From 7a832eb0294554c52454c7443924b4016f447fef Mon Sep 17 00:00:00 2001
From: bangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Mon, 18 Mar 2013 23:11:22 +0000
Subject: [PATCH] Add a heat equation solver. Remove the file with surface
 points that belongs to the previous incarnation of step-26 that was never
 finished.

git-svn-id: https://svn.dealii.org/trunk@28935 0785d39b-7218-0410-832d-ea1e28bc413d
---
 deal.II/examples/step-26/step-26.cc     |    754 +-
 deal.II/examples/step-26/surface-points | 199202 ---------------------
 2 files changed, 192 insertions(+), 199764 deletions(-)
 delete mode 100644 deal.II/examples/step-26/surface-points

diff --git a/deal.II/examples/step-26/step-26.cc b/deal.II/examples/step-26/step-26.cc
index 25ebd7f654..136d4aecb2 100644
--- a/deal.II/examples/step-26/step-26.cc
+++ b/deal.II/examples/step-26/step-26.cc
@@ -1,672 +1,302 @@
-/* Author: Wolfgang Bangerth, University of Heidelberg, 1999 */
+/* Author: Wolfgang Bangerth, Texas A&M University, 2008 */
 
 /*    $Id$       */
 /*                                                                */
-/*    Copyright (C) 1999-2007, 2011-2012 by the deal.II authors */
+/*    Copyright (C) 2013 by the deal.II authors */
 /*                                                                */
 /*    This file is subject to QPL and may not be  distributed     */
 /*    without copyright and license information. Please refer     */
 /*    to the file deal.II/doc/license.html for the  text  and     */
 /*    further information on this license.                        */
 
-// @sect3{Include files}
-
-// The first few (many?) include files have already been used in the previous
-// example, so we will not explain their meaning here again.
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.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/solver_cg.h>
+#include <deal.II/lac/precondition.h>
+#include <deal.II/lac/constraint_matrix.h>
 #include <deal.II/grid/tria.h>
-#include <deal.II/grid/tria_boundary.h>
-#include <deal.II/dofs/dof_handler.h>
 #include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
 #include <deal.II/grid/tria_accessor.h>
 #include <deal.II/grid/tria_iterator.h>
+#include <deal.II/dofs/dof_handler.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_q.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/data_out.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/solver_cg.h>
-#include <deal.II/lac/precondition.h>
 
-#include <deal.II/numerics/data_out.h>
 #include <fstream>
 #include <iostream>
 
-// This is new, however: in the previous example we got some unwanted output
-// from the linear solvers. If we want to suppress it, we have to include this
-// file and add a single line somewhere to the program (see the main()
-// function below for that):
-#include <deal.II/base/logstream.h>
-
 
-#include <algorithm>
-#include <numeric>
-
-// The last step is as in all previous programs:
 namespace Step26
 {
   using namespace dealii;
 
-  class PointCloudSurface : public StraightBoundary<3>
+  template<int dim>
+  class HeatEquation
   {
   public:
-    /**
-     * Constructor.
-     */
-    PointCloudSurface (const std::string &filename);
-
-    /**
-     * Let the new point be the
-     * arithmetic mean of the two
-     * vertices of the line.
-     *
-     * Refer to the general
-     * documentation of this class
-     * and the documentation of the
-     * base class for more
-     * information.
-     */
-    virtual Point<3>
-    get_new_point_on_line (const Triangulation<3>::line_iterator &line) const;
-
-    /**
-     * Let the new point be the
-     * arithmetic mean of the four
-     * vertices of this quad and the
-     * four midpoints of the lines,
-     * which are already created at
-     * the time of calling this
-     * function.
-     *
-     * Refer to the general
-     * documentation of this class
-     * and the documentation of the
-     * base class for more
-     * information.
-     */
-    virtual Point<3>
-    get_new_point_on_quad (const Triangulation<3>::quad_iterator &quad) const;
-
-    /**
-     * Gives <tt>n=points.size()</tt>
-     * points that splits the
-     * StraightBoundary line into
-     * $n+1$ partitions of equal
-     * lengths.
-     *
-     * Refer to the general
-     * documentation of this class
-     * and the documentation of the
-     * base class.
-     */
-    virtual void
-    get_intermediate_points_on_line (const Triangulation<3>::line_iterator &line,
-                                     std::vector<Point<3> > &points) const;
-
-    /**
-     * Gives <tt>n=points.size()=m*m</tt>
-     * points that splits the
-     * p{StraightBoundary} quad into
-     * <tt>(m+1)(m+1)</tt> subquads of equal
-     * size.
-     *
-     * Refer to the general
-     * documentation of this class
-     * and the documentation of the
-     * base class.
-     */
-    virtual void
-    get_intermediate_points_on_quad (const Triangulation<3>::quad_iterator &quad,
-                                     std::vector<Point<3> > &points) const;
-
-    /**
-     * A function that, given a point
-     * <code>p</code>, returns the closest
-     * point on the surface defined by the
-     * input file. For the time being, we
-     * simply return the closest point in the
-     * point cloud, rather than doing any
-     * sort of interpolation.
-     */
-    Point<3> closest_point (const Point<3> &p) const;
-  private:
-    std::vector<Point<3> > point_list;
-  };
-
-
-  PointCloudSurface::PointCloudSurface (const std::string &filename)
-  {
-    // first read in all the points
-    {
-      std::ifstream in (filename.c_str());
-      AssertThrow (in, ExcIO());
-
-      while (in)
-        {
-          Point<3> p;
-          in >> p;
-          point_list.push_back (p);
-        }
+    HeatEquation();
+    void run();
 
-      AssertThrow (point_list.size() > 1, ExcIO());
-    }
+  private:
+    void setup_system();
+    void solve_u();
+    void output_results() const;
 
-    // next fit a linear model through the data cloud to rectify it in a local
-    // coordinate system
-    //
-    // the first step is to move the center of mass of the points to the
-    // origin
-    {
-      const Point<3> c_o_m = std::accumulate (point_list.begin(),
-                                              point_list.end(),
-                                              Point<3>()) /
-                             point_list.size();
-      for (unsigned int i=0; i<point_list.size(); ++i)
-        point_list[i] -= c_o_m;
-    }
+    Triangulation<dim> triangulation;
+    FE_Q<dim> fe;
+    DoFHandler<dim> dof_handler;
 
-    // next do a least squares fit to the function ax+by. this leads to the
-    // following equations:
+    ConstraintMatrix constraints;
 
-    // min f(a,b) = sum_i (zi-a xi - b yi)^2 / 2
-    //
-    // f_a = sum_i (zi - a xi - b yi) xi = 0 f_b = sum_i (zi - a xi - b yi) yi
-    // = 0
-    //
-    // f_a = (sum_i zi xi) - (sum xi^2) a - (sum xi yi) b = 0 f_a = (sum_i zi
-    // yi) - (sum xi yi) a - (sum yi^2) b = 0
-    {
-      double A[2][2] = {{0,0},{0,0}};
-      double B[2] = {0,0};
+    SparsityPattern sparsity_pattern;
+    SparseMatrix<double> mass_matrix;
+    SparseMatrix<double> laplace_matrix;
+    SparseMatrix<double> matrix_u;
 
-      for (unsigned int i=0; i<point_list.size(); ++i)
-        {
-          A[0][0] += point_list[i][0] * point_list[i][0];
-          A[0][1] += point_list[i][0] * point_list[i][1];
-          A[1][1] += point_list[i][1] * point_list[i][1];
+    Vector<double> solution_u;
+    Vector<double> old_solution_u;
+    Vector<double> system_rhs;
 
-          B[0] += point_list[i][0] * point_list[i][2];
-          B[1] += point_list[i][1] * point_list[i][2];
-        }
+    double time, time_step;
+    unsigned int timestep_number;
+    const double theta;
+  };
 
-      const double det = A[0][0]*A[1][1]-2*A[0][1];
-      const double a = (A[1][1] * B[0] - A[0][1] * B[1]) / det;
-      const double b = (A[0][0] * B[1] - A[0][1] * B[0]) / det;
+  //-------------------------------------
 
+  template<int dim>
+  class RightHandSide: public Function<dim>
+  {
+  public:
+    RightHandSide() :
+    Function<dim>(),
+    period (0.2)
+    {}
 
-      // with this information, we can rotate the points so that the
-      // corresponding least-squares fit would be the x-y plane
-      const Point<2> gradient_direction
-        = Point<2>(a,b) / std::sqrt(a*a+b*b);
-      const Point<2> orthogonal_direction
-        = Point<2>(-b,a) / std::sqrt(a*a+b*b);
+    virtual double value(const Point<dim> &p,
+                         const unsigned int component = 0) const;
 
-      const double stretch_factor = std::sqrt(1.+a*a+b*b);
+  private:
+    const double period;
+  };
 
-      for (unsigned int i=0; i<point_list.size(); ++i)
-        {
-          // we can do that by, for each point, first subtract the points in
-          // the plane:
-          point_list[i][2] -= a*point_list[i][0] + b*point_list[i][1];
-
-          // we made a mistake here, though: we've shrunk the plan in the
-          // direction parallel to the gradient. we will have to correct for
-          // this:
-          const Point<2> xy (point_list[i][0],
-                             point_list[i][1]);
-          const double grad_distance = xy * gradient_direction;
-          const double orth_distance = xy * orthogonal_direction;
-
-          // we then have to stretch the points in the gradient direction. the
-          // stretch factor is defined above (zero if the original plane was
-          // already the xy plane, infinity if it was vertical)
-          const Point<2> new_xy
-            = (grad_distance * stretch_factor * gradient_direction +
-               orth_distance * orthogonal_direction);
-          point_list[i][0] = new_xy[0];
-          point_list[i][1] = new_xy[1];
-        }
-    }
-  }
+  template<int dim>
+  double RightHandSide<dim>::value(const Point<dim> &p,
+                                   const unsigned int component) const
+  {
+    Assert (component == 0, ExcInternalError());
+    Assert (dim == 2, ExcNotImplemented());
 
+    return std::cos(p[0]*numbers::PI/2) * std::cos(p[1]*numbers::PI/2);
 
-  Point<3>
-  PointCloudSurface::closest_point (const Point<3> &p) const
-  {
-    double distance = p.distance (point_list[0]);
-    Point<3> point = point_list[0];
+    const double time = this->get_time();
+    const double point_within_period = (time/period - std::floor(time/period));
 
-    for (std::vector<Point<3> >::const_iterator i=point_list.begin();
-         i != point_list.end(); ++i)
+    if ((point_within_period >= 0.0) && (point_within_period <= 0.2))
       {
-        const double d = p.distance (*i);
-        if (d < distance)
-          {
-            distance = d;
-            point = *i;
-          }
+	if ((p[0] > 0.5) && (p[1] > -0.5))
+	  return 1;
+	else
+	  return 0;
       }
-
-    return point;
+    else if ((point_within_period >= 0.5) && (point_within_period <= 0.7))
+      {
+	if ((p[0] > -0.5) && (p[1] > 0.5))
+	  return 1;
+	else
+	  return 0;
+      }
+    else
+      return 0;
   }
 
-
-  Point<3>
-  PointCloudSurface::
-  get_new_point_on_line (const Triangulation<3>::line_iterator &line) const
+  template<int dim>
+  class BoundaryValuesU: public Function<dim>
   {
-    return closest_point (StraightBoundary<3>::get_new_point_on_line (line));
-  }
-
-
+  public:
+    BoundaryValuesU() :
+      Function<dim>()
+    {
+    }
+    virtual ~BoundaryValuesU()
+    {
+    }
+    virtual double value(const Point<dim> &p,
+                         const unsigned int component = 0) const;
+  };
 
-  Point<3>
-  PointCloudSurface::
-  get_new_point_on_quad (const Triangulation<3>::quad_iterator &quad) const
+  template<int dim>
+  double BoundaryValuesU<dim>::value(const Point<dim> &/*p*/,
+                                     const unsigned int component) const
   {
-    return closest_point (StraightBoundary<3>::get_new_point_on_quad (quad));
+    Assert(component == 0, ExcInternalError());
+    return 0; // Zero-Dirichlet Boundary
   }
 
-
-
-  void
-  PointCloudSurface::
-  get_intermediate_points_on_line (const Triangulation<3>::line_iterator &line,
-                                   std::vector<Point<3> > &points) const
+  template<int dim>
+  HeatEquation<dim>::HeatEquation() :
+    fe(1), dof_handler(triangulation), time_step(1. / 1000), theta(0.5)
   {
-    StraightBoundary<3>::get_intermediate_points_on_line (line,
-                                                          points);
-    for (unsigned int i=0; i<points.size(); ++i)
-      points[i] = closest_point(points[i]);
   }
 
-
-
-  void
-  PointCloudSurface::
-  get_intermediate_points_on_quad (const Triangulation<3>::quad_iterator &quad,
-                                   std::vector<Point<3> > &points) const
+  template<int dim>
+  void HeatEquation<dim>::setup_system()
   {
-    StraightBoundary<3>::get_intermediate_points_on_quad (quad,
-                                                          points);
-    for (unsigned int i=0; i<points.size(); ++i)
-      points[i] = closest_point(points[i]);
-  }
-
-
-
-  PointCloudSurface pds("surface-points");
+    //    GridGenerator::hyper_L (triangulation);
+    GridGenerator::hyper_cube (triangulation, -1, 1);
+    triangulation.refine_global (7);
 
+    std::cout << "Number of active cells: " << triangulation.n_active_cells()
+              << std::endl;
 
+    dof_handler.distribute_dofs(fe);
 
+    std::cout << "Number of degrees of freedom: " << dof_handler.n_dofs()
+              << std::endl << std::endl;
 
+    sparsity_pattern.reinit(dof_handler.n_dofs(), dof_handler.n_dofs(),
+                            dof_handler.max_couplings_between_dofs());
+    DoFTools::make_sparsity_pattern(dof_handler, sparsity_pattern);
+    sparsity_pattern.compress();
 
+    mass_matrix.reinit(sparsity_pattern);
+    laplace_matrix.reinit(sparsity_pattern);
+    matrix_u.reinit(sparsity_pattern);
 
+    MatrixCreator::create_mass_matrix(dof_handler, QGauss<dim>(3), mass_matrix);
+    MatrixCreator::create_laplace_matrix(dof_handler, QGauss<dim>(3),
+                                         laplace_matrix);
 
+    solution_u.reinit(dof_handler.n_dofs());
+    old_solution_u.reinit(dof_handler.n_dofs());
+    system_rhs.reinit(dof_handler.n_dofs());
 
-  // @sect3{The <code>LaplaceProblem</code> class template}
+    constraints.close();
+  }
 
-  // This is again the same <code>LaplaceProblem</code> class as in the
-  // previous example. The only difference is that we have now declared it as
-  // a class with a template parameter, and the template parameter is of
-  // course the spatial dimension in which we would like to solve the Laplace
-  // equation. Of course, several of the member variables depend on this
-  // dimension as well, in particular the Triangulation class, which has to
-  // represent quadrilaterals or hexahedra, respectively. Apart from this,
-  // everything is as before.
-  template <int dim>
-  class LaplaceProblem
+  template<int dim>
+  void HeatEquation<dim>::solve_u()
   {
-  public:
-    LaplaceProblem ();
-    void run ();
-
-  private:
-    void make_grid_and_dofs ();
-    void assemble_system ();
-    void solve ();
-    void output_results () const;
-
-    Triangulation<dim>   triangulation;
-    FE_Q<dim>            fe;
-    DoFHandler<dim>      dof_handler;
-
-    SparsityPattern      sparsity_pattern;
-    SparseMatrix<double> system_matrix;
-
-    Vector<double>       solution;
-    Vector<double>       system_rhs;
-  };
-
-
-  // @sect3{Right hand side and boundary values}
-
+    SolverControl solver_control(1000, 1e-8 * system_rhs.l2_norm());
+    SolverCG<> cg(solver_control);
 
+    cg.solve(matrix_u, solution_u, system_rhs, PreconditionIdentity());
 
+    std::cout << "   u-equation: " << solver_control.last_step()
+              << " CG iterations." << std::endl;
+  }
 
-  template <int dim>
-  class BoundaryValues : public Function<dim>
+  template<int dim>
+  void HeatEquation<dim>::output_results() const
   {
-  public:
-    BoundaryValues () : Function<dim>() {}
-
-    virtual double value (const Point<dim>   &p,
-                          const unsigned int  component = 0) const;
-  };
+    DataOut<dim> data_out;
 
+    data_out.attach_dof_handler(dof_handler);
+    data_out.add_data_vector(solution_u, "U");
 
+    data_out.build_patches();
 
-  template <int dim>
-  double BoundaryValues<dim>::value (const Point<dim> &p,
-                                     const unsigned int /*component*/) const
-  {
-    return std::max(p[dim-1], -5.);
+    const std::string filename = "solution-"
+                                 + Utilities::int_to_string(timestep_number, 3) + ".vtk";
+    std::ofstream output(filename.c_str());
+    data_out.write_vtk(output);
   }
 
-
-
-  // @sect3{Implementation of the <code>LaplaceProblem</code> class}
-
-  // Next for the implementation of the class template that makes use of the
-  // functions above. As before, we will write everything as templates that
-  // have a formal parameter <code>dim</code> that we assume unknown at the
-  // time we define the template functions. Only later, the compiler will find
-  // a declaration of <code>LaplaceProblem@<2@></code> (in the
-  // <code>main</code> function, actually) and compile the entire class with
-  // <code>dim</code> replaced by 2, a process referred to as `instantiation
-  // of a template'. When doing so, it will also replace instances of
-  // <code>RightHandSide@<dim@></code> by <code>RightHandSide@<2@></code> and
-  // instantiate the latter class from the class template.
-  //
-  // In fact, the compiler will also find a declaration
-  // <code>LaplaceProblem@<3@></code> in <code>main()</code>. This will cause
-  // it to again go back to the general <code>LaplaceProblem@<dim@></code>
-  // template, replace all occurrences of <code>dim</code>, this time by 3,
-  // and compile the class a second time. Note that the two instantiations
-  // <code>LaplaceProblem@<2@></code> and <code>LaplaceProblem@<3@></code> are
-  // completely independent classes; their only common feature is that they
-  // are both instantiated from the same general template, but they are not
-  // convertible into each other, for example, and share no code (both
-  // instantiations are compiled completely independently).
-
-
-  // @sect4{LaplaceProblem::LaplaceProblem}
-
-  // After this introduction, here is the constructor of the
-  // <code>LaplaceProblem</code> class. It specifies the desired polynomial
-  // degree of the finite elements and associates the DoFHandler to the
-  // triangulation just as in the previous example program, step-3:
-  template <int dim>
-  LaplaceProblem<dim>::LaplaceProblem () :
-    fe (1),
-    dof_handler (triangulation)
-  {}
-
-
-  // @sect4{LaplaceProblem::make_grid_and_dofs}
-
-  // Grid creation is something inherently dimension dependent. However, as
-  // long as the domains are sufficiently similar in 2D or 3D, the library can
-  // abstract for you. In our case, we would like to again solve on the square
-  // [-1,1]x[-1,1] in 2D, or on the cube [-1,1]x[-1,1]x[-1,1] in 3D; both can
-  // be termed <code>hyper_cube</code>, so we may use the same function in
-  // whatever dimension we are. Of course, the functions that create a
-  // hypercube in two and three dimensions are very much different, but that
-  // is something you need not care about. Let the library handle the
-  // difficult things.
-  //
-  // Likewise, associating a degree of freedom with each vertex is something
-  // which certainly looks different in 2D and 3D, but that does not need to
-  // bother you either. This function therefore looks exactly like in the
-  // previous example, although it performs actions that in their details are
-  // quite different if <code>dim</code> happens to be 3. The only significant
-  // difference from a user's perspective is the number of cells resulting,
-  // which is much higher in three than in two space dimensions!
-  template <int dim>
-  void LaplaceProblem<dim>::make_grid_and_dofs ()
+  template<int dim>
+  void HeatEquation<dim>::run()
   {
-    GridGenerator::hyper_cube (triangulation, -30, 30);
+    setup_system();
 
-    for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
-      if (triangulation.begin()->face(f)->center()[2] > 15)
-        {
-          triangulation.begin()->face(f)->set_boundary_indicator (1);
-          for (unsigned int i=0; i<GeometryInfo<dim>::lines_per_face; ++i)
-            triangulation.begin()->face(f)->line(i)->set_boundary_indicator (1);
-          break;
-        }
-    triangulation.set_boundary (1, pds);
+    VectorTools::interpolate(dof_handler, ZeroFunction<dim>(), solution_u);
 
+    timestep_number = 0;
+    output_results();
 
-    for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
-      if (triangulation.begin()->vertex(v)[2] > 0)
-        triangulation.begin()->vertex(v)
-          = pds.closest_point (Point<3>(triangulation.begin()->vertex(v)[0],
-                                        triangulation.begin()->vertex(v)[1],
-                                        0));
+    VectorTools::interpolate(dof_handler, ZeroFunction<dim>(),
+                             old_solution_u);
 
-    for (unsigned int i=0; i<4; ++i)
+    Vector<double> tmp(solution_u.size());
+    Vector<double> forcing_terms(solution_u.size());
+
+    for (timestep_number = 1, time = time_step; time <= 0.5;
+         time += time_step, ++timestep_number)
       {
-        for (typename Triangulation<dim>::active_cell_iterator
-             cell = triangulation.begin_active();
-             cell != triangulation.end(); ++cell)
-          for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
-            if (cell->face(f)->boundary_indicator() == 1)
-              cell->set_refine_flag ();
-
-        triangulation.execute_coarsening_and_refinement ();
-
-        std::cout << "Refinement cycle " << i << std::endl
-                  << "   Number of active cells: "
-                  << triangulation.n_active_cells()
-                  << std::endl
-                  << "   Total number of cells: "
-                  << triangulation.n_cells()
+        std::cout << "Time step " << timestep_number << " at t=" << time
                   << std::endl;
 
-      }
-
-
-    dof_handler.distribute_dofs (fe);
-
-    std::cout << "   Number of degrees of freedom: "
-              << dof_handler.n_dofs()
-              << std::endl;
-
-    sparsity_pattern.reinit (dof_handler.n_dofs(),
-                             dof_handler.n_dofs(),
-                             dof_handler.max_couplings_between_dofs());
-    DoFTools::make_sparsity_pattern (dof_handler, sparsity_pattern);
-    sparsity_pattern.compress();
-
-    system_matrix.reinit (sparsity_pattern);
-
-    solution.reinit (dof_handler.n_dofs());
-    system_rhs.reinit (dof_handler.n_dofs());
-  }
-
+        mass_matrix.vmult(system_rhs, old_solution_u);
 
-  // @sect4{LaplaceProblem::assemble_system}
-
-  // Unlike in the previous example, we would now like to use a non-constant
-  // right hand side function and non-zero boundary values. Both are tasks
-  // that are readily achieved with a only a few new lines of code in the
-  // assemblage of the matrix and right hand side.
-  //
-  // More interesting, though, is the way we assemble matrix and right hand
-  // side vector dimension independently: there is simply no difference to the
-  // two-dimensional case. Since the important objects used in this function
-  // (quadrature formula, FEValues) depend on the dimension by way of a
-  // template parameter as well, they can take care of setting up properly
-  // everything for the dimension for which this function is compiled. By
-  // declaring all classes which might depend on the dimension using a
-  // template parameter, the library can make nearly all work for you and you
-  // don't have to care about most things.
-  template <int dim>
-  void LaplaceProblem<dim>::assemble_system ()
-  {
-    MatrixTools::create_laplace_matrix (dof_handler,
-                                        QGauss<dim>(2),
-                                        system_matrix);
-    system_rhs = 0;
-
-    std::map<unsigned int,double> boundary_values;
-    VectorTools::interpolate_boundary_values (dof_handler,
-                                              0,
-                                              BoundaryValues<dim>(),
-                                              boundary_values);
-    MatrixTools::apply_boundary_values (boundary_values,
-                                        system_matrix,
-                                        solution,
-                                        system_rhs);
-  }
+        laplace_matrix.vmult(tmp, old_solution_u);
+        system_rhs.add(-(1 - theta) * time_step, tmp); //I omit here a time_step
 
+        RightHandSide<dim> rhs_function;
+        rhs_function.set_time(time);
+        VectorTools::create_right_hand_side(dof_handler, QGauss<dim>(2),
+                                            rhs_function, tmp);
+        forcing_terms = tmp;
+        forcing_terms *= theta; // I omit here a time_step
 
-  // @sect4{LaplaceProblem::solve}
+        rhs_function.set_time(time - time_step);
+        VectorTools::create_right_hand_side(dof_handler, QGauss<dim>(2),
+                                            rhs_function, tmp);
 
-  // Solving the linear system of equations is something that looks almost
-  // identical in most programs. In particular, it is dimension independent,
-  // so this function is copied verbatim from the previous example.
-  template <int dim>
-  void LaplaceProblem<dim>::solve ()
-  {
-    // NEW
-    SolverControl           solver_control (dof_handler.n_dofs(),
-                                            1e-12*system_rhs.l2_norm());
-    SolverCG<>              cg (solver_control);
+        forcing_terms.add((1 - theta) * time_step, tmp);
 
-    PreconditionSSOR<> preconditioner;
-    preconditioner.initialize(system_matrix, 1.2);
-
-    cg.solve (system_matrix, solution, system_rhs,
-              preconditioner);
-  }
-
-
-  // @sect4{LaplaceProblem::output_results}
-
-  // This function also does what the respective one did in step-3. No changes
-  // here for dimension independence either.
-  //
-  // The only difference to the previous example is that we want to write
-  // output in GMV format, rather than for gnuplot (GMV is another graphics
-  // program that, contrary to gnuplot, shows data in nice colors, allows
-  // rotation of geometries with the mouse, and generates reasonable
-  // representations of 3d data; for ways to obtain it see the ReadMe file of
-  // deal.II). To write data in this format, we simply replace the
-  // <code>data_out.write_gnuplot</code> call by
-  // <code>data_out.write_gmv</code>.
-  //
-  // Since the program will run both 2d and 3d versions of the laplace solver,
-  // we use the dimension in the filename to generate distinct filenames for
-  // each run (in a better program, one would check whether `dim' can have
-  // other values than 2 or 3, but we neglect this here for the sake of
-  // brevity).
-  template <int dim>
-  void LaplaceProblem<dim>::output_results () const
-  {
-    DataOut<dim> data_out;
-
-    data_out.attach_dof_handler (dof_handler);
-    data_out.add_data_vector (solution, "solution");
-
-    data_out.build_patches ();
-
-    std::ofstream output (dim == 2 ?
-                          "solution-2d.gmv" :
-                          "solution-3d.gmv");
-    data_out.write_gmv (output);
-  }
+        system_rhs.add(time_step, forcing_terms);
 
+        {
+          BoundaryValuesU<dim> boundary_values_u_function;
+          boundary_values_u_function.set_time(time);
 
+          std::map<unsigned int, double> boundary_values;
+          VectorTools::interpolate_boundary_values(dof_handler, 0,
+                                                   boundary_values_u_function, boundary_values);
 
-  // @sect4{LaplaceProblem::run}
+          matrix_u.copy_from(mass_matrix);
+          matrix_u.add(theta * time_step, laplace_matrix); // I omit here a time_step*theta
+          MatrixTools::apply_boundary_values(boundary_values, matrix_u,
+                                             solution_u, system_rhs);
+        }
+        solve_u();
 
-  // This is the function which has the top-level control over
-  // everything. Apart from one line of additional output, it is the same as
-  // for the previous example.
-  template <int dim>
-  void LaplaceProblem<dim>::run ()
-  {
-    std::cout << "Solving problem in " << dim << " space dimensions." << std::endl;
+        output_results();
 
-    make_grid_and_dofs();
-    assemble_system ();
-    solve ();
-    output_results ();
+        old_solution_u = solution_u;
+      }
   }
 }
 
-
-// @sect3{The <code>main</code> function}
-
-// And this is the main function. It also looks mostly like in step-3, but if
-// you look at the code below, note how we first create a variable of type
-// <code>LaplaceProblem@<2@></code> (forcing the compiler to compile the class
-// template with <code>dim</code> replaced by <code>2</code>) and run a 2d
-// simulation, and then we do the whole thing over in 3d.
-//
-// In practice, this is probably not what you would do very frequently (you
-// probably either want to solve a 2d problem, or one in 3d, but not both at
-// the same time). However, it demonstrates the mechanism by which we can
-// simply change which dimension we want in a single place, and thereby force
-// the compiler to recompile the dimension independent class templates for the
-// dimension we request. The emphasis here lies on the fact that we only need
-// to change a single place. This makes it rather trivial to debug the program
-// in 2d where computations are fast, and then switch a single place to a 3 to
-// run the much more computing intensive program in 3d for `real'
-// computations.
-//
-// Each of the two blocks is enclosed in braces to make sure that the
-// <code>laplace_problem_2d</code> variable goes out of scope (and releases
-// the memory it holds) before we move on to allocate memory for the 3d
-// case. Without the additional braces, the <code>laplace_problem_2d</code>
-// variable would only be destroyed at the end of the function, i.e. after
-// running the 3d problem, and would needlessly hog memory while the 3d run
-// could actually use it.
-//
-// Finally, the first line of the function is used to suppress some output.
-// Remember that in the previous example, we had the output from the linear
-// solvers about the starting residual and the number of the iteration where
-// convergence was detected. This can be suppressed through the
-// <code>deallog.depth_console(0)</code> call.
-//
-// The rationale here is the following: the deallog (i.e. deal-log, not
-// de-allog) variable represents a stream to which some parts of the library
-// write output. It redirects this output to the console and if required to a
-// file. The output is nested in a way so that each function can use a prefix
-// string (separated by colons) for each line of output; if it calls another
-// function, that may also use its prefix which is then printed after the one
-// of the calling function. Since output from functions which are nested deep
-// below is usually not as important as top-level output, you can give the
-// deallog variable a maximal depth of nested output for output to console and
-// file. The depth zero which we gave here means that no output is written. By
-// changing it you can get more information about the innards of the library.
-int main ()
+int main()
 {
   try
     {
       using namespace dealii;
       using namespace Step26;
 
-      deallog.depth_console (0);
+      deallog.depth_console(0);
+
+      HeatEquation<2> heat_equation_solver;
+      heat_equation_solver.run();
 
-      LaplaceProblem<3> laplace_problem_3d;
-      laplace_problem_3d.run ();
     }
   catch (std::exception &exc)
     {
       std::cerr << std::endl << std::endl
                 << "----------------------------------------------------"
                 << std::endl;
-      std::cerr << "Exception on processing: " << std::endl
-                << exc.what() << std::endl
-                << "Aborting!" << std::endl
+      std::cerr << "Exception on processing: " << std::endl << exc.what()
+                << std::endl << "Aborting!" << std::endl
                 << "----------------------------------------------------"
                 << std::endl;
 
@@ -677,8 +307,8 @@ int main ()
       std::cerr << std::endl << std::endl
                 << "----------------------------------------------------"
                 << std::endl;
-      std::cerr << "Unknown exception!" << std::endl
-                << "Aborting!" << std::endl
+      std::cerr << "Unknown exception!" << std::endl << "Aborting!"
+                << std::endl
                 << "----------------------------------------------------"
                 << std::endl;
       return 1;
diff --git a/deal.II/examples/step-26/surface-points b/deal.II/examples/step-26/surface-points
deleted file mode 100644
index 06c17bc98d..0000000000
--- a/deal.II/examples/step-26/surface-points
+++ /dev/null
@@ -1,199202 +0,0 @@
-		 100.000702 64.444870 18.640993
-		 100.001732 58.902710 15.242172
-		 100.003227 61.463951 16.076944
-		 100.006111 61.650089 16.086910
-		 100.008110 57.082504 14.420845
-		 100.008537 62.520744 16.962706
-		 10.001202 56.855850 -7.629524
-		 10.001554 58.377510 -6.702730
-		 100.017540 59.961662 16.179766
-		 100.019104 61.271141 16.155931
-		 100.019402 65.486839 19.577337
-		 100.020836 65.672371 19.579966
-		 100.021027 64.623596 18.729914
-		 100.022263 67.759712 21.275852
-		 100.022972 59.083233 15.336061
-		 100.023674 57.265400 14.488837
-		 10.002565 46.178841 -11.539805
-		 100.030266 65.854836 19.618811
-		 100.031487 60.144032 16.241335
-		 10.003348 46.376587 -11.537080
-		 100.034447 64.804901 18.787405
-		 100.034851 66.712395 20.490171
-		 100.035156 60.329926 16.253040
-		 100.035728 63.752766 17.941080
-		 100.035797 61.078152 16.238670
-		 10.003754 55.872288 -7.660773
-		 100.038864 60.515800 16.265440
-		 100.040543 57.447708 14.564336
-		 100.042076 61.824642 16.249334
-		 100.042709 60.701557 16.279892
-		 100.043449 60.888432 16.278502
-		 100.045784 62.694252 17.131380
-		 10.004656 51.236549 -9.581793
-		 100.050140 59.261642 15.459518
-		 100.053658 57.631260 14.620840
-		 100.058922 64.981941 18.896219
-		 100.061073 66.887749 20.606680
-		 100.061508 62.875450 17.199224
-		 10.007089 44.035114 -12.545167
-		 100.074310 57.812305 14.713459
-		 100.074501 63.057632 17.254875
-		 100.075668 67.923332 21.517727
-		 100.076317 66.022865 19.827442
-		 100.083374 67.064568 20.704491
-		 100.087883 59.436562 15.631111
-		 100.090866 61.994549 16.472155
-		 100.094849 63.917332 18.211142
-		 100.099335 63.235420 17.365744
-		 100.101952 57.991070 14.839401
-		 100.105995 67.241211 20.804350
-		 100.115295 65.146477 19.153843
-		 10.011702 53.559151 -8.649872
-		 100.122711 62.170326 16.615950
-		 10.012673 48.515648 -10.602343
-		 100.128403 66.188332 20.063452
-		 10.012884 45.982822 -11.592372
-		 100.132256 59.609089 15.835029
-		 100.134087 58.168442 14.984985
-		 10.013704 58.184128 -6.760799
-		 100.139801 64.087044 18.414787
-		 100.140167 67.413055 20.957655
-		 100.142906 63.406101 17.565250
-		 10.014887 41.884617 -13.574464
-		 100.152702 58.349888 15.068696
-		 100.164810 62.342213 16.808329
-		 100.167046 58.532776 15.130359
-		 100.168304 59.784328 15.998121
-		 100.175049 66.355789 20.274775
-		 100.177879 64.259201 18.587055
-		 100.181488 65.307114 19.456329
-		 100.184837 58.714401 15.210201
-		 100.191704 59.963554 16.104029
-		 100.193550 67.576942 21.199200
-		 100.200775 63.571430 17.829426
-		 100.201126 64.436836 18.690355
-		 100.201767 60.147324 16.146217
-		 100.202255 60.521412 16.139502
-		 100.202278 60.334347 16.143690
-		 100.204582 60.707813 16.145515
-		 10.020597 51.042603 -9.657804
-		 100.207863 58.894363 15.313117
-		 100.207886 62.513699 17.004513
-		 100.208588 60.893494 16.160715
-		 100.211090 65.481773 19.588947
-		 100.211334 66.527336 20.436777
-		 100.212578 61.079308 16.174498
-		 100.213661 61.266121 16.174107
-		 100.213852 64.618408 18.744150
-		 100.222664 61.450199 16.211346
-		 100.226418 65.661911 19.654709
-		 100.229668 64.798683 18.814240
-		 100.230621 59.074234 15.416235
-		 10.023313 55.680271 -7.751896
-		 100.233643 62.691345 17.119911
-		 100.242561 66.700706 20.576151
-		 100.244522 62.874283 17.165791
-		 100.249741 67.739487 21.454386
-		 100.255127 59.253548 15.525524
-		 100.257378 61.625057 16.370146
-		 100.259109 63.736416 18.096378
-		 100.259888 63.055580 17.232111
-		 10.025993 48.320618 -10.667483
-		 100.261971 64.972626 18.959612
-		 100.261978 65.834084 19.814993
-		 100.264511 66.877670 20.673069
-		 10.027419 57.991074 -6.824481
-		 10.028183 53.365910 -8.728141
-		 100.285469 59.430782 15.664100
-		 100.286530 67.054581 20.770348
-		 100.293571 61.799412 16.533905
-		 100.297737 67.905190 21.671587
-		 100.300491 63.227432 17.418148
-		 10.030302 43.840439 -12.656449
-		 100.304710 66.003288 20.008574
-		 10.030633 50.650280 -9.713679
-		 100.308914 67.231293 20.868673
-		 100.312363 61.979786 16.616913
-		 10.031318 50.847610 -9.711220
-		 100.315308 63.901958 18.353388
-		 100.316589 59.607716 15.804996
-		 100.326180 65.134163 19.252838
-		 10.032937 45.788334 -11.688521
-		 100.332375 62.159595 16.706976
-		 10.033606 50.453648 -9.731759
-		 100.337791 59.787792 15.900807
-		 10.033841 41.688644 -13.666801
-		 100.349197 59.971184 15.948731
-		 100.349609 66.171486 20.211603
-		 10.035273 48.124882 -10.715206
-		 100.353600 60.156902 15.964468
-		 100.353783 64.074005 18.527214
-		 100.355919 60.343220 15.971826
-		 100.362778 62.335705 16.844276
-		 100.365723 60.527111 16.012901
-		 100.368736 67.392578 21.141171
-		 100.371986 63.387829 17.746969
-		 100.380569 60.709240 16.076942
-		 100.382980 64.249420 18.658401
-		 100.385620 65.297318 19.524466
-		 10.038827 55.487228 -7.825045
-		 100.391273 66.340820 20.400236
-		 100.393356 62.511681 16.981792
-		 100.397354 60.890511 16.152081
-		 100.398338 64.430000 18.725111
-		 100.412346 67.560310 21.338470
-		 100.413185 62.691410 17.069660
-		 100.413963 64.610344 18.793886
-		 100.414383 61.071777 16.226948
-		 100.417580 65.471024 19.668270
-		 100.419914 66.515213 20.528437
-		 100.428154 61.254124 16.285997
-		 100.428268 62.872841 17.135338
-		 100.429314 63.553230 18.009125
-		 100.440521 64.786514 18.912792
-		 100.450424 61.433376 16.386810
-		 100.450836 66.688744 20.665277
-		 100.452202 65.643532 19.823942
-		 100.459595 67.726433 21.552071
-		 100.460121 63.047966 17.280224
-		 10.046725 53.173069 -8.815616
-		 100.476738 63.722160 18.225605
-		 100.479301 61.610283 16.517199
-		 100.482414 66.861786 20.807068
-		 100.485802 64.955414 19.118967
-		 100.486633 65.816032 19.979284
-		 100.500282 61.789925 16.610022
-		 10.050298 47.930092 -10.788013
-		 100.505249 67.038269 20.908285
-		 10.050729 57.800552 -6.932127
-		 100.508743 67.891586 21.775076
-		 100.511139 61.973000 16.657358
-		 100.518394 65.989471 20.122162
-		 100.519402 63.892666 18.419939
-		 100.526924 62.154377 16.726427
-		 100.536896 67.211075 21.049841
-		 100.539734 63.205482 17.647655
-		 100.546112 65.118332 19.394560
-		 10.054816 41.492802 -13.768233
-		 100.556450 64.065178 18.587433
-		 100.557022 62.330544 16.862539
-		 10.055902 50.260883 -9.836891
-		 100.559540 66.159065 20.308157
-		 100.580254 64.242577 18.693752
-		 100.582199 62.508389 16.975050
-		 100.584984 67.377037 21.268320
-		 100.593361 66.331436 20.460648
-		 100.595100 65.285439 19.617983
-		 100.596848 64.422562 18.767702
-		 100.599976 63.369892 17.924480
-		 10.060064 45.594830 -11.816424
-		 100.602661 62.687897 17.066004
-		 100.617241 67.549377 21.413292
-		 10.062499 55.296185 -7.934549
-		 100.625099 66.504646 20.602114
-		 100.628227 64.596909 18.909344
-		 10.063089 52.979675 -8.893394
-		 100.637566 65.454918 19.811062
-		 100.640221 62.860977 17.238491
-		 100.640991 63.541233 18.110840
-		 10.065509 43.647335 -12.821613
-		 100.657967 67.718102 21.597040
-		 100.660622 66.676132 20.761944
-		 100.669029 64.767555 19.094362
-		 100.675201 65.626183 19.981592
-		 100.681999 63.712471 18.297752
-		 10.068612 57.608555 -7.014975
-		 100.693291 66.848648 20.909086
-		 100.702637 65.801338 20.104006
-		 100.706421 67.883476 21.817226
-		 10.071006 41.296379 -13.848843
-		 100.710907 63.021862 17.564184
-		 100.718437 64.934700 19.320145
-		 100.718605 63.885216 18.464123
-		 100.727142 67.020576 21.061739
-		 100.727859 65.977272 20.216726
-		 10.074036 47.736797 -10.900516
-		 100.748070 64.060532 18.597046
-		 100.758804 63.190907 17.783720
-		 100.762878 65.103668 19.522800
-		 100.764748 66.148476 20.383770
-		 100.766052 67.190308 21.237358
-		 100.774612 64.236740 18.717054
-		 10.077521 50.067905 -9.938993
-		 100.788422 67.366730 21.336634
-		 10.079432 52.786213 -8.970445
-		 100.794388 66.322449 20.516512
-		 100.803253 63.361057 17.987076
-		 100.807381 65.272423 19.725117
-		 10.080865 45.400352 -11.916655
-		 100.809898 64.409622 18.877279
-		 100.821480 67.538635 21.485559
-		 100.830070 66.494041 20.676613
-		 10.083317 51.998894 -9.007666
-		 10.083881 57.415810 -7.086842
-		 100.840202 63.533844 18.155346
-		 100.852249 64.579720 19.070475
-		 100.856773 67.709534 21.644390
-		 100.865883 66.665298 20.838100
-		 100.876511 63.706776 18.319969
-		 10.088021 41.099964 -13.932439
-		 10.088846 55.105656 -8.055913
-		 10.091293 47.542305 -10.983271
-		 100.913208 63.879433 18.487032
-		 10.092822 45.204388 -11.976561
-		 10.093253 52.198055 -9.047166
-		 100.938004 64.056465 18.598368
-		 10.094789 47.345417 -11.005172
-		 10.097180 52.593037 -9.054398
-		 10.101335 49.875271 -10.050872
-		 10.101338 52.396889 -9.078419
-		 10.101428 43.454197 -12.989997
-		 10.104673 51.806442 -9.108394
-		 10.104776 56.240906 -7.202295
-		 10.106004 43.058563 -13.023809
-		 10.106209 40.903622 -14.021354
-		 10.106443 43.256744 -13.018799
-		 10.107475 49.284637 -10.094850
-		 10.108162 49.482048 -10.092410
-		 10.108521 54.913441 -8.147561
-		 10.108848 49.679455 -10.089946
-		 10.109529 45.009094 -12.057730
-		 10.113775 47.151134 -11.096390
-		 10.119234 56.441257 -7.263066
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2.39.5