Comment on the rapid convergence of the Newton method.

git-svn-id: https://svn.dealii.org/trunk@16157 0785d39b-7218-0410-832d-ea1e28bc413d

diff --git a/deal.II/examples/step-33/doc/intro.dox b/deal.II/examples/step-33/doc/intro.dox
index f4f6999dbb401ea12855b92246db37051def6a6e..1512993e133f5ad493225f2581b5420960b8812a 100644 (file)
--- a/deal.II/examples/step-33/doc/intro.dox
+++ b/deal.II/examples/step-33/doc/intro.dox
@@ -180,7 +180,10 @@ $\mathbf z$, we arrive at a linear system for $\delta \mathbf W$:
 @f}
 This linear system is, in general, neither symmetric nor has any
 particular definiteness properties. We will either use a direct solver
-or Trilinos' GMRES implementation to solve it.
+or Trilinos' GMRES implementation to solve it. As will become apparent from
+the <a href="#Results">results shown below</a>, this fully implicit iteration
+converges very rapidly (typically in 3 steps) and with the quadratic
+convergence order expected from a Newton method.
 
 
 <h3> Auto-Differentiation </h3>

diff --git a/deal.II/examples/step-33/doc/results.dox b/deal.II/examples/step-33/doc/results.dox
index 458b755113c5a159e17443d6e301e9e346f3c5dc..c56fa2f6490f7fb205ae456276f6347194da057a 100644 (file)
--- a/deal.II/examples/step-33/doc/results.dox
+++ b/deal.II/examples/step-33/doc/results.dox
@@ -93,41 +93,47 @@ end
 
 When we run the program, we get the following kind of output:
 @code
-T=3.14,    Number of active cells:       2617
-   Number of degrees of freedom: 11184
-NonLin Res:       Lin Iter     Lin Res
-______________________________________
-* 1.684e-02        0007        1.84e-13
-* 4.414e-05        0006        3.82e-15
-* 1.750e-09        0006        1.56e-19
-* 6.831e-16        0000        1.56e-19
-max_df:124
-T=3.16,    Number of active cells:       2626
-   Number of degrees of freedom: 11220
-NonLin Res:       Lin Iter     Lin Res
-______________________________________
-* 1.673e-02        0007        9.64e-14
-* 4.230e-05        0006        3.83e-15
-* 8.748e-10        0006        7.67e-20
-* 6.804e-16        0000        7.67e-20
-max_df:124
-T=3.18,    Number of active cells:       2644
-   Number of degrees of freedom: 11296
-NonLin Res:       Lin Iter     Lin Res
-______________________________________
-* 1.674e-02        0007        9.29e-14
-* 3.306e-05        0007        8.07e-17
-* 4.660e-10        0006        4.05e-20
-* 6.898e-16        0000        4.05e-20
-max_df:128
-T=3.2,    Number of active cells:       2647
-   Number of degrees of freedom: 11312
-NonLin Res:       Lin Iter     Lin Res
-______________________________________
+...
+T=0.08
+   Number of active cells:       1792
+   Number of degrees of freedom: 7656
+
+   NonLin Res     Lin Iter       Lin Res
+   _____________________________________
+   2.424e-02        0008        1.56e-13
+   7.498e-05        0008        1.10e-15
+   8.871e-09        0008        8.58e-20
+   5.998e-16        (converged)
+
+T=0.1
+   Number of active cells:       1798
+   Number of degrees of freedom: 7672
+
+   NonLin Res     Lin Iter       Lin Res
+   _____________________________________
+   2.563e-02        0008        1.95e-13
+   9.165e-05        0008        1.10e-15
+   1.234e-08        0008        8.08e-20
+   9.282e-16        (converged)
+
+T=0.12
+   Number of active cells:       1801
+   Number of degrees of freedom: 7676
+
+   NonLin Res     Lin Iter       Lin Res
+   _____________________________________
+   2.732e-02        0008        1.72e-13
+   1.147e-04        0008        1.15e-15
+   1.952e-08        0008        1.49e-19
+   1.432e-15        (converged)
 ...
 @endcode
 
-This output reports the progress of the Newton iterations and the time stepping.
+This output reports the progress of the Newton iterations and the time
+stepping. Note that our implementation of the Newton iteration indeed shows
+the expected quadratic convergence order: the norm of the nonlinear residual
+in each step is roughly the norm of the previous step squared. This leads to
+the very rapid convergence we can see here.
 
 The result of running these computations is a bunch of output files that we
 can pass to our visualization program of choice. When we collate them into a