Merge pull request #15221 from bangerth/77

Update output of step-77.

examples/step-77/doc/results.dox

@@ -5,132 +5,95 @@ When running the program, you get output that looks like this:
 Mesh refinement step 0
   Target_tolerance: 0.001
 
-  Computing residual vector... norm=0.231202
+  Computing residual vector... norm=0.867975
   Computing Jacobian matrix
   Factorizing Jacobian matrix
   Solving linear system
-  Computing residual vector... norm=0.231202
-  Computing residual vector... norm=0.171585
+  Computing residual vector... norm=0.867975
+  Computing residual vector... norm=0.212073
   Solving linear system
-  Computing residual vector... norm=0.171585
-  Computing residual vector... norm=0.127245
-  Computing residual vector... norm=0.0796471
+  Computing residual vector... norm=0.212073
+  Computing residual vector... norm=0.202631
   Solving linear system
-  Computing residual vector... norm=0.0796471
-  Computing residual vector... norm=0.0625301
+  Computing residual vector... norm=0.202631
+  Computing residual vector... norm=0.165773
   Solving linear system
-  Computing residual vector... norm=0.0625301
-  Computing residual vector... norm=0.0498864
+  Computing residual vector... norm=0.165774
+  Computing residual vector... norm=0.162594
   Solving linear system
-  Computing residual vector... norm=0.0498864
-  Computing residual vector... norm=0.0407765
+  Computing residual vector... norm=0.162594
+  Computing residual vector... norm=0.148175
   Solving linear system
-  Computing residual vector... norm=0.0407765
-  Computing residual vector... norm=0.0341589
+  Computing residual vector... norm=0.148175
+  Computing residual vector... norm=0.145391
   Solving linear system
-  Computing residual vector... norm=0.0341589
-  Computing residual vector... norm=0.0292867
+  Computing residual vector... norm=0.145391
+  Computing residual vector... norm=0.137551
   Solving linear system
-  Computing residual vector... norm=0.0292867
-  Computing residual vector... norm=0.0256309
-  Computing residual vector... norm=0.0223448
+  Computing residual vector... norm=0.137551
+  Computing residual vector... norm=0.135366
   Solving linear system
-  Computing residual vector... norm=0.0223448
-  Computing residual vector... norm=0.0202797
-  Computing residual vector... norm=0.0183817
+  Computing residual vector... norm=0.135365
+  Computing residual vector... norm=0.130367
   Solving linear system
-  Computing residual vector... norm=0.0183817
-  Computing residual vector... norm=0.0170464
-  Computing residual vector... norm=0.0157967
+  Computing residual vector... norm=0.130367
+  Computing residual vector... norm=0.128704
   Computing Jacobian matrix
   Factorizing Jacobian matrix
   Solving linear system
-  Computing residual vector... norm=0.0157967
-  Computing residual vector... norm=0.0141572
-  Computing residual vector... norm=0.012657
+  Computing residual vector... norm=0.128704
+  Computing residual vector... norm=0.0302623
   Solving linear system
-  Computing residual vector... norm=0.012657
-  Computing residual vector... norm=0.0116863
-  Computing residual vector... norm=0.0107696
+  Computing residual vector... norm=0.0302624
+  Computing residual vector... norm=0.0126764
   Solving linear system
-  Computing residual vector... norm=0.0107696
-  Computing residual vector... norm=0.0100986
-  Computing residual vector... norm=0.00944829
-  Computing residual vector... norm=0.00822576
+  Computing residual vector... norm=0.0126763
+  Computing residual vector... norm=0.00488315
   Solving linear system
-  Computing residual vector... norm=0.00822576
-  Computing residual vector... norm=0.00781983
-  Computing residual vector... norm=0.00741619
-  Computing residual vector... norm=0.00661792
+  Computing residual vector... norm=0.00488322
+  Computing residual vector... norm=0.00195788
   Solving linear system
-  Computing residual vector... norm=0.00661792
-  Computing residual vector... norm=0.00630571
-  Computing residual vector... norm=0.00599457
-  Computing residual vector... norm=0.00537663
-  Solving linear system
-  Computing residual vector... norm=0.00537663
-  Computing residual vector... norm=0.00512813
-  Computing residual vector... norm=0.00488033
-  Computing residual vector... norm=0.00438751
-  Computing residual vector... norm=0.00342052
-  Solving linear system
-  Computing residual vector... norm=0.00342052
-  Computing residual vector... norm=0.00326581
-  Computing residual vector... norm=0.00311176
-  Computing residual vector... norm=0.00280617
-  Computing residual vector... norm=0.00220992
-  Solving linear system
-  Computing residual vector... norm=0.00220992
-  Computing residual vector... norm=0.00209976
-  Computing residual vector... norm=0.00199943
-  Solving linear system
-  Computing residual vector... norm=0.00199942
-  Computing residual vector... norm=0.00190953
-  Computing residual vector... norm=0.00182005
-  Computing residual vector... norm=0.00164259
-  Computing residual vector... norm=0.00129652
+  Computing residual vector... norm=0.00195781
+  Computing residual vector... norm=0.000773169
 
 
 +---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start    |     0.192s |            |
+| Total wallclock time elapsed since start    |     0.121s |            |
 |                                             |            |            |
 | Section                         | no. calls |  wall time | % of total |
 +---------------------------------+-----------+------------+------------+
-| assembling the Jacobian         |         2 |    0.0141s |       7.4% |
-| assembling the residual         |        61 |     0.168s |        88% |
-| factorizing the Jacobian        |         2 |    0.0016s |      0.83% |
-| graphical output                |         1 |   0.00385s |         2% |
-| linear system solve             |        19 |    0.0013s |      0.68% |
+| assembling the Jacobian         |         2 |    0.0151s |        12% |
+| assembling the residual         |        31 |    0.0945s |        78% |
+| factorizing the Jacobian        |         2 |   0.00176s |       1.5% |
+| graphical output                |         1 |   0.00504s |       4.2% |
+| linear system solve             |        15 |  0.000893s |      0.74% |
 +---------------------------------+-----------+------------+------------+
 
 
 Mesh refinement step 1
   Target_tolerance: 0.0001
 
-  Computing residual vector... norm=0.0883422
+  Computing residual vector... norm=0.2467
   Computing Jacobian matrix
   Factorizing Jacobian matrix
   Solving linear system
-  Computing residual vector... norm=0.0883422
-  Computing residual vector... norm=0.0607066
-  Solving linear system
-  Computing residual vector... norm=0.0607066
-  Computing residual vector... norm=0.0437266
+  Computing residual vector... norm=0.246699
+  Computing residual vector... norm=0.0357783
   Solving linear system
-  Computing residual vector... norm=0.0437266
-  Computing residual vector... norm=0.0327999
+  Computing residual vector... norm=0.0357784
+  Computing residual vector... norm=0.0222161
   Solving linear system
-  Computing residual vector... norm=0.0327999
-  Computing residual vector... norm=0.0255418
+  Computing residual vector... norm=0.022216
+  Computing residual vector... norm=0.0122148
   Solving linear system
-  Computing residual vector... norm=0.0255417
-  Computing residual vector... norm=0.0206042
+  Computing residual vector... norm=0.0122149
+  Computing residual vector... norm=0.00750795
   Solving linear system
-  Computing residual vector... norm=0.0206042
-  Computing residual vector... norm=0.0171602
+  Computing residual vector... norm=0.00750787
+  Computing residual vector... norm=0.00439629
   Solving linear system
-  Computing residual vector... norm=0.0171602
-  Computing residual vector... norm=0.014689
+  Computing residual vector... norm=0.00439638
+  Computing residual vector... norm=0.00265093
   Solving linear system
 
 [...]
@@ -143,18 +106,25 @@ Mesh refinement step 0
 Mesh refinement step 0
   Target_tolerance: 0.001
 
-  Computing residual vector... norm=0.231202
+  Computing residual vector... norm=0.867975
   Computing Jacobian matrix
   Factorizing Jacobian matrix
   Solving linear system
-  Computing residual vector... norm=0.231202
-  Computing residual vector... norm=0.171585
+  Computing residual vector... norm=0.867975
+  Computing residual vector... norm=0.212073
   Solving linear system
-  Computing residual vector... norm=0.171585
-  Computing residual vector... norm=0.127245
-  Computing residual vector... norm=0.0796471
+  Computing residual vector... norm=0.212073
+  Computing residual vector... norm=0.202631
+  Solving linear system
+  Computing residual vector... norm=0.202631
+  Computing residual vector... norm=0.165773
+  Solving linear system
+  Computing residual vector... norm=0.165774
+  Computing residual vector... norm=0.162594
+  Solving linear system
+  Computing residual vector... norm=0.162594
+  Computing residual vector... norm=0.148175
   Solving linear system
-  Computing residual vector... norm=0.0796471
   ...
 @endcode
 What is happening is this:
@@ -169,11 +139,15 @@ What is happening is this:
   i.e., do line search. To this end, KINSOL requires us to compute the
   residual vector $F(U_k + \alpha_k \delta U_k)$ for different step lengths
   $\alpha_k$. For the first step above, it finds an acceptable $\alpha_k$
-  after two tries, the second time around it takes three tries.
+  after two tries, and that's generally what will happen in later line
+  searches as well.
 - Having found a suitable updated solution $U_{k+1}$, the process is
   repeated except now KINSOL is happy with the current Jacobian matrix
   and does not instruct us to re-build the matrix and its factorization,
-  and instead asks us to solve a linear system with that same matrix.
+  instead asking us to solve a linear system with that same matrix. That
+  will happen several times over, and only after ten solves with the same
+  matrix are we instructed to build a matrix again, using what is by then an
+  already substantially improved solution as linearization point.
 
 The program also writes the solution to a VTU file at the end
 of each mesh refinement cycle, and it looks as follows:
@@ -202,6 +176,7 @@ The key takeaway messages of this program are the following:
   times, without us having to implement the intricacies of algorithms
   that determine when we need to rebuild this information.
 
+
 <a name="extensions"></a>
 <h3> Possibilities for extensions </h3>