From: Wolfgang Bangerth Date: Sun, 13 Feb 2011 19:18:13 +0000 (+0000) Subject: Change the formula to place interior nodes in the new part of the GridGenerator:... X-Git-Tag: v8.0.0~4349 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=62f295f7ef28bda82d6b53ada181275aee51a56c;p=dealii.git Change the formula to place interior nodes in the new part of the GridGenerator::hyper_shell function. git-svn-id: https://svn.dealii.org/trunk@23349 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/doxygen/images/hyper_shell_96_cut.png b/deal.II/doc/doxygen/images/hyper_shell_96_cut.png index 0ec6a3f143..ac963ad3c3 100644 Binary files a/deal.II/doc/doxygen/images/hyper_shell_96_cut.png and b/deal.II/doc/doxygen/images/hyper_shell_96_cut.png differ diff --git a/deal.II/include/deal.II/grid/grid_generator.h b/deal.II/include/deal.II/grid/grid_generator.h index 906ae7d2fa..c87de9b967 100644 --- a/deal.II/include/deal.II/grid/grid_generator.h +++ b/deal.II/include/deal.II/grid/grid_generator.h @@ -613,7 +613,7 @@ class GridGenerator * is based on a once refined version of * the one with n_cells=12, * where all internal nodes are re-placed - * along a shell halfway between the + * along a shell somewhere between the * inner and outer boundary of the * domain. The following two images * compare half of the hyper shell for diff --git a/deal.II/source/grid/grid_generator.cc b/deal.II/source/grid/grid_generator.cc index c071965ba7..9666862117 100644 --- a/deal.II/source/grid/grid_generator.cc +++ b/deal.II/source/grid/grid_generator.cc @@ -2366,6 +2366,67 @@ GridGenerator::hyper_shell (Triangulation<3>& tria, tmp.set_boundary(1, boundary); tmp.refine_global (1); + // let's determine the distance at + // which the interior nodes should be + // from the center. let's say we + // measure distances in multiples of + // outer_radius and call + // r=inner_radius. + // + // then note + // that we now have 48 faces on the + // inner and 48 on the outer sphere, + // each with an area of approximately + // 4*pi/48*r^2 and 4*pi/48, for + // a face edge length of approximately + // sqrt(pi/12)*r and sqrt(pi/12) + // + // let's say we put the interior nodes + // at a distance rho, then a measure of + // deformation for the inner cells + // would be + // di=max(sqrt(pi/12)*r/(rho-r), + // (rho-r)/sqrt(pi/12)/r) + // and for the outer cells + // do=max(sqrt(pi/12)/(1-rho), + // (1-rho)/sqrt(pi/12)) + // + // we now seek a rho so that the + // deformation of cells on the inside + // and outside is equal. there are in + // principle four possibilities for one + // of the branches of do== one of the + // branches of di, though not all of + // them satisfy do==di, of + // course. however, we are not + // interested in cases where the inner + // cell is long and skinny and the + // outer one tall -- yes, they have the + // same aspect ratio, but in different + // space directions. + // + // so it only boils down to the + // following two possibilities: the + // first branch of each max(.,.) + // functions are equal, or the second + // one are. on the other hand, since + // they two branches are reciprocals of + // each other, if one pair of branches + // is equal, so is the other + // + // this yields the following equation + // for rho: + // sqrt(pi/12)*r/(rho-r) + // == sqrt(pi/12)/(1-rho) + // with solution rho=2r/(1+r) + const double r = inner_radius / outer_radius; + const double pi = numbers::PI; + const double rho = 2*r/(1+r); + + // then this is the distance of the + // interior nodes from the center: + const double middle_radius = rho * outer_radius; + // mark vertices we've already moved or // that we want to ignore: we don't // want to move vertices at the inner @@ -2394,11 +2455,8 @@ GridGenerator::hyper_shell (Triangulation<3>& tria, // between inner and outer // sphere const Point<3> old_distance = cell->vertex(v) - p; - const double old_radius = cell->vertex(v).distance(p); - const double new_radius = (inner_radius + outer_radius)/2; - - cell->vertex(v) = p + old_distance * (new_radius / old_radius); + cell->vertex(v) = p + old_distance * (middle_radius / old_radius); vertex_already_treated[cell->vertex_index(v)] = true; } diff --git a/tests/deal.II/grid_hyper_shell_04/cmp/generic b/tests/deal.II/grid_hyper_shell_04/cmp/generic index 5d18ade8de..d9441cb8be 100644 --- a/tests/deal.II/grid_hyper_shell_04/cmp/generic +++ b/tests/deal.II/grid_hyper_shell_04/cmp/generic @@ -1,14 +1,14 @@ 0.00000 -0.500000 0.00000 0 0 -0.162529 -0.444037 0.162529 0 0 --0.243793 -0.666055 0.243793 0 0 -0.00000 -0.750000 0.00000 0 0 +-0.216705 -0.592049 0.216705 0 0 +0.00000 -0.666667 0.00000 0 0 0.00000 -0.500000 0.00000 0 0 -0.162529 -0.444037 -0.162529 0 0 -0.353553 -0.353553 0.00000 0 0 --0.530330 -0.530330 0.00000 0 0 --0.243793 -0.666055 -0.243793 0 0 +-0.471405 -0.471405 0.00000 0 0 +-0.216705 -0.592049 -0.216705 0 0 -0.162529 -0.444037 -0.162529 0 0 0.00000 -0.500000 0.00000 0 0 @@ -17,22 +17,22 @@ -0.162529 -0.444037 0.162529 0 0 -0.353553 -0.353553 0.00000 0 0 --0.243793 -0.666055 0.243793 0 0 --0.530330 -0.530330 0.00000 0 0 +-0.216705 -0.592049 0.216705 0 0 +-0.471405 -0.471405 0.00000 0 0 -0.00000 -0.750000 0.00000 0 0 --0.243793 -0.666055 -0.243793 0 0 +0.00000 -0.666667 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