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);
}
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);
}
public Vector CalcLagrangeMultipliers(Feti1FlexibilityMatrix flexibility, IFetiPreconditioner preconditioner,
Feti1Projection projection, Vector disconnectedDisplacements, Vector rigidBodyModesWork, double globalForcesNorm,
SolverLogger logger)
{
// PCPG starts from the particular lagrange multipliers: λ0 = Q * G * inv(G^T * Q * G) * e
Vector lagranges = projection.CalcParticularLagrangeMultipliers(rigidBodyModesWork);
IFetiPcgConvergence pcpgConvergenceStrategy =
pcgConvergenceStrategyFactory.CreateConvergenceStrategy(globalForcesNorm);
var pcpg = new PcpgAlgorithm(maxIterationsProvider, pcpgConvergenceTolerance, pcpgConvergenceStrategy);
IterativeStatistics stats =
pcpg.Solve(flexibility, preconditioner, projection, disconnectedDisplacements, lagranges);
if (!stats.HasConverged)
{
throw new IterativeSolverNotConvergedException(Feti1Solver.name + " did not converge to a solution. PCPG"
+ $" algorithm run for {stats.NumIterationsRequired} iterations and the residual norm ratio was"
+ $" {stats.ResidualNormRatioEstimation}");
}
// Log statistics about PCG execution
logger.LogIterativeAlgorithm(stats.NumIterationsRequired, stats.ResidualNormRatioEstimation);
return(lagranges);
}