]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Introduce assemble_boundary_term function. New subsections.
authorRalf Hartmann <Ralf.Hartmann@dlr.de>
Tue, 20 Nov 2001 17:55:56 +0000 (17:55 +0000)
committerRalf Hartmann <Ralf.Hartmann@dlr.de>
Tue, 20 Nov 2001 17:55:56 +0000 (17:55 +0000)
git-svn-id: https://svn.dealii.org/trunk@5221 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/examples/step-12/step-12.cc

index 5bea1272c8d40f0ba7f203092fd941c2b92f510e..c34c8ef336ab0c7f7a227fdd8beb101937cabe2f 100644 (file)
@@ -185,6 +185,8 @@ void BoundaryValues<dim>::value_list(const std::vector<Point<dim> > &points,
     }
 }
 
+                                // @sect3{Class: DGTransportEquation}
+                                //
                                 // Next we define the equation-
                                 // dependent and DG-method-dependent
                                 // class ``DGTransportEquation''. Its
@@ -206,25 +208,32 @@ class DGTransportEquation
                            FullMatrix<double> &u_v_matrix,
                            Vector<double> &cell_vector);
     
+    void assemble_boundary_term(const FEFaceValues<dim>& fe_v,
+                               FullMatrix<double> &u_v_matrix,
+                               Vector<double> &cell_vector);
+    
     void assemble_face_term1(const FEFaceValuesBase<dim>& fe_v,
                             const FEFaceValuesBase<dim>& fe_v_neighbor,
                             FullMatrix<double> &u_v_matrix,
-                            FullMatrix<double> &un_v_matrix,
-                            Vector<double> &cell_vector);
+                            FullMatrix<double> &un_v_matrix);
 
     void assemble_face_term2(const FEFaceValuesBase<dim>& fe_v,
                             const FEFaceValuesBase<dim>& fe_v_neighbor,
                             FullMatrix<double> &u_v_matrix,
                             FullMatrix<double> &un_v_matrix,
                             FullMatrix<double> &u_vn_matrix,
-                            FullMatrix<double> &un_vn_matrix,
-                            Vector<double> &cell_vector);
+                            FullMatrix<double> &un_vn_matrix);
   private:
     Beta<dim> beta_function;
     RHS<dim> rhs_function;
     BoundaryValues<dim> boundary_function;
 };
 
+                                // @sect4{Function: assemble_cell_term}
+                                //
+                                // The ``assemble_cell_term''
+                                // function assembles the cell terms
+                                // of the discretization.
                                 // ``u_v_matrix'' is a cell matrix,
                                 // i.e. for a DG method of degree 1,
                                 // it is of size 4 times 4, and
@@ -240,7 +249,7 @@ void DGTransportEquation<dim>::assemble_cell_term(
   Vector<double> &cell_vector)
 {
                                   // First we ask ``fe_v'' for the
-                                  // shape grads, shape values and
+                                  // shape gradients, shape values and
                                   // quadrature weights,
   const vector<vector<Tensor<1,2> > > &grad_v = fe_v.get_shape_grads ();
   const FullMatrix<double> &v = fe_v.get_shape_values ();
@@ -256,11 +265,9 @@ void DGTransportEquation<dim>::assemble_cell_term(
   rhs_function.value_list (fe_v.get_quadrature_points(), rhs);
   
                                   // and the cell matrix and cell
-                                  // vector are assembled as in
-                                  // previous tutorial steps.  Here,
-                                  // the terms $-(u,\beta\cdot\nabla
-                                  // v)_K$ and $(f,v)_K$ are
-                                  // assembled.
+                                  // vector are assembled due to the
+                                  // terms $-(u,\beta\cdot\nabla
+                                  // v)_K$ and $(f,v)_K$.
   for (unsigned int point=0; point<fe_v.n_quadrature_points; ++point)
     for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i) 
       {
@@ -273,14 +280,83 @@ void DGTransportEquation<dim>::assemble_cell_term(
       }
 }
 
+                                // @sect4{Function: assemble_boundary_term}
+                                //
+                                // The ``assemble_boundary_term''
+                                // function assembles the face terms
+                                // at boundary faces.  When this
+                                // function is invoked, ``fe_v'' is
+                                // already reinited with the current
+                                // cell and current face. Hence it
+                                // provides the shape values on that
+                                // boundary face.
+template <int dim>
+void DGTransportEquation<dim>::assemble_boundary_term(
+  const FEFaceValues<dim>& fe_v,    
+  FullMatrix<double> &u_v_matrix,
+  Vector<double> &cell_vector)
+{
+                                  // First we check whether the
+                                  // current face is really at the
+                                  // boundary.
+  Assert(fe_v.get_face()->at_boundary(), ExcInternalError());
+  
+                                  // Again, as in the previous
+                                  // function, we ask the FEValues
+                                  // object for the shape values and
+                                  // the quadrature weights
+  const FullMatrix<double> &v = fe_v.get_shape_values ();
+  const vector<double> &JxW = fe_v.get_JxW_values ();
+                                  // but here also for the normals.
+  const vector<Point<dim> > &normals = fe_v.get_normal_vectors ();
+
+                                  // We evaluate the flow field
+                                  // and the boundary values at the
+                                  // quadrature points.
+  vector<Point<dim> > beta (fe_v.n_quadrature_points);
+  vector<double> g(fe_v.n_quadrature_points);
+  
+  beta_function.value_list (fe_v.get_quadrature_points(), beta);
+  boundary_function.value_list (fe_v.get_quadrature_points(), g);
+
+                                  // Then we assemble cell vector and
+                                  // cell matrix according to the DG
+                                  // method given in the
+                                  // introduction.
+  for (unsigned int point=0; point<fe_v.n_quadrature_points; ++point)
+    {
+      double beta_n=beta[point] * normals[point];      
+      if (beta_n>0)
+                                        // We assemble the term
+                                        // $(\beta\cdot n
+                                        // u,v)_{\partial K_+}$,
+       for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
+         for (unsigned int j=0; j<fe_v.dofs_per_cell; ++j)
+           u_v_matrix(i,j) += beta_n *
+                              v(j,point) *
+                              v(i,point) *
+                              JxW[point];
+      else
+                                        // and the term $(\beta\cdot
+                                        // n g,v)_{\partial
+                                        // K_-\cap\partial\Omega}$,
+       for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
+         cell_vector(i) -= beta_n *
+                           g[point] *
+                           v(i,point) *
+                           JxW[point];
+    }
+}
 
+                                // @sect4{Function: assemble_face_term1}
+                                //
                                 // The ``assemble_face_term1''
                                 // function assembles the face terms
                                 // corresponding to the first version
-                                // of the DG method, cf. above. Then,
-                                // the face terms are given as a sum
-                                // of integrals over all cell
-                                // boundaries.
+                                // of the DG method, cf. above. For
+                                // that case, the face terms are
+                                // given as a sum of integrals over
+                                // all cell boundaries.
                                 //
                                 // When this function is invoked,
                                 // ``fe_v'' and ``fe_v_neighbor'' are
@@ -292,8 +368,7 @@ void DGTransportEquation<dim>::assemble_cell_term(
                                 // on the face.
                                 //
                                 // In addition to the cell matrix
-                                // ``u_v_matrix'' and the
-                                // ``cell_vector'' this function has
+                                // ``u_v_matrix'' this function has
                                 // got a new argument
                                 // ``un_v_matrix'', that stores
                                 // contributions to the system matrix
@@ -309,41 +384,38 @@ void DGTransportEquation<dim>::assemble_face_term1(
   const FEFaceValuesBase<dim>& fe_v,
   const FEFaceValuesBase<dim>& fe_v_neighbor,      
   FullMatrix<double> &u_v_matrix,
-  FullMatrix<double> &un_v_matrix,
-  Vector<double> &cell_vector)
+  FullMatrix<double> &un_v_matrix)
 {
-                                  // Again, we ask the FEValues
-                                  // objects for the shape values and
-                                  // the quadrature weights
+                                  // First we check that the current
+                                  // face is not at the boundary by
+                                  // accident.
+  Assert(!fe_v.get_face()->at_boundary(), ExcInternalError());
+  
+                                  // Again, as in the previous
+                                  // function, we ask the FEValues
+                                  // objects for the shape values,
+                                  // the quadrature weights and the
+                                  // normals
   const FullMatrix<double> &v = fe_v.get_shape_values ();
   const FullMatrix<double> &v_neighbor = fe_v_neighbor.get_shape_values ();  
   const vector<double> &JxW = fe_v.get_JxW_values ();
-                                  // but also for the normals.
   const vector<Point<dim> > &normals = fe_v.get_normal_vectors ();
 
-                                  // We also evaluate the flow field
-                                  // at the quadrature points
+                                  // and we evaluate the flow field
+                                  // at the quadrature points.
   vector<Point<dim> > beta (fe_v.n_quadrature_points);
-  
   beta_function.value_list (fe_v.get_quadrature_points(), beta);
 
-                                  // and the boundary values if the
-                                  // current face belongs to the
-                                  // boundary.
-  vector<double> g(fe_v.n_quadrature_points);
-  DoFHandler<dim>::face_iterator face=fe_v.get_face();
-  if (face->at_boundary())
-    boundary_function.value_list (fe_v.get_quadrature_points(), g);
-
-                                  // Then we assemble the cell matrix
-                                  // and cell vector according to the
-                                  // DG method given in the
+                                  // Then we assemble the cell
+                                  // matrices according to the DG
+                                  // method given in the
                                   // introduction.
   for (unsigned int point=0; point<fe_v.n_quadrature_points; ++point)
     {
       double beta_n=beta[point] * normals[point];
       if (beta_n>0)
-                                        // The term $(\beta\cdot n
+                                        // We assemble the term
+                                        // $(\beta\cdot n
                                         // u,v)_{\partial K_+}$,
        for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
          for (unsigned int j=0; j<fe_v.dofs_per_cell; ++j)
@@ -352,40 +424,30 @@ void DGTransportEquation<dim>::assemble_face_term1(
                               v(i,point) *
                               JxW[point];
       else
-       {
-                                          // at the boundary the term
-                                          // $(\beta\cdot n
-                                          // g,v)_{\partial
-                                          // K_-\cap\partial\Omega}$,
-         if (face->at_boundary())
-           for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
-             cell_vector(i) -= beta_n *
-                               g[point] *
+                                        // and the
+                                        // term $(\beta\cdot n
+                                        // \hat u,v)_{\partial
+                                        // K_-}$.
+       for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
+         for (unsigned int k=0; k<fe_v_neighbor.dofs_per_cell; ++k)
+           un_v_matrix(i,k) += beta_n *
+                               v_neighbor(k,point) *
                                v(i,point) *
                                JxW[point];
-         else
-                                            // and on inner faces the
-                                            // term $(\beta\cdot n
-                                            // \hat u,v)_{\partial
-                                            // K_-}$
-           for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
-             for (unsigned int k=0; k<fe_v_neighbor.dofs_per_cell; ++k)
-               un_v_matrix(i,k) += beta_n *
-                                   v_neighbor(k,point) *
-                                   v(i,point) *
-                                   JxW[point];
-       }
     }
 }
 
-                                // Now we look at the assembling
-                                // function that assembles the face
-                                // terms corresponding to the second
+                                // @sect4{Function: assemble_face_term2}
+                                //
+                                // Now we look at the
+                                // ``assemble_face_term2'' function
+                                // that assembles the face terms
+                                // corresponding to the second
                                 // version of the DG method,
-                                // cf. above. Then, the face terms
-                                // are given as a sum of integrals
-                                // over all faces.  Here we need two
-                                // additional cell matrices
+                                // cf. above. For that case the face
+                                // terms are given as a sum of
+                                // integrals over all faces.  Here we
+                                // need two additional cell matrices
                                 // ``u_vn_matrix'' and
                                 // ``un_vn_matrix'' that will store
                                 // contributions due to terms
@@ -398,8 +460,7 @@ void DGTransportEquation<dim>::assemble_face_term2(
   FullMatrix<double> &u_v_matrix,
   FullMatrix<double> &un_v_matrix,
   FullMatrix<double> &u_vn_matrix,
-  FullMatrix<double> &un_vn_matrix,
-  Vector<double> &cell_vector)
+  FullMatrix<double> &un_vn_matrix)
 {
                                   // the first few lines are the same
   const FullMatrix<double> &v = fe_v.get_shape_values ();
@@ -411,17 +472,12 @@ void DGTransportEquation<dim>::assemble_face_term2(
   
   beta_function.value_list (fe_v.get_quadrature_points(), beta);
 
-  vector<double> g(fe_v.n_quadrature_points);
-  DoFHandler<dim>::face_iterator face=fe_v.get_face();
-  if (face->at_boundary())
-    boundary_function.value_list (fe_v.get_quadrature_points(), g);
-
   for (unsigned int point=0; point<fe_v.n_quadrature_points; ++point)
     {
       double beta_n=beta[point] * normals[point];
       if (beta_n>0)
        {
-                                          // This terms we've already seen,
+                                          // This terms we've already seen.
          for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
            for (unsigned int j=0; j<fe_v.dofs_per_cell; ++j)
              u_v_matrix(i,j) += beta_n *
@@ -429,54 +485,45 @@ void DGTransportEquation<dim>::assemble_face_term2(
                                 v(i,point) *
                                 JxW[point];
 
-                                          // on inner faces we
-                                          // additionally have the
-                                          // term $(\beta\cdot n
-                                          // u,\hat v)_{\partial K_+},
-         if (!face->at_boundary())
-           for (unsigned int k=0; k<fe_v_neighbor.dofs_per_cell; ++k)
-             for (unsigned int j=0; j<fe_v.dofs_per_cell; ++j)
-               u_vn_matrix(k,j) -= beta_n *
-                                   v(j,point) *
-                                   v_neighbor(k,point) *
-                                   JxW[point];
+                                          // We additionally assemble
+                                          // the term $(\beta\cdot n
+                                          // u,\hat v)_{\partial
+                                          // K_+},
+         for (unsigned int k=0; k<fe_v_neighbor.dofs_per_cell; ++k)
+           for (unsigned int j=0; j<fe_v.dofs_per_cell; ++j)
+             u_vn_matrix(k,j) -= beta_n *
+                                 v(j,point) *
+                                 v_neighbor(k,point) *
+                                 JxW[point];
        }
       else
        {
-                                          // this one we already know,
-         if (face->at_boundary())
-           for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
-             cell_vector(i) -= beta_n *
-                               g[point] *
-                               v(i,point) *
-                               JxW[point];
-         else
-           {
-                                              // this one also,
-             for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
-               for (unsigned int l=0; l<fe_v_neighbor.dofs_per_cell; ++l)
-                 un_v_matrix(i,l) += beta_n *
-                                     v_neighbor(l,point) *
-                                     v(i,point) *
-                                     JxW[point];
-
-                                              // and this is another
-                                              // new one:
-                                              // $(\beta\cdot n \hat
-                                              // u,\hat v)_{\partial
-                                              // K_-}$.
-             for (unsigned int k=0; k<fe_v_neighbor.dofs_per_cell; ++k)
-               for (unsigned int l=0; l<fe_v_neighbor.dofs_per_cell; ++l)
-                 un_vn_matrix(k,l) -= beta_n *
-                                      v_neighbor(l,point) *
-                                      v_neighbor(k,point) *
-                                      JxW[point];
-           }
+                                          // This one we've already
+                                          // seen, too.
+         for (unsigned int i=0; i<fe_v.dofs_per_cell; ++i)
+           for (unsigned int l=0; l<fe_v_neighbor.dofs_per_cell; ++l)
+             un_v_matrix(i,l) += beta_n *
+                                 v_neighbor(l,point) *
+                                 v(i,point) *
+                                 JxW[point];
+
+                                          // And this is another new
+                                          // one: $(\beta\cdot n \hat
+                                          // u,\hat v)_{\partial
+                                          // K_-}$.
+         for (unsigned int k=0; k<fe_v_neighbor.dofs_per_cell; ++k)
+           for (unsigned int l=0; l<fe_v_neighbor.dofs_per_cell; ++l)
+             un_vn_matrix(k,l) -= beta_n *
+                                  v_neighbor(l,point) *
+                                  v_neighbor(k,point) *
+                                  JxW[point];
        }
     }
 }
 
 
+                                // @sect3{Class: DGMethod}
+                                //
                                 // After these preparations, we
                                 // proceed with the main part of this
                                 // program. The main class, here
@@ -600,12 +647,15 @@ void DGMethod<dim>::setup_system ()
 };
 
 
+                                // @sect4{Function: assemble_system1}
+                                //
                                 // We proceed with the
                                 // ``assemble_system1'' function that
                                 // implements the DG discretization
                                 // in its first version. This
                                 // function repeatedly calls the
-                                // ``assemble_cell_term'' and
+                                // ``assemble_cell_term'',
+                                // ``assemble_boundary_term'' and
                                 // ``assemble_face_term1'' functions
                                 // of the DGTransportEquation object.
                                 // The ``assemble_face_term1''
@@ -623,8 +673,7 @@ void DGMethod<dim>::setup_system ()
                                 // introduction:
                                 //
                                 // 1. face is at boundary (current
-                                // cell: FEFaceValues, neighboring
-                                // cell does not exist);
+                                // cell: FEFaceValues);
                                 //
                                 // 2. neighboring cell is finer
                                 // (current cell: FESubfaceValues,
@@ -788,33 +837,17 @@ void DGMethod<dim>::assemble_system1 ()
 
                                               // and assemble the
                                               // corresponding face
-                                              // terms. Here, the
-                                              // second and fourth
-                                              // arguments are only
-                                              // dummy arguments. On
-                                              // the boundary of the
-                                              // domain the
-                                              // ``assemble_face_term1''
-                                              // function will not
-                                              // access to shape
-                                              // values on the
-                                              // non-existent
-                                              // neighboring
-                                              // cell. Also,
-                                              // ``un_v_matrix'' will
-                                              // be unchanged.
-             dg.assemble_face_term1(fe_v_face,
-                                    fe_v_face,
-                                    u_v_matrix,
-                                    un_v_matrix,
-                                    cell_vector);
+                                              // terms.
+             dg.assemble_boundary_term(fe_v_face,
+                                       u_v_matrix,
+                                       cell_vector);
            }
          else
            {
-                                              // When we are not on the
-                                              // boundary of the
-                                              // domain then there
-                                              // must exist a
+                                              // Now we are not on
+                                              // the boundary of the
+                                              // domain, therefore
+                                              // there must exist a
                                               // neighboring cell.
              neighbor = cell->neighbor(face_no);
 
@@ -911,8 +944,7 @@ void DGMethod<dim>::assemble_system1 ()
                      dg.assemble_face_term1(fe_v_subface,
                                             fe_v_face_neighbor,
                                             u_v_matrix,
-                                            un_v_matrix,
-                                            cell_vector);
+                                            un_v_matrix);
                      
                                                       // get dof
                                                       // indices of
@@ -985,8 +1017,7 @@ void DGMethod<dim>::assemble_system1 ()
                      dg.assemble_face_term1(fe_v_face,
                                             fe_v_face_neighbor,
                                             u_v_matrix,
-                                            un_v_matrix,
-                                            cell_vector);
+                                            un_v_matrix);
                                                       // End of ``if
                                                       // (neighbor->level()
                                                       // ==
@@ -1041,8 +1072,7 @@ void DGMethod<dim>::assemble_system1 ()
                      dg.assemble_face_term1(fe_v_face,
                                             fe_v_subface_neighbor,
                                             u_v_matrix,
-                                            un_v_matrix,
-                                            cell_vector);
+                                            un_v_matrix);
                    }
 
                                                   // Get dof indices
@@ -1085,7 +1115,8 @@ void DGMethod<dim>::assemble_system1 ()
 };
 
 
-
+                                // @sect4{Function: assemble_system2}
+                                //
                                 // We proceed with the
                                 // ``assemble_system2'' function that
                                 // implements the DG discretization
@@ -1169,14 +1200,6 @@ void DGMethod<dim>::assemble_system2 ()
   
   Vector<double>  cell_vector (dofs_per_cell);
 
-                                  // Furthermore, here we define a
-                                  // dummy matrix and rhs to
-                                  // emphasize when arguments of the
-                                  // ``assemble_face_term2''
-                                  // functions will not be access.
-  FullMatrix<double> dummy_matrix;
-  Vector<double>     dummy_rhs;
-
                                   // The following lines are roughly
                                   // the same as in the previous
                                   // function.
@@ -1205,13 +1228,9 @@ void DGMethod<dim>::assemble_system2 ()
            {
              fe_v_face.reinit (cell, face_no);
 
-             dg.assemble_face_term2(fe_v_face,
-                                    fe_v_face,
-                                    u_v_matrix,
-                                    dummy_matrix,
-                                    dummy_matrix,
-                                    dummy_matrix,
-                                    cell_vector);
+             dg.assemble_boundary_term(fe_v_face,
+                                       u_v_matrix,
+                                       cell_vector);
            }
          else
            {
@@ -1242,8 +1261,7 @@ void DGMethod<dim>::assemble_system2 ()
                                             u_v_matrix,
                                             un_v_matrix,
                                             u_vn_matrix,
-                                            un_vn_matrix,
-                                            dummy_rhs);
+                                            un_vn_matrix);
                  
                      neighbor_child->get_dof_indices (dofs_neighbor);
                                                                
@@ -1281,8 +1299,7 @@ void DGMethod<dim>::assemble_system2 ()
                                             u_v_matrix,
                                             un_v_matrix,
                                             u_vn_matrix,
-                                            un_vn_matrix,
-                                            dummy_rhs);
+                                            un_vn_matrix);
 
                      neighbor->get_dof_indices (dofs_neighbor);
 

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