pcg.hpp

// FEAT3: Finite Element Analysis Toolbox, Version 3
// Copyright (C) 2010 by Stefan Turek & the FEAT group
// FEAT3 is released under the GNU General Public License version 3,
// see the file 'copyright.txt' in the top level directory for details.
 
#pragma once
 
// includes, FEAT
#include <kernel/solver/iterative.hpp>
 
namespace FEAT
{
  namespace Solver
  {
    template<typename Matrix_, typename Filter_>
    class PCG :
      public PreconditionedIterativeSolver<typename Matrix_::VectorTypeR>
    {
    public:
      typedef Matrix_ MatrixType;
      typedef Filter_ FilterType;
      typedef typename MatrixType::VectorTypeR VectorType;
      typedef typename MatrixType::DataType DataType;
      typedef PreconditionedIterativeSolver<VectorType> BaseClass;
      typedef SolverBase<VectorType> PrecondType;
 
    protected:
      const MatrixType& _system_matrix;
      const FilterType& _system_filter;
      VectorType _vec_r;
      VectorType _vec_p;
      VectorType _vec_t;
 
    public:
      explicit PCG(const MatrixType& matrix, const FilterType& filter,
        std::shared_ptr<PrecondType> precond = nullptr) :
        BaseClass("PCG", precond),
        _system_matrix(matrix),
        _system_filter(filter)
      {
        // set communicator by system matrix
        this->_set_comm_by_matrix(matrix);
      }
 
      explicit PCG(const String& section_name, const PropertyMap* section,
      const MatrixType& matrix, const FilterType& filter, std::shared_ptr<PrecondType> precond = nullptr) :
        BaseClass("PCG", section_name, section, precond),
        _system_matrix(matrix),
        _system_filter(filter)
      {
        // set communicator by system matrix
        this->_set_comm_by_matrix(matrix);
      }
 
      virtual String name() const override
      {
        return "PCG";
      }
 
      virtual void init_symbolic() override
      {
        BaseClass::init_symbolic();
        // create three temporary vectors
        _vec_r = this->_system_matrix.create_vector_r();
        _vec_p = this->_system_matrix.create_vector_r();
        _vec_t = this->_system_matrix.create_vector_r();
      }
 
      virtual void done_symbolic() override
      {
        this->_vec_t.clear();
        this->_vec_p.clear();
        this->_vec_r.clear();
        BaseClass::done_symbolic();
      }
 
      virtual Status apply(VectorType& vec_cor, const VectorType& vec_def) override
      {
        // save defect
        this->_vec_r.copy(vec_def);
 
        // clear solution vector
        vec_cor.format();
 
        // apply solver
        this->_status = _apply_intern(vec_cor);
 
        // plot summary
        this->plot_summary();
 
        // return status
        return this->_status;
      }
 
      virtual Status correct(VectorType& vec_sol, const VectorType& vec_rhs) override
      {
        // compute defect
        this->_system_matrix.apply(this->_vec_r, vec_sol, vec_rhs, -DataType(1));
        this->_system_filter.filter_def(this->_vec_r);
 
        // apply solver
        this->_status = _apply_intern(vec_sol);
 
        // plot summary
        this->plot_summary();
 
        // return status
        return this->_status;
      }
 
    protected:
      virtual Status _apply_intern(VectorType& vec_sol)
      {
        IterationStats pre_iter(*this);
        Statistics::add_solver_expression(std::make_shared<ExpressionStartSolve>(this->name()));
 
        const MatrixType& matrix(this->_system_matrix);
        const FilterType& filter(this->_system_filter);
        VectorType& vec_r(this->_vec_r);
        VectorType& vec_p(this->_vec_p);
        // Note: q and z are temporary vectors whose usage does
        // not overlap, so we use the same vector for them
        VectorType& vec_q(this->_vec_t);
        VectorType& vec_z(this->_vec_t);
 
        // Note:
        // In the algorithm below, the following relations hold:
        // q[k] = A * p[k]
        // z[k] = M^{-1} * r[k]
 
        // set initial defect:
        // r[0] := b - A*x[0]
        Status status = this->_set_initial_defect(vec_r, vec_sol);
        if(status != Status::progress)
        {
          pre_iter.destroy();
          Statistics::add_solver_expression(std::make_shared<ExpressionEndSolve>(this->name(), status, this->get_num_iter()));
          return status;
        }
 
        // apply preconditioner to defect vector
        // p[0] := M^{-1} * r[0]
        if(!this->_apply_precond(vec_p, vec_r, filter))
        {
          pre_iter.destroy();
          Statistics::add_solver_expression(std::make_shared<ExpressionEndSolve>(this->name(), Status::aborted, this->get_num_iter()));
          return Status::aborted;
        }
 
        // compute initial gamma:
        // gamma[0] := < r[0], p[0] >
        DataType gamma = vec_r.dot(vec_p);
 
        pre_iter.destroy();
 
        // start iterating
        while(status == Status::progress)
        {
          IterationStats stat(*this);
 
          // q[k] := A*p[k]
          matrix.apply(vec_q, vec_p);
          filter.filter_def(vec_q);
 
          // compute alpha
          // alpha[k] := gamma[k] / < q[k], p[k] >
          DataType alpha = gamma / vec_q.dot(vec_p);
 
          // update solution vector:
          // x[k+1] := x[k] + alpha[k] * p[k]
          vec_sol.axpy(vec_p, alpha);
 
          // update defect vector:
          // r[k+1] := r[k] - alpha[k] * q[k]
          vec_r.axpy(vec_q, -alpha);
 
          // compute defect norm
          status = this->_set_new_defect(vec_r, vec_sol);
          if(status != Status::progress)
          {
            stat.destroy();
            Statistics::add_solver_expression(std::make_shared<ExpressionEndSolve>(this->name(), status, this->get_num_iter()));
            return status;
          }
 
          // apply preconditioner
          // z[k+1] := M^{-1} * r[k+1]
          if(!this->_apply_precond(vec_z, vec_r, filter))
          {
            stat.destroy();
            Statistics::add_solver_expression(std::make_shared<ExpressionEndSolve>(this->name(), Status::aborted, this->get_num_iter()));
            return Status::aborted;
          }
 
          // compute new gamma:
          // gamma[k+1] := < r[k+1] , z[k+1] >
          DataType gamma2 = gamma;
          gamma = vec_r.dot(vec_z);
 
          // compute beta:
          // beta[k] := gamma[k+1] / gamma[k]
          DataType beta = gamma / gamma2;
 
          // update direction vector:
          // p[k+1] := z[k+1] + beta[k] * p[k]
          vec_p.scale(vec_p, beta);
          vec_p.axpy(vec_z); 
        }
 
        // we should never reach this point...
        Statistics::add_solver_expression(std::make_shared<ExpressionEndSolve>(this->name(), Status::undefined, this->get_num_iter()));
        return Status::undefined;
      }
    }; // class PCG<...>
 
    template<typename Matrix_, typename Filter_>
    inline std::shared_ptr<PCG<Matrix_, Filter_>> new_pcg(
      const Matrix_& matrix, const Filter_& filter,
      std::shared_ptr<SolverBase<typename Matrix_::VectorTypeL>> precond = nullptr)
    {
      return std::make_shared<PCG<Matrix_, Filter_>>(matrix, filter, precond);
    }
 
    template<typename Matrix_, typename Filter_>
    inline std::shared_ptr<PCG<Matrix_, Filter_>> new_pcg(
      const String& section_name, const PropertyMap* section,
      const Matrix_& matrix, const Filter_& filter,
      std::shared_ptr<SolverBase<typename Matrix_::VectorTypeL>> precond = nullptr)
    {
      return std::make_shared<PCG<Matrix_, Filter_>>(section_name, section, matrix, filter, precond);
    }
  } // namespace Solver
} // namespace FEAT