From 2700d939e242628415e25ca2dd805e862a56232b Mon Sep 17 00:00:00 2001 From: bangerth Date: Thu, 24 Jun 2010 13:47:14 +0000 Subject: [PATCH] Talk about connection to step-16. git-svn-id: https://svn.dealii.org/trunk@21318 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-37/doc/intro.dox | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/deal.II/examples/step-37/doc/intro.dox b/deal.II/examples/step-37/doc/intro.dox index 74e53a7630..9d488ece7f 100644 --- a/deal.II/examples/step-37/doc/intro.dox +++ b/deal.II/examples/step-37/doc/intro.dox @@ -367,8 +367,8 @@ hand, most of the more frequently used preconditioners such as SSOR, ILU or algebraic multigrid (AMG) can now no longer be used here because their implementation requires knowledge of the elements of the system matrix. -One solution is to use multigrid methods as shown in @ref step_16 -"step-16". They are known to be very fast, and they are suitable for our +One solution is to use multigrid methods as shown in +step-16. They are known to be very fast, and they are suitable for our purpose since they can be designed based purely on matrix-vector products. All one needs to do is to find a smoother that works with matrix-vector products only (our choice requires knowledge of the diagonal entries of the matrix, @@ -388,8 +388,11 @@ SOR/Gauss–Seidel smoothing relies on substitutions, which can often only be parallelized by working on diagonal sub-blocks of the matrix, which decreases efficiency. -The implementation into the multigrid framework is then straightforward. We -will only need some minor modifications compared to step-16. +The implementation into the multigrid framework is then straightforward. This +program is based on an earlier version of step-16 that demonstrated multigrid +on uniformly refined grids. However, the present matrix-free techniques would +obviously also apply to the adaptive meshes the current step-16 uses. +

The test case

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