Make step-29 marginally easier to understand.

diff --git a/examples/step-29/step-29.cc b/examples/step-29/step-29.cc
index 57f68cd6dd0fd1a603ffc2b065b2c9054effe24c..4c806846f6c6caceb17d9a3924c598274e648094 100644 (file)
--- a/examples/step-29/step-29.cc
+++ b/examples/step-29/step-29.cc
@@ -736,13 +736,15 @@ namespace Step29
   // As already mentioned in the introduction, the system matrix is neither
   // symmetric nor definite, and so it is not quite obvious how to come up
   // with an iterative solver and a preconditioner that do a good job on this
-  // matrix.  We chose instead to go a different way and solve the linear
+  // matrix. (For more on this topic, see also the
+  // <a href="#extensions">Possibilities for extensions</a> section below.)
+  // We chose instead to go a different way and solve the linear
   // system with the sparse LU decomposition provided by UMFPACK. This is
   // often a good first choice for 2d problems and works reasonably well even
-  // for a large number of DoFs.  The deal.II interface to UMFPACK is given by
-  // the SparseDirectUMFPACK class, which is very easy to use and allows us to
-  // solve our linear system with just 3 lines of code.
-
+  // for moderately large numbers of DoFs.  The deal.II interface to UMFPACK
+  // is implemented in the SparseDirectUMFPACK class, which is very easy to
+  // use and allows us to solve our linear system with just 3 lines of code.
+  //
   // Note again that for compiling this example program, you need to have the
   // deal.II library built with UMFPACK support.
   template <int dim>
@@ -752,18 +754,16 @@ namespace Step29
     Timer timer;
 
     // The code to solve the linear system is short: First, we allocate an
-    // object of the right type. The following <code>initialize</code> call
-    // provides the matrix that we would like to invert to the
-    // SparseDirectUMFPACK object, and at the same time kicks off the
-    // LU-decomposition. Hence, this is also the point where most of the
-    // computational work in this program happens.
+    // object of the right type. The following call to
+    // SparseDirectUMFPACK::solve() takes as argument the matrix to decompose,
+    // and a vector that upon input equals the right hand side of the linear
+    // system to be solved, and upon output contains the solution of the linear
+    // system. To satisfy this input/output requirement, we first assign the
+    // right hand side vector to the `solution` variable.
     SparseDirectUMFPACK A_direct;
-    A_direct.initialize(system_matrix);
 
-    // After the decomposition, we can use <code>A_direct</code> like a matrix
-    // representing the inverse of our system matrix, so to compute the
-    // solution we just have to multiply with the right hand side vector:
-    A_direct.vmult(solution, system_rhs);
+    solution = system_rhs;
+    A_direct.solve(system_matrix, solution);
 
     timer.stop();
     std::cout << "done (" << timer.cpu_time() << "s)" << std::endl;