public Vector Multiply(Vector vector)
{
var result = Vector.CreateZero(vector.Length);
preconditioner.SolveLinearSystem(vector, result);
return(result);
}
public void SolveLinearSystem(IVectorView rhsVector, IVector lhsVector)
{
//TODO: remove casts. I think PCG, LinearTransformation and preconditioners should be generic, bounded by
// IVectorView and IVector
var lhs = (Vector)lhsVector;
var rhs = (Vector)rhsVector;
fetiPreconditioner.SolveLinearSystem(rhs, lhs);
}
private PcgPreconditioner DefinePcgPreconditioner(IFetiPreconditioner preconditioner, Feti1Projection projection)
{
if (projectionSidePreconditioner == ProjectionSide.None)
{
// x = prec(A) * y => x = prec(F) * y
return(new PcgPreconditioner((x, y) => preconditioner.SolveLinearSystem(y, x)));
}
else if (projectionSidePreconditioner == ProjectionSide.Left)
{
// x = prec(A) * y => x = (P * prec(F)) * y => x = P * (prec(F) * y)
return(new PcgPreconditioner((y, x) =>
{
int order = y.Length;
var temp = Vector.CreateZero(order);
preconditioner.SolveLinearSystem(y, temp);
projection.ProjectVector(temp, x, false);
}));
}
else if (projectionSidePreconditioner == ProjectionSide.Both)
{
// x = prec(A) * y => x = (P * prec(F) * P^T) * y => x = P * (prec(F) * (P^T * y))
return(new PcgPreconditioner((y, x) =>
{
int order = y.Length;
var temp1 = Vector.CreateZero(order);
projection.ProjectVector(y, temp1, true);
var temp2 = Vector.CreateZero(order);
preconditioner.SolveLinearSystem(temp1, temp2);
projection.ProjectVector(temp2, x, false);
}));
}
else
{
throw new ArgumentException(
"The FETI-1 preconditioner can be multiplied from the left side, both sides or not at all.");
}
}
internal IterativeStatistics Solve(IInterfaceFlexibilityMatrix matrix, IFetiPreconditioner preconditioner,
IInterfaceProjection projector, Vector rhs, Vector lagrangeMultipliers)
{
int n = matrix.Order;
int maxIterations = maxIterationsProvider.GetMaxIterations(matrix.Order);
// r0 = d - F * λ0
var residual = matrix.Multiply(lagrangeMultipliers);
residual.LinearCombinationIntoThis(-1.0, rhs, 1.0);
// Other allocations
var w = Vector.CreateZero(n);
var y = Vector.CreateZero(n);
var z = Vector.CreateZero(n);
var direction = Vector.CreateZero(n);
var matrixTimesDirection = Vector.CreateZero(n);
double residualDotProductPrevious = double.NaN;
double residualNormRatio = double.NaN;
double beta = double.NaN;
for (int iter = 1; iter <= maxIterations; ++iter)
{
// w(m-1) = P * r(m-1)
projector.ProjectVector(residual, w, false);
// z(m-1) = preconditioner * w(m-1)
preconditioner.SolveLinearSystem(w, z);
// Check convergence: usually if ||z|| / ||f|| < tolerance
residualNormRatio = convergence.EstimateResidualNormRatio(lagrangeMultipliers, z);
if (residualNormRatio <= residualTolerance)
{
//TODO: is it correct to check for convergence here? How many iterations should I return?
return(new IterativeStatistics
{
AlgorithmName = name,
HasConverged = true,
NumIterationsRequired = iter - 1, //TODO: not sure about this.
ResidualNormRatioEstimation = residualNormRatio
});
}
// y(m-1) = P * z(m-1)
projector.ProjectVector(z, y, false);
double residualDotProductCurrent = y.DotProduct(w);
if (iter == 1)
{
// β(1) = 0
beta = 0;
// p(1) = y0
direction.CopyFrom(y);
}
else
{
// β(m) = (y(m-1) * w(m-1)) / (y(m-2) * w(m-2))
beta = residualDotProductCurrent / residualDotProductPrevious;
// p(m) = y(m-1) + β(m) * p(m-1), if m > 1
direction.LinearCombinationIntoThis(beta, y, 1.0);
}
residualDotProductPrevious = residualDotProductCurrent;
// γ(m) = (y(m-1) * w(m-1)) / (p(m) * F * p(m))
matrix.Multiply(direction, matrixTimesDirection);
double stepSize = (y * w) / (direction * matrixTimesDirection);
// λ(m) = λ(m-1) + γ(m) * p(m)
lagrangeMultipliers.AxpyIntoThis(direction, stepSize);
// r(m) = r(m-1) -γ(m) * F * p(m)
residual.AxpyIntoThis(matrixTimesDirection, -stepSize);
}
return(new IterativeStatistics
{
AlgorithmName = name,
HasConverged = false,
NumIterationsRequired = maxIterations,
ResidualNormRatioEstimation = residualNormRatio
});
}