From: Wolfgang Bangerth Date: Wed, 6 Jul 2016 16:14:51 +0000 (-0500) Subject: Better connect step-56 throughout the tutorials. X-Git-Tag: v8.5.0-rc1~924^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F2752%2Fhead;p=dealii.git Better connect step-56 throughout the tutorials. --- diff --git a/examples/step-16/doc/results.dox b/examples/step-16/doc/results.dox index f1835761b5..bf6d2a96e5 100644 --- a/examples/step-16/doc/results.dox +++ b/examples/step-16/doc/results.dox @@ -78,6 +78,13 @@ it becomes even more difficult if the program is to run in %parallel on machines coupled through MPI, for example. In that case, it would be simpler if one could use a black-box preconditioner that uses some sort of multigrid hierarchy for good performance but can figure out -level matrices and similar things out by itself. Algebraic multigrid +level matrices and similar things by itself. Algebraic multigrid methods do exactly this, and we will use them in -step-31 for the solution of a Stokes problem. +step-31 for the solution of a Stokes problemm and in step-32 and +step-40 for a parallel variation. + +Finally, one may want to think how to use geometric multigrid for +other kinds of problems, specifically +@ref vector_valued "vector valued problems". This is the topic of +step-56 where we use the techniques shown here for the Stokes +equation. diff --git a/examples/step-22/doc/results.dox b/examples/step-22/doc/results.dox index 52868456a1..52af0f34ed 100644 --- a/examples/step-22/doc/results.dox +++ b/examples/step-22/doc/results.dox @@ -727,12 +727,15 @@ because GMRES(k) scales worse with the problem size than CG, as we discussed above. Nonetheless, the improvement by a factor of 3-6 for moderate problem sizes is quite impressive. -
Combining block preconditioner and multigrid
+ +
Combining the block preconditioner and multigrid
An ultimate linear solver for this problem could be imagined as a combination of an optimal preconditioner for $A$ (e.g. multigrid) and the block preconditioner described above, which is the approach taken in the step-31 -tutorial program. +and step-32 tutorial programs (where we use an algebraic multigrid +method) and step-56 (where we use a geometric multigrid method). +
No block matrices and vectors
Another possibility that can be taken into account is to not set up a block