private Vector CreateInterfaceProblemRhs(FetiDPFlexibilityMatrix flexibility,
IFetiDPCoarseProblemSolver coarseProblemSolver, Vector globalFcStar, Vector dr)
{
// rhs = dr - FIrc * inv(KccStar) * fcStar
Vector rhs = coarseProblemSolver.MultiplyInverseCoarseProblemMatrixTimes(globalFcStar);
rhs = flexibility.MultiplyFIrc(rhs);
rhs = dr - rhs;
return(rhs);
}
public static void TestInterfaceProblemCreation()
{
// Setup the model and solver
Model model = Quads4x4MappingMatricesTests.CreateModel();
Dictionary <int, HashSet <INode> > cornerNodes = Quads4x4MappingMatricesTests.DefineCornerNodes(model);
var fetiMatrices = new DenseFetiDPSubdomainMatrixManager.Factory();
var cornerNodeSelection = new UsedDefinedCornerNodes(cornerNodes);
var solver = new FetiDPSolver.Builder(cornerNodeSelection, fetiMatrices).BuildSolver(model);
model.ConnectDataStructures();
solver.OrderDofs(false);
solver.Initialize();
// Mock the stiffness matrices and force vectors
Dictionary <int, IFetiDPSubdomainMatrixManager> matrixManagers = MockStiffnesses();
Vector dr = VectorDr;
// Access private fields of FetiDPSolver
FieldInfo fi = typeof(FetiDPSolver).GetField("lagrangeEnumerator", BindingFlags.NonPublic | BindingFlags.Instance);
var lagrangeEnumerator = (FetiDPLagrangeMultipliersEnumerator)fi.GetValue(solver);
fi = typeof(FetiDPSolver).GetField("dofSeparator", BindingFlags.NonPublic | BindingFlags.Instance);
var dofSeparator = (FetiDPDofSeparator)fi.GetValue(solver);
// Hardcoded coarse problem matrix and rhs
var coarseSolver = new DenseFetiDPCoarseProblemSolver(model.Subdomains);
Vector globalFcStar = VectorFcStar;
Matrix inverseKccStar = MatrixKccStar.Invert(); // It must be set as a private field using reflection.
fi = typeof(DenseFetiDPCoarseProblemSolver).GetField("inverseGlobalKccStar",
BindingFlags.NonPublic | BindingFlags.Instance);
fi.SetValue(coarseSolver, inverseKccStar);
// Create the rhs vector of the interface problem
FetiDPInterfaceProblemSolver interfaceSolver = new FetiDPInterfaceProblemSolver.Builder().Build();
var flexibility = new FetiDPFlexibilityMatrix(dofSeparator, lagrangeEnumerator, matrixManagers);
Vector fcStar = VectorFcStar;
MethodInfo method = interfaceSolver.GetType().GetMethod("CreateInterfaceProblemRhs",
BindingFlags.NonPublic | BindingFlags.Instance); // reflection for the private method
Vector interfaceRhs = (Vector)method.Invoke(interfaceSolver, new object[] { flexibility, coarseSolver, fcStar, dr });
// Create the matrix of the interface problem by multiplying with identity matrix
int numLagranges = lagrangeEnumerator.NumLagrangeMultipliers;
var interfaceMatrixImplicit =
new FetiDPInterfaceProblemSolver.InterfaceProblemMatrix(flexibility, coarseSolver);
Matrix interfaceMatrix = MultiplyWithIdentity(numLagranges, numLagranges, interfaceMatrixImplicit.Multiply); // Action<T> is contravariant!!!
// Check against expected linear system
double tol = 1E-13;
Assert.True(InterfaceProblemVector.Equals(interfaceRhs, tol));
Assert.True(InterfaceProblemMatrix.Equals(interfaceMatrix, tol));
}
public static void TestFlexibilityMatrices()
{
// Setup the model and solver
Model model = Quads4x4MappingMatricesTests.CreateModel();
Dictionary <int, HashSet <INode> > cornerNodes = Quads4x4MappingMatricesTests.DefineCornerNodes(model);
var fetiMatrices = new DenseFetiDPSubdomainMatrixManager.Factory();
var cornerNodeSelection = new UsedDefinedCornerNodes(cornerNodes);
var solver = new FetiDPSolver.Builder(cornerNodeSelection, fetiMatrices).BuildSolver(model);
model.ConnectDataStructures();
solver.OrderDofs(false);
solver.Initialize();
// Mock the stiffness matrices
Dictionary <int, IFetiDPSubdomainMatrixManager> matrixManagers = MockStiffnesses();
// Access private fields of FetiDPSolver
FieldInfo fi = typeof(FetiDPSolver).GetField("lagrangeEnumerator", BindingFlags.NonPublic | BindingFlags.Instance);
var lagrangeEnumerator = (FetiDPLagrangeMultipliersEnumerator)fi.GetValue(solver);
fi = typeof(FetiDPSolver).GetField("dofSeparator", BindingFlags.NonPublic | BindingFlags.Instance);
var dofSeparator = (FetiDPDofSeparator)fi.GetValue(solver);
// Create the flexibility matrices by multiplying with identity matrices
int numLagranges = lagrangeEnumerator.NumLagrangeMultipliers;
int numCornerDofs = dofSeparator.NumGlobalCornerDofs;
var flexibility = new FetiDPFlexibilityMatrix(dofSeparator, lagrangeEnumerator, matrixManagers);
Matrix FIrr = MultiplyWithIdentity(numLagranges, numLagranges, flexibility.MultiplyFIrr);
Matrix FIrc = MultiplyWithIdentity(numLagranges, numLagranges, (x, y) => y.CopyFrom(flexibility.MultiplyFIrc(x)));
// Check against expected matrices
double tol = 1E-11;
Assert.True(MatrixFIrr.Equals(FIrr, tol));
Assert.True(MatrixFIrc.Equals(FIrc, tol));
}
public static void TestInterfaceProblemSolution()
{
// Setup the model and solver
Model model = Quads4x4MappingMatricesTests.CreateModel();
Dictionary <int, HashSet <INode> > cornerNodes = Quads4x4MappingMatricesTests.DefineCornerNodes(model);
var fetiMatrices = new DenseFetiDPSubdomainMatrixManager.Factory();
var cornerNodeSelection = new UsedDefinedCornerNodes(cornerNodes);
var solver = new FetiDPSolver.Builder(cornerNodeSelection, fetiMatrices).BuildSolver(model);
model.ConnectDataStructures();
solver.OrderDofs(false);
solver.Initialize();
// Mock the stiffness matrices and force vectors
Dictionary <int, IFetiDPSubdomainMatrixManager> matrixManagers = MockStiffnesses();
Dictionary <int, IFetiSubdomainMatrixManager> matrixManagersPreconditioning = MockStiffnessesForPreconditioning();
Dictionary <int, Matrix> Krr = MatricesKrr;
Vector dr = VectorDr;
// Access private fields of FetiDPSolver
FieldInfo fi = typeof(FetiDPSolver).GetField("lagrangeEnumerator", BindingFlags.NonPublic | BindingFlags.Instance);
var lagrangeEnumerator = (FetiDPLagrangeMultipliersEnumerator)fi.GetValue(solver);
fi = typeof(FetiDPSolver).GetField("dofSeparator", BindingFlags.NonPublic | BindingFlags.Instance);
var dofSeparator = (FetiDPDofSeparator)fi.GetValue(solver);
// Hardcoded coarse problem matrix and rhs
var coarseSolver = new DenseFetiDPCoarseProblemSolver(model.Subdomains);
Vector globalFcStar = VectorFcStar;
Matrix inverseKccStar = MatrixKccStar.Invert(); // It must be set as a private field using reflection.
fi = typeof(DenseFetiDPCoarseProblemSolver).GetField("inverseGlobalKccStar",
BindingFlags.NonPublic | BindingFlags.Instance);
fi.SetValue(coarseSolver, inverseKccStar);
// Dirichlet preconditioner
var precondFactory = new DirichletPreconditioner.Factory();
var repackagedKrr = new Dictionary <int, IMatrixView>();
foreach (var idMatrixPair in Krr)
{
repackagedKrr[idMatrixPair.Key] = idMatrixPair.Value;
}
var stiffnessDistribution = new HomogeneousStiffnessDistribution(model, dofSeparator);
stiffnessDistribution.Update(null);
IFetiPreconditioner preconditioner = precondFactory.CreatePreconditioner(model,
stiffnessDistribution, dofSeparator, lagrangeEnumerator, matrixManagersPreconditioning);
// Solve the interface problem
FetiDPInterfaceProblemSolver interfaceSolver = new FetiDPInterfaceProblemSolver.Builder().Build();
var flexibility = new FetiDPFlexibilityMatrix(dofSeparator, lagrangeEnumerator, matrixManagers);
var logger = new SolverLogger("mock FETI-DP");
(Vector lagranges, Vector uc) = interfaceSolver.SolveInterfaceProblem(
flexibility, preconditioner, coarseSolver, globalFcStar, dr, GlobalForcesNorm, logger);
// Check against expected solution
double tol = 1E-7;
Assert.True(SolutionLagrangeMultipliers.Equals(lagranges, tol));
Assert.True(SolutionCornerDisplacements.Equals(uc, tol));
}
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);
}
internal InterfaceProblemMatrix(FetiDPFlexibilityMatrix flexibility, IFetiDPCoarseProblemSolver coarseProblemSolver)
{
this.flexibility = flexibility;
this.coarseProblemSolver = coarseProblemSolver;
}
