From: bangerth Date: Tue, 13 Jan 2009 17:40:26 +0000 (+0000) Subject: Fix HalfHyperShellBoundary in 3d. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=9b880ddde450a4f640ec949d553b472324a260e0;p=dealii-svn.git Fix HalfHyperShellBoundary in 3d. git-svn-id: https://svn.dealii.org/trunk@18215 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/deal.II/include/grid/tria_boundary_lib.h b/deal.II/deal.II/include/grid/tria_boundary_lib.h index 265eea6096..bf4ad320c8 100644 --- a/deal.II/deal.II/include/grid/tria_boundary_lib.h +++ b/deal.II/deal.II/include/grid/tria_boundary_lib.h @@ -2,7 +2,7 @@ // $Id$ // Version: $Name$ // -// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 by the deal.II authors +// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2009 by the deal.II authors // // This file is subject to QPL and may not be distributed // without copyright and license information. Please refer @@ -461,7 +461,7 @@ class HyperShellBoundary : public HyperBallBoundary * * @ingroup boundary * - * @author Wolfgang Bangerth, 2000 + * @author Wolfgang Bangerth, 2000, 2009 */ template class HalfHyperShellBoundary : public HyperShellBoundary @@ -471,8 +471,17 @@ class HalfHyperShellBoundary : public HyperShellBoundary * Constructor. The center of the * spheres defaults to the * origin. - */ - HalfHyperShellBoundary (const Point ¢er = Point()); + * + * If the radii are not specified, the + * class tries to infer them from the + * location of points on the + * boundary. This works in 2d, but not in + * 3d. As a consequence, in 3d these + * radii must be given. + */ + HalfHyperShellBoundary (const Point ¢er = Point(), + const double inner_radius = -1, + const double outer_radius = -1); /** * Construct a new point on a line. @@ -525,6 +534,13 @@ class HalfHyperShellBoundary : public HyperShellBoundary virtual void get_normals_at_vertices (const typename Triangulation::face_iterator &face, typename Boundary::FaceVertexNormals &face_vertex_normals) const; + + private: + /** + * Inner and outer radii of the shell. + */ + const double inner_radius; + const double outer_radius; }; diff --git a/deal.II/deal.II/source/grid/tria_boundary_lib.cc b/deal.II/deal.II/source/grid/tria_boundary_lib.cc index 139d4540bb..803508b3b7 100644 --- a/deal.II/deal.II/source/grid/tria_boundary_lib.cc +++ b/deal.II/deal.II/source/grid/tria_boundary_lib.cc @@ -2,7 +2,7 @@ // $Id$ // Version: $Name$ // -// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 by the deal.II authors +// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2009 by the deal.II authors // // This file is subject to QPL and may not be distributed // without copyright and license information. Please refer @@ -694,7 +694,8 @@ get_normals_at_vertices (const typename Triangulation::face_iterator &face, template -HyperShellBoundary::HyperShellBoundary (const Point ¢er) : +HyperShellBoundary::HyperShellBoundary (const Point ¢er) + : HyperBallBoundary(center, 0.) { this->compute_radius_automatically=true; @@ -707,9 +708,20 @@ HyperShellBoundary::HyperShellBoundary (const Point ¢er) : template -HalfHyperShellBoundary::HalfHyperShellBoundary (const Point ¢er) : - HyperShellBoundary (center) -{} +HalfHyperShellBoundary::HalfHyperShellBoundary (const Point ¢er, + const double inner_radius, + const double outer_radius) + : + HyperShellBoundary (center), + inner_radius (inner_radius), + outer_radius (outer_radius) +{ + if (dim > 2) + Assert ((inner_radius >= 0) && + (outer_radius > 0) && + (outer_radius > inner_radius), + ExcMessage ("Inner and outer radii must be specified explicitly in 3d.")); +} @@ -718,19 +730,61 @@ Point HalfHyperShellBoundary:: get_new_point_on_line (const typename Triangulation::line_iterator &line) const { - // first check whether the two end - // points of the line are on the - // axis of symmetry. if so, then - // return the mid point - if ((line->vertex(0)(0) == this->center(0)) && - (line->vertex(1)(0) == this->center(0))) - return (line->vertex(0) + line->vertex(1))/2; + switch (dim) + { + // in 2d, first check whether the two + // end points of the line are on the + // axis of symmetry. if so, then return + // the mid point + case 2: + { + if ((line->vertex(0)(0) == this->center(0)) + && + (line->vertex(1)(0) == this->center(0))) + return (line->vertex(0) + line->vertex(1))/2; + else + // otherwise we are on the outer or + // inner part of the shell. proceed + // as in the base class + return HyperShellBoundary::get_new_point_on_line (line); + } + + // in 3d, a line is a straight + // line if it is on the symmetry + // plane and if not both of its + // end points are on either the + // inner or outer sphere + case 3: + { + + if (((line->vertex(0)(0) == this->center(0)) + && + (line->vertex(1)(0) == this->center(0))) + && + !(((std::fabs (line->vertex(0).distance (this->center) + - inner_radius) < 1e-12 * outer_radius) + && + (std::fabs (line->vertex(1).distance (this->center) + - inner_radius) < 1e-12 * outer_radius)) + || + ((std::fabs (line->vertex(0).distance (this->center) + - outer_radius) < 1e-12 * outer_radius) + && + (std::fabs (line->vertex(1).distance (this->center) + - outer_radius) < 1e-12 * outer_radius)))) + return (line->vertex(0) + line->vertex(1))/2; + else + // otherwise we are on the outer or + // inner part of the shell. proceed + // as in the base class + return HyperShellBoundary::get_new_point_on_line (line); + } + + default: + Assert (false, ExcNotImplemented()); + } - - // otherwise we are on the outer or - // inner part of the shell. proceed - // as in the base class - return HyperShellBoundary::get_new_point_on_line (line); + return Point(); } @@ -755,16 +809,46 @@ Point HalfHyperShellBoundary:: get_new_point_on_quad (const typename Triangulation::quad_iterator &quad) const { - // same thing as for the new point - // on the line + // if this quad is on the symmetry plane, + // take the center point and project it + // outward to the same radius as the + // centers of the two radial lines if ((quad->vertex(0)(0) == this->center(0)) && (quad->vertex(1)(0) == this->center(0)) && (quad->vertex(2)(0) == this->center(0)) && (quad->vertex(3)(0) == this->center(0))) - return (quad->vertex(0) + quad->vertex(1) + - quad->vertex(2) + quad->vertex(3) )/4; - + { + const Point quad_center = (quad->vertex(0) + quad->vertex(1) + + quad->vertex(2) + quad->vertex(3) )/4; + const Point quad_center_offset = quad_center - this->center; + + if (std::fabs (quad->line(0)->center().distance(this->center) - + quad->line(1)->center().distance(this->center)) + < 1e-12 * outer_radius) + { + // lines 0 and 1 are radial + const double needed_radius + = quad->line(0)->center().distance(this->center); + + return (this->center + + quad_center_offset/quad_center_offset.norm() * needed_radius); + } + else if (std::fabs (quad->line(2)->center().distance(this->center) - + quad->line(3)->center().distance(this->center)) + < 1e-12 * outer_radius) + { + // lines 2 and 3 are radial + const double needed_radius + = quad->line(2)->center().distance(this->center); + + return (this->center + + quad_center_offset/quad_center_offset.norm() * needed_radius); + } + else + Assert (false, ExcInternalError()); + } + // otherwise we are on the outer or // inner part of the shell. proceed // as in the base class @@ -779,15 +863,59 @@ HalfHyperShellBoundary:: get_intermediate_points_on_line (const typename Triangulation::line_iterator &line, std::vector > &points) const { - // check whether center of object is - // at x==0, since then it belongs - // to the plane part of the - // boundary - const Point line_center = line->center(); - if (line_center(0) == this->center(0)) - return StraightBoundary::get_intermediate_points_on_line (line, points); - else - return HyperShellBoundary::get_intermediate_points_on_line (line, points); + switch (dim) + { + // in 2d, first check whether the two + // end points of the line are on the + // axis of symmetry. if so, then return + // the mid point + case 2: + { + if ((line->vertex(0)(0) == this->center(0)) + && + (line->vertex(1)(0) == this->center(0))) + StraightBoundary::get_intermediate_points_on_line (line, points); + else + // otherwise we are on the outer or + // inner part of the shell. proceed + // as in the base class + HyperShellBoundary::get_intermediate_points_on_line (line, points); + } + + // in 3d, a line is a straight + // line if it is on the symmetry + // plane and if not both of its + // end points are on either the + // inner or outer sphere + case 3: + { + + if (((line->vertex(0)(0) == this->center(0)) + && + (line->vertex(1)(0) == this->center(0))) + && + !(((std::fabs (line->vertex(0).distance (this->center) + - inner_radius) < 1e-12 * outer_radius) + && + (std::fabs (line->vertex(1).distance (this->center) + - inner_radius) < 1e-12 * outer_radius)) + || + ((std::fabs (line->vertex(0).distance (this->center) + - outer_radius) < 1e-12 * outer_radius) + && + (std::fabs (line->vertex(1).distance (this->center) + - outer_radius) < 1e-12 * outer_radius)))) + StraightBoundary::get_intermediate_points_on_line (line, points); + else + // otherwise we are on the outer or + // inner part of the shell. proceed + // as in the base class + HyperShellBoundary::get_intermediate_points_on_line (line, points); + } + + default: + Assert (false, ExcNotImplemented()); + } } @@ -798,6 +926,8 @@ HalfHyperShellBoundary:: get_intermediate_points_on_quad (const typename Triangulation::quad_iterator &quad, std::vector > &points) const { + Assert (dim < 3, ExcNotImplemented()); + // check whether center of object is // at x==0, since then it belongs // to the plane part of the diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h index 69566252c3..9336435948 100644 --- a/deal.II/doc/news/changes.h +++ b/deal.II/doc/news/changes.h @@ -662,6 +662,15 @@ inconvenience this causes.

deal.II

    +
  1. +

    + New: The GridGenerator::half_hyper_shell function now also exists in 3d. + However, to use it with the HalfHyperShellBoundary class, one has to + pass inner and outer radii to the constructor. +
    + (Martin Kronbichler, WB, 2009/01/13) +

    +
  2. New: The restriction and embedding matrices for FE_Q are now implemented. diff --git a/tests/bits/grid_generator_06.cc b/tests/bits/grid_generator_06.cc new file mode 100644 index 0000000000..7d3dcc2d1b --- /dev/null +++ b/tests/bits/grid_generator_06.cc @@ -0,0 +1,95 @@ +//--------------------------------------------------------------------------- +// $Id$ +// Version: $Name$ +// +// Copyright (C) 2005, 2006, 2009 by the deal.II authors +// +// This file is subject to QPL and may not be distributed +// without copyright and license information. Please refer +// to the file deal.II/doc/license.html for the text and +// further information on this license. +// +//--------------------------------------------------------------------------- + + +// Test GridGenerator::half_hyper_shell in 2d and 3d, making sure that we get +// the boundary right. in 3d, we need to specify the inner and outer radii + +#include "../tests.h" +#include +#include +#include +#include +#include +#include + +#include +#include + + +template +void test_1(std::ostream& out) +{ + Point p1; + p1[0] = 2.; + if (dim>1) p1[1] = -1.; + if (dim>2) p1[2] = 0.; + + GridOut go; + deallog << "half_hyper_shell without specifying radii" << std::endl; + Triangulation tr; + GridGenerator::half_hyper_shell(tr, p1, 4., 6.); + + if (dim == 2) + { + // test with now specifying the inner and + // outer radius + static HalfHyperShellBoundary boundary (p1); + tr.set_boundary (0, boundary); + + tr.refine_global (2); + + go.write_gnuplot(tr, out); + } +} + +template +void test_2(std::ostream& out) +{ + Point p1; + p1[0] = 2.; + if (dim>1) p1[1] = -1.; + if (dim>2) p1[2] = 0.; + + GridOut go; + deallog << "half_hyper_shell with specifying radii" << std::endl; + Triangulation tr; + GridGenerator::half_hyper_shell(tr, p1, 4., 6.); + + // test with now specifying the inner and + // outer radius + static HalfHyperShellBoundary boundary (p1, 4., 6.); + tr.set_boundary (0, boundary); + + tr.refine_global (1); + + go.write_gnuplot(tr, out); +} + + +int main() +{ + std::ofstream logfile("grid_generator_06/output"); + deallog.attach(logfile); + deallog.depth_console(0); + deallog.threshold_double(1.e-10); + + deallog.push("2d"); + test_1<2>(logfile); + test_2<2>(logfile); + deallog.pop(); + deallog.push("3d"); + test_1<3>(logfile); + test_2<3>(logfile); + deallog.pop(); +} diff --git a/tests/bits/grid_generator_06/cmp/generic b/tests/bits/grid_generator_06/cmp/generic new file mode 100644 index 0000000000..b17470eabe --- /dev/null +++ b/tests/bits/grid_generator_06/cmp/generic @@ -0,0 +1,2021 @@ + +DEAL:1d::hyper_cube +3.00000 0 0 +7.00000 0 0 + +DEAL:1d::subdivided_hyper_cube +1.00000 0 0 +3.00000 0 0 + +3.00000 0 0 +5.00000 0 0 + +5.00000 0 0 +7.00000 0 0 + +DEAL:1d::hyper_rectangle +2.00000 0 0 +3.00000 0 0 + +DEAL:1d::subdivided_hyper_rectangle +2.00000 0 1 +2.50000 0 1 + +2.50000 0 1 +3.00000 0 1 + +DEAL:2d::hyper_cube +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 3600 3600 + 8400 3600 + 8400 8400 + 3600 8400 + 3600 3600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 3600 + 8400 3600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 8400 3600 + 8400 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 8400 + 8400 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 3600 + 3600 8400 +DEAL:2d::subdivided_hyper_cube +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 1200 1200 + 3600 1200 + 3600 3600 + 1200 3600 + 1200 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 1200 1200 + 3600 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 1200 1200 + 1200 3600 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 3600 1200 + 6000 1200 + 6000 3600 + 3600 3600 + 3600 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 1200 + 6000 1200 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 6000 1200 + 8400 1200 + 8400 3600 + 6000 3600 + 6000 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 6000 1200 + 8400 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 8400 1200 + 8400 3600 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 1200 3600 + 3600 3600 + 3600 6000 + 1200 6000 + 1200 3600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 1200 3600 + 1200 6000 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 3600 3600 + 6000 3600 + 6000 6000 + 3600 6000 + 3600 3600 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 6000 3600 + 8400 3600 + 8400 6000 + 6000 6000 + 6000 3600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 8400 3600 + 8400 6000 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 1200 6000 + 3600 6000 + 3600 8400 + 1200 8400 + 1200 6000 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 1200 8400 + 3600 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 1200 6000 + 1200 8400 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 3600 6000 + 6000 6000 + 6000 8400 + 3600 8400 + 3600 6000 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 8400 + 6000 8400 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 6000 6000 + 8400 6000 + 8400 8400 + 6000 8400 + 6000 6000 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 8400 6000 + 8400 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 6000 8400 + 8400 8400 +DEAL:2d::hyper_rectangle +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 2400 -1200 + 3600 -1200 + 3600 2400 + 2400 2400 + 2400 -1200 +2 1 0 3 3 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 -1200 + 3600 -1200 +2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 -1200 + 3600 2400 +2 1 0 3 4 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 2400 + 3600 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 -1200 + 2400 2400 +DEAL:2d::subdivided_hyper_rectangle +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 2 900 0 25 0.0 0 0 -1 0 0 5 + 2400 -1200 + 3000 -1200 + 3000 0 + 2400 0 + 2400 -1200 +2 1 0 3 3 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 -1200 + 3000 -1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 -1200 + 2400 0 +2 3 0 1 0 2 900 0 25 0.0 0 0 -1 0 0 5 + 3000 -1200 + 3600 -1200 + 3600 0 + 3000 0 + 3000 -1200 +2 1 0 3 3 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3000 -1200 + 3600 -1200 +2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 -1200 + 3600 0 +2 3 0 1 0 4 900 0 25 0.0 0 0 -1 0 0 5 + 2400 0 + 3000 0 + 3000 1200 + 2400 1200 + 2400 0 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 0 + 2400 1200 +2 3 0 1 0 4 900 0 25 0.0 0 0 -1 0 0 5 + 3000 0 + 3600 0 + 3600 1200 + 3000 1200 + 3000 0 +2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 0 + 3600 1200 +2 3 0 1 0 4 900 0 25 0.0 0 0 -1 0 0 5 + 2400 1200 + 3000 1200 + 3000 2400 + 2400 2400 + 2400 1200 +2 1 0 3 4 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 2400 + 3000 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 1200 + 2400 2400 +2 3 0 1 0 4 900 0 25 0.0 0 0 -1 0 0 5 + 3000 1200 + 3600 1200 + 3600 2400 + 3000 2400 + 3000 1200 +2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 1200 + 3600 2400 +2 1 0 3 4 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3000 2400 + 3600 2400 +DEAL:2d::parallelogram +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 0 0 + 2400 -1200 + 6000 1200 + 3600 2400 + 0 0 +2 1 0 3 3 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 0 0 + 2400 -1200 +2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 -1200 + 6000 1200 +2 1 0 3 4 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 2400 + 6000 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 0 0 + 3600 2400 +DEAL:2d::enclosed_hyper_cube +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 6 900 0 25 0.0 0 0 -1 0 0 5 + 2400 2400 + 3600 2400 + 3600 3600 + 2400 3600 + 2400 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 2400 + 3600 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 2400 + 2400 3600 +2 3 0 1 0 5 900 0 25 0.0 0 0 -1 0 0 5 + 3600 2400 + 8400 2400 + 8400 3600 + 3600 3600 + 3600 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 2400 + 8400 2400 +2 3 0 1 0 7 900 0 25 0.0 0 0 -1 0 0 5 + 8400 2400 + 9600 2400 + 9600 3600 + 8400 3600 + 8400 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 8400 2400 + 9600 2400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 9600 2400 + 9600 3600 +2 3 0 1 0 2 900 0 25 0.0 0 0 -1 0 0 5 + 2400 3600 + 3600 3600 + 3600 8400 + 2400 8400 + 2400 3600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 3600 + 2400 8400 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 3600 3600 + 8400 3600 + 8400 8400 + 3600 8400 + 3600 3600 +2 3 0 1 0 3 900 0 25 0.0 0 0 -1 0 0 5 + 8400 3600 + 9600 3600 + 9600 8400 + 8400 8400 + 8400 3600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 9600 3600 + 9600 8400 +2 3 0 1 0 10 900 0 25 0.0 0 0 -1 0 0 5 + 2400 8400 + 3600 8400 + 3600 9600 + 2400 9600 + 2400 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 9600 + 3600 9600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 2400 8400 + 2400 9600 +2 3 0 1 0 9 900 0 25 0.0 0 0 -1 0 0 5 + 3600 8400 + 8400 8400 + 8400 9600 + 3600 9600 + 3600 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 9600 + 8400 9600 +2 3 0 1 0 11 900 0 25 0.0 0 0 -1 0 0 5 + 8400 8400 + 9600 8400 + 9600 9600 + 8400 9600 + 8400 8400 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 9600 8400 + 9600 9600 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 8400 9600 + 9600 9600 +DEAL:2d::hyper_ball +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + -145 -3745 + 4945 -3745 + 3454 -2254 + 1345 -2254 + -145 -3745 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -145 -3745 + 4945 -3745 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + -145 -3745 + 1345 -2254 + 1345 -145 + -145 1345 + -145 -3745 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -145 -3745 + -145 1345 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 1345 -2254 + 3454 -2254 + 3454 -145 + 1345 -145 + 1345 -2254 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 4945 -3745 + 4945 1345 + 3454 -145 + 3454 -2254 + 4945 -3745 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 4945 -3745 + 4945 1345 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + -145 1345 + 1345 -145 + 3454 -145 + 4945 1345 + -145 1345 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -145 1345 + 4945 1345 +DEAL:2d::cylinder +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + -3600 -1200 + 3600 -1200 + 3600 1200 + -3600 1200 + -3600 -1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -3600 -1200 + 3600 -1200 +2 1 0 3 3 -1 800 0 -1 0.0 0 0 -1 0 0 2 + 3600 -1200 + 3600 1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -3600 1200 + 3600 1200 +2 1 0 3 2 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -3600 -1200 + -3600 1200 +DEAL:2d::hyper_L +#FIG 3.2 +Landscape +Center +Inches +A4 +100.00 +Single +-3 +# generated by deal.II GridOut class +# reduce first number to scale up image +1200 2 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + -1200 -1200 + 0 -1200 + 0 0 + -1200 0 + -1200 -1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -1200 -1200 + 0 -1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 2 + -1200 -1200 + -1200 0 +2 3 0 1 0 1 900 0 25 0.0 0 0 -1 0 0 5 + 0 -1200 + 1200 -1200 + 1200 0 + 0 0 + 0 -1200 +2 1 0 3 1 -1 800 0 -1 0.0 0 0 -1 0 0 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