]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Add to the documentation.
authorWolfgang Bangerth <bangerth@math.tamu.edu>
Tue, 4 Aug 2009 20:53:09 +0000 (20:53 +0000)
committerWolfgang Bangerth <bangerth@math.tamu.edu>
Tue, 4 Aug 2009 20:53:09 +0000 (20:53 +0000)
git-svn-id: https://svn.dealii.org/trunk@19177 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/deal.II/source/grid/tria_boundary.cc

index a19e97f23459d47772fca09ff8a9d4de5a2b6ce9..d9582af5071e518a4cbb8f20510f6500a0f9c453 100644 (file)
@@ -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() ?

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