private PcgMatrix DefinePcgMatrix(Feti1FlexibilityMatrix flexibility, Feti1Projection projection)
{
//TODO: projection.ProjectVector() overwrites the rhs vector passed in. However that is not clear by the method.
// I should either always return the resulting vector (negating any optimizations) or set the convention that
// vectors passed in as results will always be overwritten. The latter forces the method that accepts them to
// clear them (if the method needs to), which is not needed if the resulting vector has just be initialized to 0.
if (projectionSideMatrix == ProjectionSide.Left)
{
// A * x = (P^T * F) * x = P^T * (F * x)
return(new PcgMatrix(flexibility.Order, (x, y) => projection.ProjectVector(flexibility.Multiply(x), y, true)));
}
else if (projectionSideMatrix == ProjectionSide.Both)
{
// A * x = (P^T * F * P) * x = P^T * (F * (P * x))
return(new PcgMatrix(flexibility.Order, (x, y) =>
{
var temp = Vector.CreateZero(flexibility.Order);
projection.ProjectVector(x, temp, false);
projection.ProjectVector(flexibility.Multiply(temp), y, true);
}));
}
else
{
throw new ArgumentException("The FETI-1 flexibility matrix can be multiplied from the left or both sides.");
}
}
public Vector CalcLagrangeMultipliers(Feti1FlexibilityMatrix flexibility, IFetiPreconditioner preconditioner,
Feti1Projection projection, Vector disconnectedDisplacements, Vector rigidBodyModesWork, double globalForcesNorm,
SolverLogger logger)
{
int systemOrder = flexibility.Order;
PcgMatrix pcgMatrix = DefinePcgMatrix(flexibility, projection);
PcgPreconditioner pcgPreconditioner = DefinePcgPreconditioner(preconditioner, projection);
// λ0 = Q * G * inv(G^T * Q * G) * e
Vector lagrangesParticular = projection.CalcParticularLagrangeMultipliers(rigidBodyModesWork);
// Calculate rhs of the projected interface system: rhs = P^T * (d - F * λ0)
var r0 = flexibility.Multiply(lagrangesParticular);
r0.LinearCombinationIntoThis(-1.0, disconnectedDisplacements, 1.0);
var pcgRhs = Vector.CreateZero(systemOrder);
projection.ProjectVector(r0, pcgRhs, true);
// 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();
var lagrangesBar = Vector.CreateZero(systemOrder);
IterativeStatistics stats = pcg.Solve(pcgMatrix, pcgPreconditioner, pcgRhs, lagrangesBar, true,
() => Vector.CreateZero(systemOrder));
if (!stats.HasConverged)
{
throw new IterativeSolverNotConvergedException(Feti1Solver.name + " did not converge to a solution. PCG"
+ $" algorithm run for {stats.NumIterationsRequired} iterations and the residual norm ratio was"
+ $" {stats.ResidualNormRatioEstimation}");
}
// Calculate the actual lagrange multipliers from the separation formula: λ = λ0 + P * λbar
var lagranges = Vector.CreateZero(systemOrder);
projection.ProjectVector(lagrangesBar, lagranges, false);
lagranges.AddIntoThis(lagrangesParticular);
// Log statistics about PCG execution
logger.LogIterativeAlgorithm(stats.NumIterationsRequired, stats.ResidualNormRatioEstimation);
return(lagranges);
}
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.");
}
}
/// <summary>
/// Calculates the actual lagrange multipliers depending on the separation formula.
/// </summary>
internal Vector CombineLagrangeMultipliers(Vector lagrangesParticular, Vector lagrangesBar, Feti1Projection projection)
{
if (lagrangeSeparation == LagrangeMultiplierSeparation.Simple)
{
// λ = λ0 + P * λbar
return(lagrangesBar + lagrangesParticular);
}
else if (lagrangeSeparation == LagrangeMultiplierSeparation.WithProjection)
{
// λ = λ0 + P * λbar
var lagranges = Vector.CreateZero(lagrangesBar.Length);
projection.ProjectVector(lagrangesBar, lagranges, false);
lagranges.AddIntoThis(lagrangesParticular);
return(lagranges);
}
else
{
throw new ArgumentException("The lagrange separation can only be: a) λ = λ0 + λbar or b) λ = λ0 + P * λbar");
}
}
