From 9b5030eba6bf6b536037dab8e7d7a7f124fa3866 Mon Sep 17 00:00:00 2001 From: David Wells Date: Fri, 4 May 2018 00:08:24 -0400 Subject: [PATCH] Update GridGenerator::hyper_shell's documentation. --- .../images/hyper_shell_6_cross_plane.png | Bin 1476 -> 0 bytes doc/doxygen/images/hypershell3d-12.png | Bin 41992 -> 92706 bytes doc/doxygen/images/hypershell3d-6.png | Bin 36600 -> 0 bytes doc/doxygen/images/hypershell3d-96.png | Bin 0 -> 180546 bytes include/deal.II/grid/grid_generator.h | 40 ++----- source/grid/grid_generator.cc | 109 +----------------- 6 files changed, 13 insertions(+), 136 deletions(-) delete mode 100644 doc/doxygen/images/hyper_shell_6_cross_plane.png delete mode 100644 doc/doxygen/images/hypershell3d-6.png create mode 100644 doc/doxygen/images/hypershell3d-96.png diff --git a/doc/doxygen/images/hyper_shell_6_cross_plane.png b/doc/doxygen/images/hyper_shell_6_cross_plane.png deleted file mode 100644 index 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If the number of initial cells @@ -722,38 +722,14 @@ namespace GridGenerator * In 3d, only certain numbers are allowed, 6 (or the default 0) for a * surface based on a hexahedron (i.e. 6 panels on the inner sphere extruded * in radial direction to form 6 cells), 12 for the rhombic dodecahedron, - * and 96 (see below). - * - * While the SphericalManifold, that is demonstrated in the documentation of - * the - * @ref manifold "documentation module on manifolds", - * creates reasonable meshes for any number of @p n_cells if attached to all - * cells and boundaries, the situation is less than ideal when only - * attaching a HyperShellBoundary. Then, only vertices on the boundaries are - * placed at the correct distance from the center. As an example, the 3d - * meshes give rise to the following meshes upon one refinement: - * - * @image html hypershell3d-6.png - * @image html hypershell3d-12.png - * - * Neither of these meshes is particularly good since one ends up with - * poorly shaped cells at the inner edge upon refinement. For example, this - * is the middle plane of the mesh for the n_cells=6: + * and 96. This choice dates from an older version of deal.II before the + * Manifold classes were implemented: today all three choices are roughly + * equivalent (after performing global refinement, of course). * - * @image html hyper_shell_6_cross_plane.png + * The grids with 12 and 96 cells are plotted below: * - * The mesh generated with n_cells=12 is better but still not - * good. As a consequence, you may also specify n_cells=96 as a - * third option. The mesh generated in this way is based on a once refined - * version of the one with n_cells=12, where all internal nodes - * are re-placed along a shell somewhere between the inner and outer - * boundary of the domain. The following two images compare half of the - * hyper shell for n_cells=12 and n_cells=96 (note - * that the doubled radial lines on the cross section are artifacts of the - * visualization): - * - * @image html hyper_shell_12_cut.png - * @image html hyper_shell_96_cut.png + * @image html hypershell3d-12.png + * @image html hypershell3d-96.png * * @note This function is declared to exist for triangulations of all space * dimensions, but throws an error if called in 1d. diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc index cd8471e8a6..1ea4cbeea5 100644 --- a/source/grid/grid_generator.cc +++ b/source/grid/grid_generator.cc @@ -3543,114 +3543,15 @@ namespace GridGenerator } else if (n == 96) { - // create a triangulation based on the - // 12-cell one where we refine the mesh - // once and then re-arrange all - // interior nodes so that the mesh is - // the least distorted - SphericalManifold<3> boundary (p); + // create a triangulation based on the 12-cell version. This function + // was needed before SphericalManifold was written: it manually + // adjusted the interior vertices to lie along concentric + // spheres. Nowadays we can just refine globally: Triangulation<3> tmp; hyper_shell (tmp, p, inner_radius, outer_radius, 12); - tmp.set_manifold(0, boundary); - tmp.set_manifold(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 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 - // or outer boundaries - std::vector vertex_already_treated (tmp.n_vertices(), false); - for (Triangulation<3>::active_cell_iterator cell = tmp.begin_active(); - cell != tmp.end(); ++cell) - for (unsigned int f=0; f::faces_per_cell; ++f) - if (cell->at_boundary(f)) - for (unsigned int v=0; v::vertices_per_face; ++v) - vertex_already_treated[cell->face(f)->vertex_index(v)] = true; - - // now move the remaining vertices - for (Triangulation<3>::active_cell_iterator cell = tmp.begin_active(); - cell != tmp.end(); ++cell) - for (unsigned int v=0; v::vertices_per_cell; ++v) - if (vertex_already_treated[cell->vertex_index(v)] == false) - { - // this is a new interior - // vertex. mesh refinement may - // have placed it at a number - // of places in radial - // direction and oftentimes not - // in a particularly good - // one. move it to halfway - // between inner and outer - // sphere - const Tensor<1,3> old_distance = cell->vertex(v) - p; - const double old_radius = cell->vertex(v).distance(p); - cell->vertex(v) = p + old_distance * (middle_radius / old_radius); - - vertex_already_treated[cell->vertex_index(v)] = true; - } - - // now copy the resulting level 1 cells - // into the new triangulation, + // now copy the resulting level 1 cells into the new triangulation, cells.resize(tmp.n_active_cells(), CellData<3>()); for (Triangulation<3>::active_cell_iterator cell = tmp.begin_active(); cell != tmp.end(); ++cell) -- 2.39.5