//TODO: Use Skyline assembler
private SkylineMatrix CreateGlobalKccStar(Dictionary <int, HashSet <INode> > cornerNodesOfSubdomains,
FetiDPDofSeparator dofSeparator, Dictionary <int, IFetiDPSubdomainMatrixManager> matrixManagers)
{
int[] skylineColHeights = FindSkylineColumnHeights(cornerNodesOfSubdomains, dofSeparator);
var skylineBuilder = SkylineBuilder.Create(dofSeparator.NumGlobalCornerDofs, skylineColHeights);
for (int s = 0; s < subdomains.Count; ++s)
{
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
// KccStar[s] = Kcc[s] - Krc[s]^T * inv(Krr[s]) * Krc[s]
if (subdomains[s].StiffnessModified)
{
Debug.WriteLine($"{this.GetType().Name}: Calculating Schur complement of remainder dofs"
+ " for the stiffness of subdomain {s}");
matrices.CalcSchurComplementOfRemainderDofs(); //TODO: At this point Kcc and Krc can be cleared. Maybe Krr too.
}
int[] subdomainToGlobalIndices = dofSeparator.CornerBooleanMatrices[s].GetRowsToColumnsMap();
IMatrixView subdomainMatrix = matrices.SchurComplementOfRemainderDofs;
skylineBuilder.AddSubmatrixSymmetric(subdomainMatrix, subdomainToGlobalIndices);
}
return(skylineBuilder.BuildSkylineMatrix());
}
/// <summary>
/// Does not mutate this object.
/// </summary>
internal Dictionary <int, Vector> CalcActualDisplacements(Vector lagranges, Vector cornerDisplacements,
Dictionary <int, Vector> fr)
{
var freeDisplacements = new Dictionary <int, Vector>();
foreach (int s in subdomains.Keys)
{
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
// ur[s] = inv(Krr[s]) * (fr[s] - Br[s]^T * lagranges - Krc[s] * Lc[s] * uc)
Vector BrLambda = lagrangeEnumerator.BooleanMatrices[s].Multiply(lagranges, true);
Vector KrcLcUc = dofSeparator.CornerBooleanMatrices[s].Multiply(cornerDisplacements);
KrcLcUc = matrices.MultiplyKrcTimes(KrcLcUc);
Vector temp = fr[s].Copy();
temp.SubtractIntoThis(BrLambda);
temp.SubtractIntoThis(KrcLcUc);
Vector ur = matrices.MultiplyInverseKrrTimes(temp);
// uf[s] = union(ur[s], ubc[s])
// Remainder dofs
var uf = Vector.CreateZero(subdomains[s].FreeDofOrdering.NumFreeDofs);
int[] remainderDofs = dofSeparator.RemainderDofIndices[s];
uf.CopyNonContiguouslyFrom(remainderDofs, ur);
// Corner dofs: ubc[s] = Bc[s] * uc
Vector ubc = dofSeparator.CornerBooleanMatrices[s].Multiply(cornerDisplacements);
int[] cornerDofs = dofSeparator.CornerDofIndices[s];
uf.CopyNonContiguouslyFrom(cornerDofs, ubc);
freeDisplacements[s] = uf;
}
return(freeDisplacements);
}
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 MultiplyTransposedFIrc(Vector vector)
{
Preconditions.CheckMultiplicationDimensions(Order, vector.Length);
// FIrc[s]^T * x = sum_over_s( Lc[s]^T * (Krc[s]^T * (inv(Krr[s]) * (Br[s]^T * x))) )
var result = Vector.CreateZero(numCornerDofs);
foreach (int s in Br.Keys)
{
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
Vector temp = Br[s].Multiply(vector, true);
temp = matrices.MultiplyInverseKrrTimes(temp);
temp = matrices.MultiplyKcrTimes(temp);
temp = Lc[s].Multiply(temp, true);
result.AddIntoThis(temp);
}
return(result);
}
public Vector CreateCoarseProblemRhs(FetiDPDofSeparator dofSeparator,
Dictionary <int, IFetiDPSubdomainMatrixManager> matrixManagers,
Dictionary <int, Vector> fr, Dictionary <int, Vector> fbc)
{
// Static condensation for the force vectors
var globalFcStar = Vector.CreateZero(dofSeparator.NumGlobalCornerDofs);
for (int s = 0; s < subdomains.Count; ++s)
{
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
// fcStar[s] = fbc[s] - Krc[s]^T * inv(Krr[s]) * fr[s]
// globalFcStar = sum_over_s(Lc[s]^T * fcStar[s])
UnsignedBooleanMatrix Lc = dofSeparator.CornerBooleanMatrices[s];
Vector temp = matrices.MultiplyInverseKrrTimes(fr[s]);
temp = matrices.MultiplyKcrTimes(temp);
Vector fcStar = fbc[s] - temp;
globalFcStar.AddIntoThis(Lc.Multiply(fcStar, true));
}
return(globalFcStar);
}
private Matrix CreateGlobalKccStar(FetiDPDofSeparator dofSeparator,
Dictionary <int, IFetiDPSubdomainMatrixManager> matrixManagers)
{
// Static condensation of remainder dofs (Schur complement).
var globalKccStar = Matrix.CreateZero(dofSeparator.NumGlobalCornerDofs, dofSeparator.NumGlobalCornerDofs);
for (int s = 0; s < subdomains.Count; ++s)
{
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
// KccStar[s] = Kcc[s] - Krc[s]^T * inv(Krr[s]) * Krc[s]
if (subdomains[s].StiffnessModified)
{
Debug.WriteLine($"{this.GetType().Name}: Calculating Schur complement of remainder dofs"
+ " for the stiffness of subdomain {s}");
matrices.CalcSchurComplementOfRemainderDofs(); //TODO: At this point Kcc and Krc can be cleared. Maybe Krr too.
}
// globalKccStar = sum_over_s(Lc[s]^T * KccStar[s] * Lc[s])
UnsignedBooleanMatrix Lc = dofSeparator.CornerBooleanMatrices[s];
globalKccStar.AddIntoThis(Lc.ThisTransposeTimesOtherTimesThis(matrices.SchurComplementOfRemainderDofs));
}
return(globalKccStar);
}
public void Solve()
{
var watch = new Stopwatch();
foreach (var linearSystem in linearSystems.Values)
{
if (linearSystem.SolutionConcrete == null)
{
linearSystem.SolutionConcrete = linearSystem.CreateZeroVectorConcrete();
}
}
// Separate the force vector
watch.Start();
var fr = new Dictionary <int, Vector>();
var fbc = new Dictionary <int, Vector>();
foreach (int s in subdomains.Keys)
{
int[] remainderDofs = dofSeparator.RemainderDofIndices[s];
int[] cornerDofs = dofSeparator.CornerDofIndices[s];
Vector f = linearSystems[s].RhsConcrete;
fr[s] = f.GetSubvector(remainderDofs);
fbc[s] = f.GetSubvector(cornerDofs);
}
watch.Stop();
Logger.LogTaskDuration("Separating vectors & matrices", watch.ElapsedMilliseconds);
watch.Reset();
if (isStiffnessModified)
{
// Separate the stiffness matrix
watch.Start();
foreach (int s in subdomains.Keys)
{
if (!subdomains[s].StiffnessModified)
{
continue;
}
IFetiDPSubdomainMatrixManager matrices = matrixManagers[s];
int[] remainderDofs = dofSeparator.RemainderDofIndices[s];
int[] cornerDofs = dofSeparator.CornerDofIndices[s];
matrices.ExtractKrr(remainderDofs);
matrices.ExtractKcrKrc(cornerDofs, remainderDofs);
matrices.ExtractKcc(cornerDofs);
}
watch.Stop();
Logger.LogTaskDuration("Separating vectors & matrices", watch.ElapsedMilliseconds);
// Reorder internal dofs if needed by the preconditioner. TODO: Should I have done this previously in Initialize()?
watch.Start();
if (preconditionerFactory.ReorderInternalDofsForFactorization)
{
foreach (ISubdomain subdomain in model.Subdomains)
{
if (subdomain.ConnectivityModified)
{
Debug.WriteLine($"{this.GetType().Name}: Reordering internal dofs of subdomain {subdomain.ID}.");
matrixManagers[subdomain.ID].ReorderInternalDofs(dofSeparator, subdomain);
}
}
}
// Calculate the preconditioner before factorizing each subdomain's Kff
preconditioner = preconditionerFactory.CreatePreconditioner(model, stiffnessDistribution, dofSeparator,
lagrangeEnumerator, matrixManagersGeneral);
watch.Stop();
Logger.LogTaskDuration("Calculating preconditioner", watch.ElapsedMilliseconds);
// Factorize each subdomain's Krr
watch.Restart();
foreach (int s in subdomains.Keys)
{
if (!subdomains[s].StiffnessModified)
{
continue;
}
//TODO: If I can reuse Krr, I can also reuse its factorization. Therefore this must be inPlace. In contrast, FETI-1 needs Kff intact for Stiffness distribution, in the current design).
Debug.WriteLine(
$"{this.GetType().Name}: Inverting the remainder-remainder stiffness matrix of subdomain {s} in place.");
matrixManagers[s].InvertKrr(true);
}
watch.Stop();
Logger.LogTaskDuration("Matrix factorization", watch.ElapsedMilliseconds);
// Define FETI-DP flexibility matrices
watch.Restart();
flexibility = new FetiDPFlexibilityMatrix(dofSeparator, lagrangeEnumerator, matrixManagers);
// Static condensation of remainder dofs (Schur complement).
coarseProblemSolver.CreateAndInvertCoarseProblemMatrix(CornerNodesOfSubdomains, dofSeparator, matrixManagers);
watch.Stop();
Logger.LogTaskDuration("Setting up interface problem", watch.ElapsedMilliseconds);
watch.Reset();
isStiffnessModified = false;
}
// Static condensation for the force vectors
watch.Start();
Vector globalFcStar = coarseProblemSolver.CreateCoarseProblemRhs(dofSeparator, matrixManagers, fr, fbc);
// Calculate the rhs vectors of the interface system
Vector dr = CalcDisconnectedDisplacements(fr);
double globalForcesNorm = CalcGlobalForcesNorm();
watch.Stop();
Logger.LogTaskDuration("Setting up interface problem", watch.ElapsedMilliseconds);
// Solve the interface problem
watch.Restart();
(Vector lagranges, Vector uc) = interfaceProblemSolver.SolveInterfaceProblem(flexibility, preconditioner,
coarseProblemSolver, globalFcStar, dr, globalForcesNorm, Logger);
watch.Stop();
Logger.LogTaskDuration("Solving interface problem", watch.ElapsedMilliseconds);
// Calculate the displacements of each subdomain
watch.Restart();
Dictionary <int, Vector> actualDisplacements = CalcActualDisplacements(lagranges, uc, fr);
foreach (var idSystem in linearSystems)
{
idSystem.Value.SolutionConcrete = actualDisplacements[idSystem.Key];
}
watch.Stop();
Logger.LogTaskDuration("Calculate displacements from lagrange multipliers", watch.ElapsedMilliseconds);
Logger.IncrementAnalysisStep();
}