From e1623c7b42d564ac4169714b6c40027a7e1915dc Mon Sep 17 00:00:00 2001 From: bangerth Date: Tue, 4 Aug 2009 20:53:09 +0000 Subject: [PATCH] Add to the documentation. git-svn-id: https://svn.dealii.org/trunk@19177 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/deal.II/source/grid/tria_boundary.cc | 22 ++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/deal.II/deal.II/source/grid/tria_boundary.cc b/deal.II/deal.II/source/grid/tria_boundary.cc index a19e97f234..d9582af507 100644 --- a/deal.II/deal.II/source/grid/tria_boundary.cc +++ b/deal.II/deal.II/source/grid/tria_boundary.cc @@ -270,6 +270,28 @@ namespace // MappingQ requests the midpoint of a // face, though, and it is for these cases // that we need to have the check available + // + // note that the factor of 1/8 for each + // of the 8 surrounding points isn't + // chosen arbitrarily. rather, we may ask + // where the harmonic map would place the + // point (0,0) if we map the square + // [-1,1]^2 onto the domain that is + // described using the 4 vertices and 4 + // edge point points of this quad. we can + // then discretize the harmonic map using + // four cells and Q1 elements on each of + // the quadrants of the square [-1,1]^2 + // and see where the midpoint would land + // (this is the procedure we choose, for + // example, in + // GridGenerator::laplace_solve) and it + // turns out that it will land at the + // mean of the 8 surrounding + // points. whether a discretization of + // the harmonic map with only 4 cells is + // adequate is a different question + // altogether, of course. return (quad->vertex(0) + quad->vertex(1) + quad->vertex(2) + quad->vertex(3) + (quad->line(0)->has_children() ? -- 2.39.5