Clarify a comment.

git-svn-id: https://svn.dealii.org/trunk@17301 0785d39b-7218-0410-832d-ea1e28bc413d

diff --git a/deal.II/examples/step-31/step-31.cc b/deal.II/examples/step-31/step-31.cc
index 1c0ed54dec8631045ab8f71c60839020a306e47c..f2e86205557909d2a4289135c45bdc5e82d5a5af 100644 (file)
--- a/deal.II/examples/step-31/step-31.cc
+++ b/deal.II/examples/step-31/step-31.cc
@@ -443,25 +443,29 @@ namespace LinearSolvers
 
 
                                   // Next is the <code>vmult</code>
-                                  // function. We implement the
-                                  // action of $P^{-1}$ as described
-                                  // above in three successive steps.
-                                  // The first step multiplies the
-                                  // velocity part of the vector by a
-                                  // preconditioner of the matrix
-                                  // <i>A</i>.  The resuling velocity
-                                  // vector is then multiplied by $B$
-                                  // and subtracted from the
-                                  // pressure.  This second step only
-                                  // acts on the pressure vector and
-                                  // is accomplished by the command
-                                  // SparseMatrix::residual. Next, we
-                                  // change the sign in the temporary
-                                  // pressure vector and finally
-                                  // multiply by the pressure mass
-                                  // matrix to get the final pressure
-                                  // vector, completing our work on
-                                  // the Stokes preconditioner:
+                                  // function. We implement the action of
+                                  // $P^{-1}$ as described above in three
+                                  // successive steps.  In formulas, we want
+                                  // to compute $Y=P^{-1}X$ where $X,Y$ are
+                                  // both vectors with two block components.
+                                  //
+                                  // The first step multiplies the velocity
+                                  // part of the vector by a preconditioner
+                                  // of the matrix <i>A</i>, i.e. we compute
+                                  // $Y_0={\tilde A}^{-1}X_0$.  The resulting
+                                  // velocity vector is then multiplied by
+                                  // $B$ and subtracted from the pressure,
+                                  // i.e. we want to compute $X_1-BY_0$.
+                                  // This second step only acts on the
+                                  // pressure vector and is accomplished by
+                                  // the residual function of our matrix
+                                  // classes, except that the sign is
+                                  // wrong. Consequently, we change the sign
+                                  // in the temporary pressure vector and
+                                  // finally multiply by the inverse pressure
+                                  // mass matrix to get the final pressure
+                                  // vector, completing our work on the
+                                  // Stokes preconditioner:
   template <class PreconditionerA, class PreconditionerMp>
   void BlockSchurPreconditioner<PreconditionerA, PreconditionerMp>::vmult (
     TrilinosWrappers::BlockVector       &dst,