/* ---------------------------------------------------------------------
 *
 * Copyright (C) 1999 - 2014 by the deal.II authors
 *
 * This file is part of the deal.II library.
 *
 * The deal.II library is free software; you can use it, redistribute
 * it, and/or modify it under the terms of the GNU Lesser General
 * Public License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 * The full text of the license can be found in the file LICENSE at
 * the top level of the deal.II distribution.
 *
 * ---------------------------------------------------------------------

 *
 * Authors: Wolfgang Bangerth, 1999,
 *          Guido Kanschat, 2011
 */



#include <deal.II/grid/tria.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/grid/grid_generator.h>

#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_accessor.h>

#include <deal.II/fe/fe_q.h>

#include <deal.II/dofs/dof_tools.h>

#include <deal.II/fe/fe_values.h>
#include <deal.II/base/quadrature_lib.h>

#include <deal.II/base/function.h>
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/matrix_tools.h>

#include <deal.II/lac/vector.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/compressed_sparsity_pattern.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/precondition.h>

#include <deal.II/numerics/data_out.h>
#include <fstream>
#include <iostream>

using namespace dealii;



class Step3
{
public:
  Step3 ();

  void run ();


private:
  void make_grid ();
  void setup_system ();
  void assemble_system ();
  void solve ();
  void output_results () const;

  Triangulation<2>     triangulation;
  FE_Q<2>              fe;
  DoFHandler<2>        dof_handler;

  SparsityPattern      sparsity_pattern;
  SparseMatrix<double> system_matrix;

  Vector<double>       solution;
  Vector<double>       system_rhs;
};


Step3::Step3 ()
  :
  fe (1),
  dof_handler (triangulation)
{}

template <int dim>
class RightHandSide : public Function<dim>
{
public:
  RightHandSide () : Function<dim>() {}

  virtual double value (const Point<dim>   &p,
                        const unsigned int  component = 0) const;
};



template <int dim>
class BoundaryValues : public Function<dim>
{
public:
  BoundaryValues () : Function<dim>() {}

  virtual double value (const Point<dim>   &p,
                        const unsigned int  component = 0) const;
};

template <int dim>
double RightHandSide<dim>::value (const Point<dim> &p,
                                  const unsigned int /*component*/) const
{
  double return_value = 0.0;
//  for (unsigned int i=0; i<dim; ++i)
    return_value =-2*p(1);//+= 4.0 * std::pow(p(i), 4.0);

  return return_value;
}


template <int dim>
double BoundaryValues<dim>::value (const Point<dim> &p,
                                   const unsigned int /*component*/) const
{
  return p(0)*p(0)*p(1);//p.square();
}


void Step3::make_grid ()
{
 // GridGenerator::hyper_cube (triangulation, -1, 1);
    GridGenerator::hyper_L (triangulation, -1, 1);
  triangulation.refine_global (5);

  std::cout << "Number of active cells: "
            << triangulation.n_active_cells()
            << std::endl;
}




void Step3::setup_system ()
{
  dof_handler.distribute_dofs (fe);
  std::cout << "Number of degrees of freedom: "
            << dof_handler.n_dofs()
            << std::endl;

  CompressedSparsityPattern c_sparsity(dof_handler.n_dofs());
  DoFTools::make_sparsity_pattern (dof_handler, c_sparsity);
  sparsity_pattern.copy_from(c_sparsity);

  system_matrix.reinit (sparsity_pattern);

  solution.reinit (dof_handler.n_dofs());
  system_rhs.reinit (dof_handler.n_dofs());
}



void Step3::assemble_system ()
{
  QGauss<2>  quadrature_formula(2);
  
  const RightHandSide<2> right_hand_side;
  
  FEValues<2> fe_values (fe, quadrature_formula,
                         update_values | update_gradients 
						 | update_quadrature_points 
						 | update_JxW_values);

  const unsigned int   dofs_per_cell = fe.dofs_per_cell;
  const unsigned int   n_q_points    = quadrature_formula.size();

  FullMatrix<double>   cell_matrix (dofs_per_cell, dofs_per_cell);
  Vector<double>       cell_rhs (dofs_per_cell);

  std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);

  DoFHandler<2>::active_cell_iterator
  cell = dof_handler.begin_active(),
  endc = dof_handler.end();
  for (; cell!=endc; ++cell)
    {
      fe_values.reinit (cell);

      cell_matrix = 0;
      cell_rhs = 0;

      for (unsigned int q_index=0; q_index<n_q_points; ++q_index)
        {
          for (unsigned int i=0; i<dofs_per_cell; ++i)
            for (unsigned int j=0; j<dofs_per_cell; ++j)
              cell_matrix(i,j) += (fe_values.shape_grad (i, q_index) *
                                   fe_values.shape_grad (j, q_index) *
                                   fe_values.JxW (q_index));

          for (unsigned int i=0; i<dofs_per_cell; ++i)
            cell_rhs(i) += (fe_values.shape_value (i, q_index) *
                            right_hand_side.value(fe_values.quadrature_point (q_index)) * //1 *
                            fe_values.JxW (q_index));
        }
      cell->get_dof_indices (local_dof_indices);

      for (unsigned int i=0; i<dofs_per_cell; ++i)
        for (unsigned int j=0; j<dofs_per_cell; ++j)
          system_matrix.add (local_dof_indices[i],
                             local_dof_indices[j],
                             cell_matrix(i,j));

      for (unsigned int i=0; i<dofs_per_cell; ++i)
        system_rhs(local_dof_indices[i]) += cell_rhs(i);
    }


  std::map<types::global_dof_index,double> boundary_values;
  VectorTools::interpolate_boundary_values (dof_handler,
                                            0,
                                            BoundaryValues<2>(),
                                            boundary_values);
  MatrixTools::apply_boundary_values (boundary_values,
                                      system_matrix,
                                      solution,
                                      system_rhs);
}



void Step3::solve ()
{
  SolverControl           solver_control (1000, 1e-12);
  SolverCG<>              solver (solver_control);

  solver.solve (system_matrix, solution, system_rhs,
                PreconditionIdentity());
}



void Step3::output_results () const
{
  DataOut<2> data_out;
  data_out.attach_dof_handler (dof_handler);
  data_out.add_data_vector (solution, "solution");
  data_out.build_patches ();

  std::ofstream output ("solution.svg");
  data_out.write_gnuplot (output);
}



void Step3::run ()
{
  make_grid ();
  setup_system ();
  assemble_system ();
  solve ();
  output_results ();
}



int main ()
{
  Step3 laplace_problem;
  laplace_problem.run ();

  return 0;
}