From: Timo Heister Date: Sun, 20 Mar 2016 14:50:29 +0000 (+0100) Subject: add volume torus and TorusManifold X-Git-Tag: v8.5.0-rc1~1185^2~2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=03f0947a66fd882729fe5529c643f99e0b0f0572;p=dealii.git add volume torus and TorusManifold --- diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h index a7395bba71..5b90ff144c 100644 --- a/include/deal.II/grid/grid_generator.h +++ b/include/deal.II/grid/grid_generator.h @@ -761,9 +761,18 @@ namespace GridGenerator /** - * Produce the surface meshing of the torus. The axis of the torus is the - * $y$-axis while the plane of the torus is the $x$-$z$ plane. The boundary - * of this object can be described by the TorusBoundary class. + * Produce the volume or surface mesh of a torus. The axis of the torus is + * the $y$-axis while the plane of the torus is the $x$-$z$ plane. The + * function is implemented + * + * If @p dim is 3, the mesh will be the volume of the torus. By default, + * the boundary faces will have manifold id 0 and you should attach a + * TorusManifold to it. The cells will have manifold id 1 and you should + * attach a SphericalManifold to it. + * + * If @p dim is 2, the mesh will describe the surface of the torus. All + * cells and faces will have manifold id 0 and you should attach a + * TorusManifold to it. * * @param tria The triangulation to be filled. * @@ -771,10 +780,14 @@ namespace GridGenerator * torus containing the loop of cells. Must be greater than @p r. * * @param r The inner radius of the torus. + * + * @note Implemented for Triangulation<2,3> and Triangulation<3,3>. */ - void torus (Triangulation<2,3> &tria, - const double R, - const double r); + template + void torus (Triangulation &tria, + const double R, + const double r); + /** diff --git a/include/deal.II/grid/manifold_lib.h b/include/deal.II/grid/manifold_lib.h index 21de7b0555..6ed4cd3dc6 100644 --- a/include/deal.II/grid/manifold_lib.h +++ b/include/deal.II/grid/manifold_lib.h @@ -309,6 +309,50 @@ private: }; +/** + * Manifold description for the surface of a Torus in three dimensions. The + * Torus is assumed to be in the x-z plane. The reference coordinate system + * is given by the angle $phi$ around the y axis, the angle $theta$ around + * the centerline of the torus, and the distance to the centerline $w$ + * (between 0 and 1). + * + * This class was developed to be used in conjunction with + * GridGenerator::torus. + * + * @ingroup manifold + * + * @author Timo Heister, 2016 + */ +template +class TorusManifold : public ChartManifold +{ +public: + static const int chartdim = 3; + static const int spacedim = 3; + + /** + * Constructor. Specify the radius of the centerline @p R and the radius + * of the torus itself (@p r). The variables have the same meaning as + * the parameters in GridGenerator::torus(). + */ + TorusManifold (const double R, const double r); + + /** + * Pull back operation. + */ + virtual Point + pull_back(const Point &p) const; + + /** + * Push forward operation. + */ + virtual Point + push_forward(const Point &chart_point) const; + +private: + double r, R; +}; + DEAL_II_NAMESPACE_CLOSE #endif diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc index 6ad89aa450..1236e0d1ea 100644 --- a/source/grid/grid_generator.cc +++ b/source/grid/grid_generator.cc @@ -582,12 +582,15 @@ namespace GridGenerator + template<> void - torus (Triangulation<2,3> &tria, - const double R, - const double r) + torus<2,3> (Triangulation<2,3> &tria, + const double R, + const double r) { - Assert (R>r, ExcMessage("Outer radius must be greater than inner radius.")); + Assert (R>r, ExcMessage("Outer radius R must be greater than the inner " + "radius r.")); + Assert (r>0.0, ExcMessage("The inner radius r must be positive.")); const unsigned int dim=2; const unsigned int spacedim=3; @@ -715,7 +718,32 @@ namespace GridGenerator tria.create_triangulation_compatibility (vertices, cells, SubCellData()); } - + template<> + void + torus<3,3> (Triangulation<3,3> &tria, + const double R, + const double r) + { + Assert (R>r, ExcMessage("Outer radius R must be greater than the inner " + "radius r.")); + Assert (r>0.0, ExcMessage("The inner radius r must be positive.")); + + // abuse the moebius function to generate a torus for us + GridGenerator::moebius(tria, + 6 /*n_cells*/, + 0 /*n_rotations*/, + R, + r); + + // rotate by 90 degrees around the x axis to make the torus sit in the + // x-z plane instead of the x-y plane to be consistent with the other + // torus() function. + GridTools::rotate(numbers::PI/2.0, 0, tria); + + // set manifolds as documented + tria.set_all_manifold_ids(1); + tria.set_all_manifold_ids_on_boundary(0); + } template<> void diff --git a/source/grid/manifold_lib.cc b/source/grid/manifold_lib.cc index 4740f4e65c..c3d37eb0b8 100644 --- a/source/grid/manifold_lib.cc +++ b/source/grid/manifold_lib.cc @@ -332,6 +332,49 @@ FunctionManifold::pull_back(const Point &space_ return result; } + + +template +Point<3> +TorusManifold::pull_back(const Point<3> &p) const +{ + double x = p(0); + double z = p(1); + double y = p(2); + double phi = atan2(y, x); + double theta = atan2(z, std::sqrt(x*x+y*y)-R); + double w = std::sqrt((pow(y-sin(phi)*R, 2.0)+pow(x-cos(phi)*R, 2.0)+z*z))/r; + return Point<3>(phi, theta, w); +} + +template +Point<3> +TorusManifold::push_forward(const Point<3> &chart_point) const +{ + double phi = chart_point(0); + double theta = chart_point(1); + double w = chart_point(2); + + return Point<3>(cos(phi)*R + r*w*cos(theta)*cos(phi), + r*w*sin(theta), + sin(phi)*R + r*w*cos(theta)*sin(phi) + ); +} + + +template +TorusManifold::TorusManifold (const double R, const double r) + : ChartManifold (Point<3>(2*numbers::PI, 2*numbers::PI, 0.0)), + r(r), + R(R) +{ + Assert (R>r, ExcMessage("Outer radius R must be greater than the inner " + "radius r.")); + Assert (r>0.0, ExcMessage("inner radius must be positive.")); +} + + + // explicit instantiations #include "manifold_lib.inst" diff --git a/source/grid/manifold_lib.inst.in b/source/grid/manifold_lib.inst.in index eaaf53d08d..f38840b6ce 100644 --- a/source/grid/manifold_lib.inst.in +++ b/source/grid/manifold_lib.inst.in @@ -24,7 +24,9 @@ for (deal_II_dimension : DIMENSIONS; deal_II_space_dimension : SPACE_DIMENSIONS template class FunctionManifold; template class FunctionManifold; template class FunctionManifold; +#endif +#if deal_II_dimension == deal_II_space_dimension + template class TorusManifold; #endif } - diff --git a/tests/grid/torus_01.cc b/tests/grid/torus_01.cc new file mode 100644 index 0000000000..ec5d20d066 --- /dev/null +++ b/tests/grid/torus_01.cc @@ -0,0 +1,67 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2016 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE at +// the top level of the deal.II distribution. +// +// --------------------------------------------------------------------- + +// test GridTools::torus() and TorusManifold + +#include "../tests.h" +#include +#include +#include +#include +#include +#include + +#include +#include + + +template +void test (); + +template <> +void test<3,3> () +{ + const int dim = 3; + const int spacedim = 3; + Triangulation triangulation; + + GridGenerator::torus(triangulation, 1.0, 0.4); + + static const SphericalManifold<3> desc_sphere; + static const TorusManifold<3> desc_torus(1.0, 0.4); + triangulation.set_manifold (0, desc_torus); + triangulation.set_manifold (1, desc_sphere); + + triangulation.refine_global(1); + triangulation.begin_active()->set_refine_flag(); + triangulation.execute_coarsening_and_refinement (); + + std::ofstream out ("grid-1.vtk"); + GridOut grid_out; + grid_out.write_vtk (triangulation, out); + + + GridOut().write_gnuplot (triangulation, deallog.get_file_stream()); +} + + +int main () +{ + initlog (); + + test<3,3> (); + + return 0; +} diff --git a/tests/grid/torus_01.output b/tests/grid/torus_01.output new file mode 100644 index 0000000000..6a3aa7328d --- /dev/null +++ b/tests/grid/torus_01.output @@ -0,0 +1,1321 @@ + +0.641421 0.282843 1.11097 1 0 +0.500000 0.400000 0.866025 1 0 +0.358579 0.282843 0.621076 1 0 +0.520201 4.33154e-17 0.901014 1 0 +0.641421 0.282843 1.11097 1 0 + +1.11097 0.282843 0.641421 1 0 +0.866025 0.400000 0.500000 1 0 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