From ca084abe3fd0fa87fd8b0b3aa352a7903e2c9723 Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 8 Aug 2007 21:35:43 +0000 Subject: [PATCH] More text git-svn-id: https://svn.dealii.org/trunk@14925 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-27/doc/intro.dox | 15 +++++++++------ deal.II/examples/step-27/doc/results.dox | 19 +++++++++++++++++++ 2 files changed, 28 insertions(+), 6 deletions(-) diff --git a/deal.II/examples/step-27/doc/intro.dox b/deal.II/examples/step-27/doc/intro.dox index 32fd970d61..bd4c1237bb 100644 --- a/deal.II/examples/step-27/doc/intro.dox +++ b/deal.II/examples/step-27/doc/intro.dox @@ -574,12 +574,15 @@ this tutorial program.

Eliminating constrained degrees of freedom

-A second problem particular to $hp$ methods arises because we have so many -constrained degrees of freedom: typically up to about one third of all degrees -of freedom (in 3d) are constrained because they either belong to cells with -hanging nodes or because they are on cells adjacent to cells with a higher or -lower polynomial degree. This is much more than the fraction of constrained -degrees of freedom in non-$hp$ mode. +A second problem particular to $hp$ methods arises because we have so +many constrained degrees of freedom: typically up to about one third +of all degrees of freedom (in 3d) are constrained because they either +belong to cells with hanging nodes or because they are on cells +adjacent to cells with a higher or lower polynomial degree. This is, +in fact, not much more than the fraction of constrained degrees of +freedom in non-$hp$ mode, but the difference is that each constrained +hanging node is constrained not only against the two adjacent degrees +of freedom, but is constrained against many more degrees of freedom. In previous programs, for example in step-6, we have dealt with eliminating these constrained degrees of freedom by first building an object of type diff --git a/deal.II/examples/step-27/doc/results.dox b/deal.II/examples/step-27/doc/results.dox index 957c48b172..04d7d28d22 100644 --- a/deal.II/examples/step-27/doc/results.dox +++ b/deal.II/examples/step-27/doc/results.dox @@ -1,6 +1,13 @@

Results

+In this section, we discuss a few results produced from running the +current tutorial program. More results, in particular the extension to +3d calculations and determining how much compute time the individual +components of the program take, are given in the @ref hp_paper . + +When run, this is what the program produces: +
 examples/step-27> make run
@@ -31,3 +38,15 @@ Cycle 5:
    Number of constraints       : 6196
 
+ +The first thing we learn from this is that the number of constrained +degrees of freedom is on the order of 20-25% of the total number of +degrees of freedom, at least on the later grids when we have elements +of relatively high order. This is, in fact, on the same order of +magnitude as for non-$hp$ discretizations. For example, in the last +step of the @ref step_6 "step-6" program, we have 18401 degrees of +freedom, 4104 of which are constrained. The difference is that in the +latter program, each constrained hanging node is constrained against +only the two adjacent degrees of freedom, whereas in the $hp$ case, +constrained nodes are constrained against many more degrees of +freedom. -- 2.39.5