]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Go through the rest.
authorWolfgang Bangerth <bangerth@math.tamu.edu>
Mon, 20 Feb 2012 15:19:56 +0000 (15:19 +0000)
committerWolfgang Bangerth <bangerth@math.tamu.edu>
Mon, 20 Feb 2012 15:19:56 +0000 (15:19 +0000)
git-svn-id: https://svn.dealii.org/trunk@25125 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/examples/step-44/step-44.cc

index 0641f1335ea3531c0b0b702eac78fe96bfa6d033..560a4fd7a918030ea897d92ca16f9f430f2df137 100644 (file)
@@ -3063,16 +3063,16 @@ namespace Step44
     cell->get_dof_indices(data.local_dof_indices);
 
                                     // We now extract the contribution of
-                                    // the  dof associated with the current cell
+                                    // the  dofs associated with the current cell
                                     // to the global stiffness matrix.
                                     // The discontinuous nature of the $\widetilde{p}$
                                     // and $\widetilde{J}$
                                     // interpolations mean that their is no
                                     // coupling of the local contributions at the
                                     // global level. This is not the case with the u dof.
-                                    // In other words, k_Jp, k_pJ and k_JJ, when extracted
+                                    // In other words, $k_{Jp}, k_{pJ} and k_{JJ}$, when extracted
                                     // from the global stiffness matrix are the element
-                                    // contributions. This is not the case for k_uu.
+                                    // contributions. This is not the case for $k_{uu}$.
 
                                     // Currently the matrix corresponding to
                                     // the dof associated with the current element
@@ -3089,15 +3089,15 @@ namespace Step44
                                     //  | k_pu  |     0    |   k_pJ^-1 |
                                     //  |   0   |   k_Jp   |   k_JJ    |
                                     // @endcode
-                                    // with k_con = k_uu + k_bbar
+                                    // with $k_{con} = k_{uu} + k_{\bar b}$
                                     // where
-                                    // k_bbar = k_up k_bar k_pu
+                                    // $k_{\bar b} = k_{up} k_{bar} k_{pu}$
                                     // and
-                                    // k_bar = k_Jp^{-1} k_JJ kpJ^{-1}
+                                    // $k_{bar} = k_{Jp}^{-1} k_{JJ} k_{pJ}^{-1}$.
                                     //
                                     // At this point, we need to take note of
                                     // the fact that global data already exists
-                                    // in the K_uu, K_pt, K_tp subblocks.  So
+                                    // in the $K_{uu}, K_{pt}, K_{tp}$ sub-blocks.  So
                                     // if we are to modify them, we must
                                     // account for the data that is already
                                     // there (i.e. simply add to it or remove
@@ -3106,7 +3106,7 @@ namespace Step44
                                     // operation, we need to take this into
                                     // account
                                     //
-                                    // For the K_uu block in particular, this
+                                    // For the $K_{uu}$ block in particular, this
                                     // means that contributions have been added
                                     // from the surrounding cells, so we need
                                     // to be careful when we manipulate this
@@ -3114,38 +3114,40 @@ namespace Step44
                                     // subblocks.
                                     //
                                     // This is the strategy we will employ to
-                                    // get the subblocks we want: k_store:
-                                    // Since we don't have access to k_{uu},
+                                    // get the subblocks we want:
+                                    //
+                                    // - $k_{store}$:
+                                    // Since we don't have access to $k_{uu}$,
                                     // but we know its contribution is added to
-                                    // the global K_{uu} matrix, we just want
+                                    // the global $K_{uu}$ matrix, we just want
                                     // to add the element wise
-                                    // static-condensation k_bbar.
+                                    // static-condensation $k_{\bar b}$.
                                     //
-                                    // - $k_{pJ}^-1$: Similarly, k_pJ exists in
+                                    // - $k_{pJ}^{-1}$: Similarly, $k_{pJ}$ exists in
                                     //          the subblock. Since the copy
                                     //          operation is a += operation, we
                                     //          need to subtract the existing
-                                    //          k_pJ submatrix in addition to
+                                    //          $k_{pJ}$ submatrix in addition to
                                     //          "adding" that which we wish to
                                     //          replace it with.
                                     //
-                                    // - $k_{Jp}^-1$: Since the global matrix
+                                    // - $k_{Jp}^{-1}$: Since the global matrix
                                     //          is symmetric, this block is the
                                     //          same as the one above and we
-                                    //          can simply use k_pJ^-1 as a
+                                    //          can simply use $k_{pJ}^{-1}$ as a
                                     //          substitute for this one
                                     //
                                     // We first extract element data from the
                                     // system matrix. So first we get the
                                     // entire subblock for the cell, then
-                                    // extract k for the dof associated with
+                                    // extract $k$ for the dofs associated with
                                     // the current element
     AdditionalTools::extract_submatrix(data.local_dof_indices,
                                       data.local_dof_indices,
                                       tangent_matrix,
                                       data.k_orig);
-                                    // and next the local matrices for k_pu,
-                                    // k_pJ and k_JJ
+                                    // and next the local matrices for $k_{pu}$,
+                                    // $k_{pJ}$ and $k_{JJ}$
     AdditionalTools::extract_submatrix(element_indices_p,
                                       element_indices_u,
                                       data.k_orig,
@@ -3159,30 +3161,30 @@ namespace Step44
                                       data.k_orig,
                                       data.k_JJ);
 
-                                    // To get the inverse of k_pJ, we invert it
+                                    // To get the inverse of $k_{pJ}$, we invert it
                                     // directly.  This operation is relatively
-                                    // inexpensive since k_pJ is
+                                    // inexpensive since $k_{pJ}$ is
                                     // block-diagonal.
     data.k_pJ_inv.invert(data.k_pJ);
 
                                     // Now we can make condensation terms to
-                                    // add to the k_uu block and put them in
-                                    // the cell local matrix A = k_pJ^-1 k_pu
+                                    // add to the $k_{uu}$ block and put them in
+                                    // the cell local matrix $A = k_pJ^{-1} k_{pu}$:
     data.k_pJ_inv.mmult(data.A, data.k_pu);
-                                    // B = k_JJ k_pJ^-1 k_pu
+                                    // $B = k_{JJ} k_{pJ}^{-1} k_{pu}$
     data.k_JJ.mmult(data.B, data.A);
-                                    // C = k_Jp^-1 k_JJ k_pJ^-1 k_pu
+                                    // $C = k_{Jp}^{-1} k_{JJ} k_{pJ}^{-1} k_{pu}$
     data.k_pJ_inv.Tmmult(data.C, data.B);
-                                    // k_bbar = k_up k_Jp^-1 k_JJ k_pJ^-1 k_pu
+                                    // $k_{\bar b} = k_{up} k_{Jp}^{-1} k_{JJ} k_{pJ}^{-1} k_{pu}$
     data.k_pu.Tmmult(data.k_bbar, data.C);
     AdditionalTools::replace_submatrix(element_indices_u,
                                       element_indices_u,
                                       data.k_bbar,
                                       data.cell_matrix);
 
-                                    // Next we place k_{pJ}^-1 in the k_{pJ}
+                                    // Next we place $k_{pJ}^{-1}$ in the $k_{pJ}$
                                     // block for post-processing.  Note again
-                                    // that we need to remove the k_pJ
+                                    // that we need to remove the k_{pJ}
                                     // contribution that already exists there.
     data.k_pJ_inv.add(-1.0, data.k_pJ);
     AdditionalTools::replace_submatrix(element_indices_p,
@@ -3193,7 +3195,7 @@ namespace Step44
 
 // @sect4{Solid::output_results}
 // Here we present how the results are written to file to be viewed
-// using ParaView. The method is similar to that shown in previous
+// using ParaView or Visit. The method is similar to that shown in previous
 // tutorials so will not be discussed in detail.
   template <int dim>
   void Solid<dim>::output_results() const
@@ -3216,18 +3218,20 @@ namespace Step44
                             data_component_interpretation);
 
                                     // Since we are dealing with a large
-                                    // deformation problem, it would be nice to
-                                    // display the result on a displaced grid!
-                                    // The MappingQEulerian class linked with
-                                    // the DataOut class provides an interface
-                                    // through which this can be achieved
-                                    // without physically moving the grid
-                                    // points ourselves.  We first need to copy
-                                    // the solution to a temporary vector and
-                                    // then create the Eulerian mapping. We
-                                    // also specify the polynomial degree to
-                                    // the DataOut object in order to produce a
-                                    // more refined output data set when higher
+                                    // deformation problem, it would be nice
+                                    // to display the result on a displaced
+                                    // grid!  The MappingQEulerian class
+                                    // linked with the DataOut class provides
+                                    // an interface through which this can be
+                                    // achieved without physically moving the
+                                    // grid points in the Triangulation
+                                    // object ourselves.  We first need to
+                                    // copy the solution to a temporary
+                                    // vector and then create the Eulerian
+                                    // mapping. We also specify the
+                                    // polynomial degree to the DataOut
+                                    // object in order to produce a more
+                                    // refined output data set when higher
                                     // order polynomials are used.
     Vector<double> soln(solution_n.size());
     for (unsigned int i = 0; i < soln.size(); ++i)

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