);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesHeta[column / 3, j]);
BI3.AddIntoThis(auxVector);
auxVector = s22.CrossProduct(s2);
auxVector.ScaleIntoThis(tsplines.TSplineDerivativeValuesKsi[column / 3, j]);
BI3.AddIntoThis(auxVector);
BI3.ScaleIntoThis(1 / J1);
auxVector[0] = surfaceBasisVector3[0];
auxVector[1] = surfaceBasisVector3[1];
auxVector[2] = surfaceBasisVector3[2];
auxVector.ScaleIntoThis(-tsplines.TSplineSecondDerivativesValueKsiHeta[column / 3, j]);
BI3.AddIntoThis(auxVector);
#endregion BI3
Bbending[0, column] = BI1[0];
Bbending[0, column + 1] = BI1[1];
Bbending[0, column + 2] = BI1[2];
Bbending[1, column] = BI2[0];
Bbending[1, column + 1] = BI2[1];
Bbending[1, column + 2] = BI2[2];
Bbending[2, column] = 2 * BI3[0];
Bbending[2, column + 1] = 2 * BI3[1];
Bbending[2, column + 2] = 2 * BI3[2];
}
return(Bbending);
}
private Matrix CalculateBendingDeformationMatrix(Vector surfaceBasisVector3, Nurbs2D nurbs, int j,
Vector surfaceBasisVector2, Vector surfaceBasisVectorDerivative1, Vector surfaceBasisVector1, double J1,
Vector surfaceBasisVectorDerivative2, Vector surfaceBasisVectorDerivative12, NurbsKirchhoffLoveShellElement element)
{
var elementControlPoints = element.ControlPoints.ToArray();
Matrix Bbending = Matrix.CreateZero(3, elementControlPoints.Length * 3);
for (int column = 0; column < elementControlPoints.Length * 3; column += 3)
{
#region BI1
var BI1 = surfaceBasisVector3.CrossProduct(surfaceBasisVector3);
BI1.ScaleIntoThis(nurbs.NurbsDerivativeValuesHeta[column / 3, j]);
var auxVector = surfaceBasisVector2.CrossProduct(surfaceBasisVector3);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesKsi[column / 3, j]);
BI1.AddIntoThis(auxVector);
BI1.ScaleIntoThis(surfaceBasisVector3.DotProduct(surfaceBasisVectorDerivative1));
auxVector = surfaceBasisVector1.CrossProduct(surfaceBasisVectorDerivative1);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesHeta[column / 3, j]);
BI1.AddIntoThis(auxVector);
BI1.ScaleIntoThis(1 / J1);
auxVector[0] = surfaceBasisVector3[0];
auxVector[1] = surfaceBasisVector3[1];
auxVector[2] = surfaceBasisVector3[2];
auxVector.ScaleIntoThis(-nurbs.NurbsSecondDerivativeValueKsi[column / 3, j]);
BI1.AddIntoThis(auxVector);
#endregion BI1
#region BI2
Vector BI2 = surfaceBasisVector3.CrossProduct(surfaceBasisVector3);
BI2.ScaleIntoThis(nurbs.NurbsDerivativeValuesHeta[column / 3, j]);
auxVector = surfaceBasisVector2.CrossProduct(surfaceBasisVector3);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesKsi[column / 3, j]);
BI2.AddIntoThis(auxVector);
BI2.ScaleIntoThis(surfaceBasisVector3.DotProduct(surfaceBasisVectorDerivative2));
auxVector = surfaceBasisVector1.CrossProduct(surfaceBasisVectorDerivative2);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesHeta[column / 3, j]);
BI2.AddIntoThis(auxVector);
auxVector = surfaceBasisVectorDerivative2.CrossProduct(surfaceBasisVector2);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesKsi[column / 3, j]);
BI2.AddIntoThis(auxVector);
BI2.ScaleIntoThis(1 / J1);
auxVector[0] = surfaceBasisVector3[0];
auxVector[1] = surfaceBasisVector3[1];
auxVector[2] = surfaceBasisVector3[2];
auxVector.ScaleIntoThis(-nurbs.NurbsSecondDerivativeValueHeta[column / 3, j]);
BI2.AddIntoThis(auxVector);
#endregion BI2
#region BI3
Vector BI3 = surfaceBasisVector3.CrossProduct(surfaceBasisVector3);
BI3.ScaleIntoThis(nurbs.NurbsDerivativeValuesHeta[column / 3, j]);
auxVector = surfaceBasisVector2.CrossProduct(surfaceBasisVector3);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesKsi[column / 3, j]);
BI3.AddIntoThis(auxVector);
BI3.ScaleIntoThis(surfaceBasisVector3.DotProduct(surfaceBasisVectorDerivative12));
auxVector = surfaceBasisVector1.CrossProduct(surfaceBasisVectorDerivative12);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesHeta[column / 3, j]);
BI3.AddIntoThis(auxVector);
auxVector = surfaceBasisVectorDerivative2.CrossProduct(surfaceBasisVector2);
auxVector.ScaleIntoThis(nurbs.NurbsDerivativeValuesKsi[column / 3, j]);
BI3.AddIntoThis(auxVector);
BI3.ScaleIntoThis(1 / J1);
auxVector[0] = surfaceBasisVector3[0];
auxVector[1] = surfaceBasisVector3[1];
auxVector[2] = surfaceBasisVector3[2];
auxVector.ScaleIntoThis(-nurbs.NurbsSecondDerivativeValueKsiHeta[column / 3, j]);
BI3.AddIntoThis(auxVector);
#endregion BI3
Bbending[0, column] = BI1[0];
Bbending[0, column + 1] = BI1[1];
Bbending[0, column + 2] = BI1[2];
Bbending[1, column] = BI2[0];
Bbending[1, column + 1] = BI2[1];
Bbending[1, column + 2] = BI2[2];
Bbending[2, column] = 2 * BI3[0];
Bbending[2, column + 1] = 2 * BI3[1];
Bbending[2, column + 2] = 2 * BI3[2];
}
return(Bbending);
}
