operator_coupled.h

/*  ______________________________________________________________________
 *
 *  ExaDG - High-Order Discontinuous Galerkin for the Exa-Scale
 *
 *  Copyright (C) 2021 by the ExaDG authors
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <https://www.gnu.org/licenses/>.
 *  ______________________________________________________________________
 */
 
#ifndef EXADG_INCOMPRESSIBLE_NAVIER_STOKES_SPATIAL_DISCRETIZATION_OPERATOR_COUPLED_H_
#define EXADG_INCOMPRESSIBLE_NAVIER_STOKES_SPATIAL_DISCRETIZATION_OPERATOR_COUPLED_H_
 
// ExaDG
#include <exadg/convection_diffusion/spatial_discretization/operators/combined_operator.h>
#include <exadg/incompressible_navier_stokes/spatial_discretization/spatial_operator_base.h>
#include <exadg/solvers_and_preconditioners/newton/newton_solver.h>
 
namespace ExaDG
{
namespace IncNS
{
// forward declaration
template<int dim, typename Number>
class OperatorCoupled;
 
template<int dim, typename Number>
class NonlinearOperatorCoupled
{
private:
  typedef dealii::LinearAlgebra::distributed::Vector<Number>      VectorType;
  typedef dealii::LinearAlgebra::distributed::BlockVector<Number> BlockVectorType;
 
  typedef OperatorCoupled<dim, Number> PDEOperator;
 
public:
  NonlinearOperatorCoupled()
    : pde_operator(nullptr), rhs_vector(nullptr), time(0.0), scaling_factor_mass(1.0)
  {
  }
 
  void
  initialize(PDEOperator const & pde_operator)
  {
    this->pde_operator = &pde_operator;
  }
 
  void
  update(VectorType const & rhs_vector, double const & time, double const & scaling_factor)
  {
    this->rhs_vector          = &rhs_vector;
    this->time                = time;
    this->scaling_factor_mass = scaling_factor;
  }
 
  /*
   * The implementation of the Newton solver requires a function called
   * 'evaluate_residual'.
   */
  void
  evaluate_residual(BlockVectorType & dst, BlockVectorType const & src) const
  {
    pde_operator->evaluate_nonlinear_residual(dst, src, rhs_vector, time, scaling_factor_mass);
  }
 
private:
  PDEOperator const * pde_operator;
 
  VectorType const * rhs_vector;
  double             time;
  double             scaling_factor_mass;
};
 
template<int dim, typename Number>
class LinearOperatorCoupled : public dealii::EnableObserverPointer
{
private:
  typedef dealii::LinearAlgebra::distributed::BlockVector<Number> BlockVectorType;
 
  typedef OperatorCoupled<dim, Number> PDEOperator;
 
public:
  LinearOperatorCoupled() : dealii::EnableObserverPointer(), pde_operator(nullptr)
  {
  }
 
  void
  initialize(PDEOperator const & pde_operator)
  {
    this->pde_operator = &pde_operator;
  }
 
  /*
   * The implementation of the Newton solver requires a function called
   * 'set_solution_linearization'.
   */
  void
  set_solution_linearization(BlockVectorType const & solution_linearization) const
  {
    pde_operator->set_velocity_ptr(solution_linearization.block(0));
  }
 
 
  /*
   * The implementation of linear solvers in deal.ii requires that a function called 'vmult' is
   * provided.
   */
  void
  vmult(BlockVectorType & dst, BlockVectorType const & src) const
  {
    pde_operator->apply_linearized_problem(dst, src);
  }
 
private:
  PDEOperator const * pde_operator;
};
 
template<int dim, typename Number>
class BlockPreconditioner
{
private:
  typedef dealii::LinearAlgebra::distributed::BlockVector<Number> BlockVectorType;
 
  typedef OperatorCoupled<dim, Number> PDEOperator;
 
public:
  BlockPreconditioner() : update_needed(true), pde_operator(nullptr)
  {
  }
 
  void
  initialize(PDEOperator * pde_operator_in)
  {
    pde_operator = pde_operator_in;
  }
 
  void
  update()
  {
    pde_operator->update_block_preconditioner();
 
    this->update_needed = false;
  }
 
  bool
  needs_update() const
  {
    return update_needed;
  }
 
  void
  vmult(BlockVectorType & dst, BlockVectorType const & src) const
  {
    AssertThrow(this->update_needed == false,
                dealii::ExcMessage(
                  "BlockPreconditioner can not be applied because it is not up-to-date."));
 
    pde_operator->apply_block_preconditioner(dst, src);
  }
 
  std::shared_ptr<TimerTree>
  get_timings() const
  {
    AssertThrow(false,
                dealii::ExcMessage(
                  "Function get_timings() is not implemented for BlockPreconditioner."));
 
    return std::make_shared<TimerTree>();
  }
 
private:
  bool update_needed;
 
  PDEOperator * pde_operator;
};
 
template<int dim, typename Number = double>
class OperatorCoupled : public SpatialOperatorBase<dim, Number>
{
private:
  typedef SpatialOperatorBase<dim, Number> Base;
  typedef OperatorCoupled<dim, Number>     This;
 
  typedef typename Base::MultigridPoisson MultigridPoisson;
 
  typedef typename Base::VectorType VectorType;
 
  typedef typename Base::BlockVectorType BlockVectorType;
 
public:
  /*
   * Constructor.
   */
  OperatorCoupled(std::shared_ptr<Grid<dim> const>                      grid,
                  std::shared_ptr<dealii::Mapping<dim> const>           mapping,
                  std::shared_ptr<MultigridMappings<dim, Number>> const multigrid_mappings,
                  std::shared_ptr<BoundaryDescriptor<dim> const>        boundary_descriptor,
                  std::shared_ptr<FieldFunctions<dim> const>            field_functions,
                  Parameters const &                                    parameters,
                  std::string const &                                   field,
                  MPI_Comm const &                                      mpi_comm);
 
  /*
   * Destructor.
   */
  virtual ~OperatorCoupled();
 
private:
  void
  setup_derived() final;
 
  void
  setup_preconditioners_and_solvers() final;
 
public:
  /*
   *  Update divergence penalty operator by recalculating the penalty parameter
   *  which depends on the current velocity field
   */
  void
  update_divergence_penalty_operator(VectorType const & velocity);
 
  /*
   *  Update continuity penalty operator by recalculating the penalty parameter
   *  which depends on the current velocity field
   */
  void
  update_continuity_penalty_operator(VectorType const & velocity);
 
  /*
   * Setters and getters.
   */
 
  /*
   *  This function sets the variable scaling_factor_continuity, and also the related scaling factor
   * for the pressure gradient operator.
   */
  void
  set_scaling_factor_continuity(double const scaling_factor);
 
  /*
   * Stokes equations or convective term treated explicitly: solve linear system of equations
   */
 
  /*
   * This function solves the linear Stokes problem (Stokes equations or Navier-Stokes
   * equations with an explicit treatment of the convective term). The parameter
   * scaling_factor_mass has to be specified for unsteady problem and
   * can be omitted for steady problems.
   */
  unsigned int
  solve_linear_problem(BlockVectorType &       dst,
                       BlockVectorType const & src,
                       VectorType const &      transport_velocity,
                       bool const &            update_preconditioner,
                       double const &          scaling_factor_mass = 1.0);
 
  /*
   * Convective term treated implicitly: solve non-linear system of equations
   */
 
  /*
   * This function solves the nonlinear problem.
   */
  std::tuple<unsigned int, unsigned int>
  solve_nonlinear_problem(BlockVectorType &  dst,
                          VectorType const & rhs_vector,
                          bool const &       update_preconditioner,
                          double const &     time                = 0.0,
                          double const &     scaling_factor_mass = 1.0);
 
 
  /*
   * This function evaluates the nonlinear residual.
   */
  void
  evaluate_nonlinear_residual(BlockVectorType &       dst,
                              BlockVectorType const & src,
                              VectorType const *      rhs_vector,
                              double const &          time,
                              double const &          scaling_factor_mass) const;
 
  /*
   * This function evaluates the nonlinear residual of the steady Navier-Stokes equations.
   * This function has to be implemented separately (for example, the convective term will be
   * evaluated in case of the Navier-Stokes equations and the time-derivative term is never
   * evaluated).
   */
  void
  evaluate_nonlinear_residual_steady(BlockVectorType &       dst,
                                     BlockVectorType const & src,
                                     double const &          time) const;
 
  /*
   * This function calculates the matrix-vector product for the linear(ized) problem.
   */
  void
  apply_linearized_problem(BlockVectorType & dst, BlockVectorType const & src) const;
 
  /*
   * This function calculates the right-hand side of the steady Stokes problem, or unsteady Stokes
   * problem, or unsteady Navier-Stokes problem with explicit treatment of the convective term. The
   * parameter 'time' has to be specified for unsteady problems and can be omitted for steady
   * problems.
   */
  void
  rhs_linear_problem(BlockVectorType &  dst,
                     VectorType const & transport_velocity,
                     double const &     time = 0.0) const;
 
  /*
   * Block preconditioner
   */
  void
  update_block_preconditioner();
 
  void
  apply_block_preconditioner(BlockVectorType & dst, BlockVectorType const & src) const;
 
private:
  void
  setup_solver_coupled();
 
  /*
   * Block preconditioner
   */
  void
  setup_block_preconditioner();
 
  void
  initialize_vectors();
 
  void
  initialize_preconditioner_velocity_block();
 
  void
  setup_multigrid_preconditioner_momentum();
 
  void
  setup_iterative_solver_momentum();
 
  void
  initialize_preconditioner_pressure_block();
 
  void
  setup_multigrid_preconditioner_schur_complement();
 
  void
  setup_iterative_solver_schur_complement();
 
  void
  setup_pressure_convection_diffusion_operator();
 
  void
  apply_preconditioner_velocity_block(VectorType & dst, VectorType const & src) const;
 
  void
  apply_preconditioner_pressure_block(VectorType & dst, VectorType const & src) const;
 
  void
  apply_inverse_negative_laplace_operator(VectorType & dst, VectorType const & src) const;
 
  /*
   * Newton-Krylov solver for (non-)linear problem
   */
 
  // temporary vector needed to evaluate both the nonlinear residual and the linearized operator
  VectorType mutable temp_vector;
 
  double scaling_factor_continuity;
 
  // Nonlinear operator
  NonlinearOperatorCoupled<dim, Number> nonlinear_operator;
 
  // Newton solver
  std::shared_ptr<Newton::Solver<BlockVectorType,
                                 NonlinearOperatorCoupled<dim, Number>,
                                 LinearOperatorCoupled<dim, Number>,
                                 Krylov::SolverBase<BlockVectorType>>>
    newton_solver;
 
  // Linear operator
  LinearOperatorCoupled<dim, Number> linear_operator;
 
  // Linear solver
  std::shared_ptr<Krylov::SolverBase<BlockVectorType>> linear_solver;
 
  /*
   * Block preconditioner for linear(ized) problem
   */
  typedef BlockPreconditioner<dim, Number> Preconditioner;
  Preconditioner                           block_preconditioner;
 
  // preconditioner velocity/momentum block
  std::shared_ptr<PreconditionerBase<Number>> preconditioner_momentum;
 
  std::shared_ptr<Krylov::SolverBase<VectorType>> solver_velocity_block;
 
  // preconditioner pressure/Schur-complement block
  std::shared_ptr<PreconditionerBase<Number>> multigrid_preconditioner_schur_complement;
  std::shared_ptr<PreconditionerBase<Number>> inverse_mass_preconditioner_schur_complement;
 
  std::shared_ptr<ConvDiff::CombinedOperator<dim, Number>> pressure_conv_diff_operator;
 
  std::shared_ptr<Poisson::LaplaceOperator<dim, Number, 1>> laplace_operator;
 
  std::shared_ptr<Krylov::SolverBase<VectorType>> solver_pressure_block;
 
  // temporary vectors that are necessary when using preconditioners of block-triangular type
  VectorType mutable vec_tmp_pressure;
  VectorType mutable vec_tmp_velocity, vec_tmp_velocity_2;
 
  // temporary vectors that are necessary when applying the Schur-complement preconditioner (scp)
  VectorType mutable tmp_scp_pressure;
  VectorType mutable tmp_scp_velocity, tmp_scp_velocity_2;
};
 
} // namespace IncNS
} // namespace ExaDG
 
#endif /* EXADG_INCOMPRESSIBLE_NAVIER_STOKES_SPATIAL_DISCRETIZATION_OPERATOR_COUPLED_H_ \
        */