pathfollowingfunctions.hh

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// SPDX-FileCopyrightText: 2021-2025 The Ikarus Developers ikarus@ibb.uni-stuttgart.de
// SPDX-License-Identifier: LGPL-3.0-or-later
 
#pragma once
 
#include <cmath>
#include <string>
#include <utility>
#include <vector>
 
#include <dune/common/exceptions.hh>
#include <dune/common/float_cmp.hh>
 
#include <Eigen/Core>
 
#include <ikarus/controlroutines/common.hh>
#include <ikarus/utils/concepts.hh>
#include <ikarus/utils/defaultfunctions.hh>
 
namespace Ikarus {
 
namespace Impl {
 
  template <typename NLS>
  void checkHasNoValidIDBCForceFunction() {
    static_assert(not Concepts::HasValidIDBCForceFunction<NLS>,
                  "The given path following function is not implemented to handle inhomogeneous Dirichlet BCs.");
  }
 
} // namespace Impl
 
struct SubsidiaryArgs
{
  double stepSize;              
  Eigen::VectorX<double> DD;    
  double Dlambda;               
  double f;                     
  Eigen::VectorX<double> dfdDD; 
  double dfdDlambda;            
  int currentStep;              
 
  void setZero(const Concepts::EigenType auto& firstParameter) {
    stepSize = 0.0;
    DD.resizeLike(firstParameter);
    DD.setZero();
    Dlambda = 0.0;
    f       = 0.0;
    dfdDD.resizeLike(firstParameter);
    dfdDD.setZero();
    dfdDlambda  = 0.0;
    currentStep = 0;
  }
};
 
struct ArcLength
{
  template <typename NLS>
  void operator()(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) const {
    const auto idbcDelta = idbcIncrement(req, nonlinearSolver, args.Dlambda);
    const auto root = sqrt(args.DD.squaredNorm() + idbcDelta.squaredNorm() + psi * psi * args.Dlambda * args.Dlambda);
    args.f          = root - args.stepSize;
    if (not computedInitialPredictor) {
      args.dfdDD.setZero();
      args.dfdDlambda = 0.0;
    } else {
      args.dfdDD       = args.DD / root;
      const auto Dhat0 = idbcDelta / args.Dlambda; // extracting Dhat0, assuming IDBC: Dhat = lambda * Dhat0
      args.dfdDlambda  = ((Dhat0.dot(Dhat0) + psi * psi) * args.Dlambda) / root;
    }
  }
 
  template <typename NLS>
  void initialPrediction(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) {
    auto& residual               = nonlinearSolver.residual();
    double dlambda               = 1.0;
    auto idbcDelta               = idbcIncrement(req, nonlinearSolver, dlambda);
    const auto Dhat0             = idbcDelta / dlambda;
    const auto idbcForceFunction = nonlinearSolver.idbcForceFunction();
    const auto updateFunction    = nonlinearSolver.updateFunction();
    req.parameter()              = dlambda;
    decltype(auto) R             = residual(req);
    decltype(auto) K             = derivative(residual)(req);
    auto linearSolver            = createSPDLinearSolverFromNonLinearSolver(nonlinearSolver);
 
    if constexpr (Concepts::HasValidIDBCForceFunction<NLS>)
      R += idbcForceFunction(req);
 
    linearSolver.analyzePattern(K);
    linearSolver.factorize(K);
    linearSolver.solve(args.DD, -R);
 
    const auto DD2    = args.DD.squaredNorm();
    const auto Dhat02 = Dhat0.squaredNorm();
 
    psi    = sqrt(DD2 + Dhat02);
    auto s = sqrt(DD2 + Dhat02 + psi * psi * dlambda * dlambda);
 
    args.DD      = args.DD * args.stepSize / s;
    args.Dlambda = args.stepSize / s;
 
    idbcDelta *= args.Dlambda / dlambda;
 
    updateFunction(req.globalSolution(), args.DD);
    req.parameter() = args.Dlambda;
 
    // modify the globalSolution() considering inhomogeneous Dirichlet BCs
    if constexpr (Concepts::HasValidIDBCForceFunction<NLS>)
      req.syncParameterAndGlobalSolution(updateFunction);
 
    // rescaling of psi
    psi = sqrt((idbcDelta.squaredNorm() + args.DD.squaredNorm()) / (args.Dlambda * args.Dlambda));
 
    computedInitialPredictor = true;
  }
 
  template <typename NLS>
  void intermediatePrediction(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) {
    if (not computedInitialPredictor)
      DUNE_THROW(Dune::InvalidStateException, "initialPrediction has to be called before intermediatePrediction.");
    nonlinearSolver.updateFunction()(req.globalSolution(), args.DD);
    req.parameter() += args.Dlambda;
    if constexpr (Concepts::HasValidIDBCForceFunction<NLS>)
      req.syncParameterAndGlobalSolution(nonlinearSolver.updateFunction());
  }
 
  constexpr std::string name() const { return "Arc length"; }
 
private:
  double psi{0.0};
  bool computedInitialPredictor{false};
};
 
struct LoadControlSubsidiaryFunction
{
  template <typename NLS>
  void operator()(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) const {
    Impl::checkHasNoValidIDBCForceFunction<NLS>();
    args.f = args.Dlambda - args.stepSize;
    args.dfdDD.setZero();
    args.dfdDlambda = 1.0;
  }
 
  template <typename NLS>
  void initialPrediction(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) {
    Impl::checkHasNoValidIDBCForceFunction<NLS>();
    args.Dlambda             = args.stepSize;
    req.parameter()          = args.Dlambda;
    computedInitialPredictor = true;
  }
 
  template <typename NLS>
  void intermediatePrediction(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) {
    Impl::checkHasNoValidIDBCForceFunction<NLS>();
    if (not computedInitialPredictor)
      DUNE_THROW(Dune::InvalidStateException, "initialPrediction has to be called before intermediatePrediction.");
    req.parameter() += args.Dlambda;
  }
 
  constexpr std::string name() const { return "Load Control"; }
 
private:
  bool computedInitialPredictor{false};
};
 
struct DisplacementControl
{
  explicit DisplacementControl(std::vector<int> p_controlledIndices)
      : controlledIndices{std::move(p_controlledIndices)} {}
 
  template <typename NLS>
  void operator()(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) const {
    Impl::checkHasNoValidIDBCForceFunction<NLS>();
    const auto controlledDOFsNorm = args.DD(controlledIndices).norm();
    args.f                        = controlledDOFsNorm - args.stepSize;
    args.dfdDlambda               = 0.0;
    args.dfdDD.setZero();
    args.dfdDD(controlledIndices) = args.DD(controlledIndices) / controlledDOFsNorm;
  }
 
  template <typename NLS>
  void initialPrediction(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) {
    Impl::checkHasNoValidIDBCForceFunction<NLS>();
    args.DD(controlledIndices).array() = args.stepSize;
    req.globalSolution()               = args.DD;
    computedInitialPredictor           = true;
  }
 
  template <typename NLS>
  void intermediatePrediction(typename NLS::Domain& req, NLS& nonlinearSolver, SubsidiaryArgs& args) {
    Impl::checkHasNoValidIDBCForceFunction<NLS>();
    if (not computedInitialPredictor)
      DUNE_THROW(Dune::InvalidStateException, "initialPrediction has to be called before intermediatePrediction.");
    req.globalSolution() += args.DD;
  }
 
  constexpr std::string name() const { return "Displacement Control"; }
 
private:
  std::vector<int> controlledIndices; 
  bool computedInitialPredictor{false};
};
} // namespace Ikarus