From 3703ead3245f2f6b4418da79cfe6633156d5cba1 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Tue, 8 Feb 2011 15:15:03 +0000 Subject: [PATCH] Add a paragraph of possible extensions. git-svn-id: https://svn.dealii.org/trunk@23304 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-2/doc/results.dox | 22 +++++++++++++++++++--- 1 file changed, 19 insertions(+), 3 deletions(-) diff --git a/deal.II/examples/step-2/doc/results.dox b/deal.II/examples/step-2/doc/results.dox index 1b592564d7..c9a6e0f44c 100644 --- a/deal.II/examples/step-2/doc/results.dox +++ b/deal.II/examples/step-2/doc/results.dox @@ -31,7 +31,7 @@ might be nonzero; of course the fact whether the entry actually is zero or not depends on the equation under consideration, but the indicated positions in the matrix tell us which shape functions can and which can't couple, if the equation is a local, i.e. differential -one): +one):
@@ -51,7 +51,23 @@ clustered around the main diagonal of the matrix after renumbering. Although this might not be apparent, the number of nonzero entries is the same in both pictures, of course. -A common observation is that the more refined the grid is, the better -the clustering around the diagonal will get. +

Possible extensions

+ +Just as with step-1, you may want to play with the program a bit to +familiarize yourself with deal.II. For example, in the +distribute_dofs function, we use linear finite elements +(that's what the argument "1" to the FE_Q object is). Explore how the +sparsity pattern changes if you use higher order elements, for example +cubic or quintic ones (by using 3 and 5 as the respective arguments). + +Or, you could see how the sparsity pattern changes with more +refinements. You will see that not only the size of the matrix +changes, but also its bandwidth (the distance from the diagonal of +those nonzero elements of the matrix that are farthest away from the +diagonal), though the ratio of bandwidth to size typically shrinks, +i.e. the matrix clusters more around the diagonal. + +Another idea of experiments would be to try other renumbering +strategies than Cuthill-McKee from the DoFRenumbering namespace. -- 2.39.5