]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Implement evaluating the x-derivative at a point.
authorWolfgang Bangerth <bangerth@math.tamu.edu>
Wed, 24 Apr 2002 13:21:12 +0000 (13:21 +0000)
committerWolfgang Bangerth <bangerth@math.tamu.edu>
Wed, 24 Apr 2002 13:21:12 +0000 (13:21 +0000)
git-svn-id: https://svn.dealii.org/trunk@5727 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/examples/step-14/step-14.cc

index 084a5289d7628712e52695cc71df84a895e54646..a9274c154a808552b44fad02821df4575110d47b 100644 (file)
@@ -171,6 +171,213 @@ namespace Evaluation
   };
 
 
+                                  // @sect4{The PointXDerivativeEvaluation class}
+
+                                  // Besides the class implementing
+                                  // the evaluation of the solution
+                                  // at one point, we here provide
+                                  // one which evaluates the gradient
+                                  // at a grid point. Since in
+                                  // general the gradient of a finite
+                                  // element function is not
+                                  // continuous at a vertex, we have
+                                  // to be a little bit more careful
+                                  // here. What we do is to loop over
+                                  // all cells, even if we have found
+                                  // the point already on once cell,
+                                  // and use the mean value of the
+                                  // gradient at the vertex taken
+                                  // from all adjacent cells.
+                                  //
+                                  // Given the interface of the
+                                  // ``PointValueEvaluation'' class,
+                                  // the declaration of this class
+                                  // provides little surprise, and
+                                  // neither does the constructor:
+  template <int dim>
+  class PointXDerivativeEvaluation : public EvaluationBase<dim>
+  {
+    public:
+      PointXDerivativeEvaluation (const Point<dim>   &evaluation_point,
+                                 TableHandler       &results_table);
+      
+      virtual void operator () (const DoFHandler<dim> &dof_handler,
+                               const Vector<double>  &solution) const;
+      
+      DeclException1 (ExcEvaluationPointNotFound,
+                     Point<dim>,
+                     << "The evaluation point " << arg1
+                     << " was not found among the vertices of the present grid.");
+    private:
+      const Point<dim>  evaluation_point;
+      TableHandler     &results_table;
+  };
+
+
+  template <int dim>
+  PointXDerivativeEvaluation<dim>::
+  PointXDerivativeEvaluation (const Point<dim>   &evaluation_point,
+                             TableHandler       &results_table)
+                 :
+                 evaluation_point (evaluation_point),
+                 results_table (results_table)
+  {};
+  
+
+                                  // The more interesting things
+                                  // happen inside the function doing
+                                  // the actual evaluation:
+  template <int dim>
+  void
+  PointXDerivativeEvaluation<dim>::
+  operator () (const DoFHandler<dim> &dof_handler,
+              const Vector<double>  &solution) const 
+  {
+                                    // This time initialize the
+                                    // return value with something
+                                    // useful, since we will have to
+                                    // add up a number of
+                                    // contributions and take the
+                                    // mean value afterwards...
+    double point_derivative = 0;
+
+                                    // ...then have some objects of
+                                    // which the meaning wil become
+                                    // clear below...
+    QTrapez<dim>  vertex_quadrature;
+    FEValues<dim> fe_values (dof_handler.get_fe(),
+                            vertex_quadrature,
+                            update_gradients | update_q_points);
+    std::vector<Tensor<1,dim> >
+      solution_gradients (vertex_quadrature.n_quadrature_points);
+    
+                                    // ...and next loop over all cells
+                                    // and their vertices, and count
+                                    // how often the vertex has been
+                                    // found:
+    typename DoFHandler<dim>::active_cell_iterator
+      cell = dof_handler.begin_active(),
+      endc = dof_handler.end();
+    unsigned int evaluation_point_hits = 0;
+    for (; cell!=endc; ++cell)
+      for (unsigned int vertex=0;
+          vertex<GeometryInfo<dim>::vertices_per_cell;
+          ++vertex)
+       if (cell->vertex(vertex) == evaluation_point)
+         {
+                                            // Things are now no more
+                                            // as simple, since we
+                                            // can't get the gradient
+                                            // of the finite element
+                                            // field as before, where
+                                            // we simply had to pick
+                                            // one degree of freedom
+                                            // at a vertex.
+                                            //
+                                            // Rather, we have to
+                                            // evaluate the finite
+                                            // element field on this
+                                            // cell, and at a certain
+                                            // point. As you know,
+                                            // evaluating finite
+                                            // element fields at
+                                            // certain points is done
+                                            // through the
+                                            // ``FEValues'' class, so
+                                            // we use that. The
+                                            // question is: the
+                                            // ``FEValues'' object
+                                            // needs to be a given a
+                                            // quadrature formula and
+                                            // can then compute the
+                                            // values of finite
+                                            // element quantities at
+                                            // the quadrature
+                                            // points. Here, we don't
+                                            // want to do quadrature,
+                                            // we simply want to
+                                            // specify some points!
+                                            //
+                                            // Nevertheless, the same
+                                            // way is chosen: use a
+                                            // special quadrature
+                                            // rule with points at
+                                            // the vertices, since
+                                            // these are what we are
+                                            // interested in. The
+                                            // appropriate rule is
+                                            // the trapezoidal rule,
+                                            // so that is the reason
+                                            // why we used that one
+                                            // above.
+                                            //
+                                            // Thus: initialize the
+                                            // ``FEValues'' object on
+                                            // this cell,
+           fe_values.reinit (cell);
+                                            // and extract the
+                                            // gradients of the
+                                            // solution vector at the
+                                            // vertices:
+           fe_values.get_function_grads (solution,
+                                         solution_gradients);
+
+                                            // Now we have the
+                                            // gradients at all
+                                            // vertices, so pick out
+                                            // that one which belongs
+                                            // to the evaluation
+                                            // point (note that the
+                                            // order of vertices is
+                                            // not necessarily the
+                                            // same as that of the
+                                            // quadrature points):
+           unsigned int q_point = 0;
+           for (; q_point<solution_gradients.size(); ++q_point)
+             if (fe_values.quadrature_point(q_point) ==
+                 evaluation_point)
+               break;
+
+                                            // Check that the
+                                            // evaluation point was
+                                            // indeed found,
+           Assert (q_point < solution_gradients.size(),
+                   ExcInternalError());
+                                            // and if so take the
+                                            // x-derivative of the
+                                            // gradient there as the
+                                            // value which we are
+                                            // interested in, and
+                                            // increase the counter
+                                            // indicating how often
+                                            // we have added to that
+                                            // variable:
+           point_derivative += solution_gradients[q_point][0];
+           ++evaluation_point_hits;
+         };
+
+                                    // Now we have looped over all
+                                    // cells and vertices, so check
+                                    // whether the point was found:
+    AssertThrow (evaluation_point_hits > 0,
+                ExcEvaluationPointNotFound(evaluation_point));
+
+                                    // We have simply summed up the
+                                    // contributions of all adjacent
+                                    // cells, so we still have to
+                                    // compute the mean value. Once
+                                    // this is done, enter the result
+                                    // into the provided table:
+    point_derivative /= evaluation_point_hits;
+    results_table.add_value ("DoFs", dof_handler.n_dofs());
+    results_table.add_value ("d_x u(x_0)", point_derivative);
+
+    std::cout << "   Point x-derivative=" << point_derivative  //TODO
+             << std::endl;
+  };
+
+
+  
                                   // @sect4{The GridOutput class}
 
                                   // Since this program has a more
@@ -560,7 +767,7 @@ namespace LaplaceSolver
   void
   Solver<dim>::LinearSystem::solve (Vector<double> &solution) const
   {
-    SolverControl           solver_control (1000, 1e-16);
+    SolverControl           solver_control (10000, 1e-12); //TODO!
     PrimitiveVectorMemory<> vector_memory;
     SolverCG<>              cg (solver_control, vector_memory);
 
@@ -2728,8 +2935,8 @@ template <int dim>
 void solve_problem ()
 {
   Triangulation<dim> triangulation (Triangulation<dim>::smoothing_on_refinement);
-  const FE_Q<dim>          primal_fe(3);
-  const FE_Q<dim>          dual_fe(4);
+  const FE_Q<dim>          primal_fe(1);
+  const FE_Q<dim>          dual_fe(2);
   const QGauss4<dim>       quadrature;
   const QGauss4<dim-1>     face_quadrature;
 
@@ -2755,12 +2962,15 @@ void solve_problem ()
   TableHandler results_table;
   Evaluation::PointValueEvaluation<dim>
     postprocessor1 (Point<dim>(0.75,0.75), results_table);
+  Evaluation::PointXDerivativeEvaluation<dim>
+    postprocessor2 (Point<dim>(0.75,0.75), results_table);
   Evaluation::GridOutput<dim>
-    postprocessor2 ("grid");
+    postprocessor3 ("grid");
 
   std::list<Evaluation::EvaluationBase<dim> *> postprocessor_list;
   postprocessor_list.push_back (&postprocessor1);
-  postprocessor_list.push_back (&postprocessor2);  
+  postprocessor_list.push_back (&postprocessor2);
+  postprocessor_list.push_back (&postprocessor3);
 
   run_simulation (*solver, postprocessor_list);
 

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