DEAL_II_NAMESPACE_OPEN
/**
- * Manifold description for a spherical space coordinate system.
+ * Manifold description for a polar coordinate system.
*
* You can use this Manifold object to describe any sphere, circle,
- * hypersphere or hyperdisc in two or three dimensions, both as a co-dimension
- * one manifold descriptor or as co-dimension zero manifold descriptor.
+ * hypersphere or hyperdisc in two or three dimensions, both as a
+ * co-dimension one manifold descriptor or as co-dimension zero
+ * manifold descriptor, provided that the north and south poles (in
+ * three dimensions) are excluded from the Manifold (as they are
+ * singular).
*
* The two template arguments match the meaning of the two template arguments
* in Triangulation<dim, spacedim>, however this Manifold can be used to
* describe both thin and thick objects, and the behavior is identical when
- * dim <= spacedim, i.e., the functionality of SphericalManifold<2,3> is
- * identical to SphericalManifold<3,3>.
- *
- * The two dimensional implementation of this class works by transforming
- * points to spherical coordinates, taking the average in that coordinate
- * system, and then transforming back the point to Cartesian coordinates. For
- * the three dimensional case, we use a simpler approach: we take the average
- * of the norm of the points, and use this value to shift the average point
- * along the radial direction. In order for this manifold to work correctly,
- * it cannot be attached to cells containing the center of the coordinate
- * system. This point is a singular point of the coordinate transformation,
- * and there taking averages does not make any sense.
+ * dim <= spacedim, i.e., the functionality of PolarManifold<2,3> is
+ * identical to PolarManifold<3,3>.
*
- * This class is used in step-1 and step-2 to describe the boundaries of
- * circles. Its use is also discussed in the results section of step-6.
+ * This class works by transforming points to polar coordinates (in
+ * both two and three dimensions), taking the average in that
+ * coordinate system, and then transforming back the point to
+ * Cartesian coordinates. In order for this manifold to work
+ * correctly, it cannot be attached to cells containing the center of
+ * the coordinate system or the north and south poles in three
+ * dimensions. These points are singular points of the coordinate
+ * transformation, and taking averages around these points does not
+ * make any sense.
*
* @ingroup manifold
*
- * @author Luca Heltai, 2014
+ * @author Luca Heltai, Mauro Bardelloni, 2014-2016
*/
template <int dim, int spacedim = dim>
-class SphericalManifold : public ChartManifold<dim, spacedim, spacedim>
+class PolarManifold : public ChartManifold<dim, spacedim, spacedim>
{
public:
/**
* it takes the middle point, and project it along the radius using the
* average radius of the surrounding points.
*/
- SphericalManifold(const Point<spacedim> center = Point<spacedim>());
+ PolarManifold(const Point<spacedim> center = Point<spacedim>());
/**
* Pull back the given point from the Euclidean space. Will return the polar
virtual Point<spacedim>
push_forward(const Point<spacedim> &chart_point) const;
-
/**
* Given a point in the spacedim dimensional Euclidean space, this
* method returns the derivatives of the function $F$ that maps from
DerivativeForm<1,spacedim,spacedim>
push_forward_gradient(const Point<spacedim> &chart_point) const;
-
- /**
- * Let the new point be the average sum of surrounding vertices.
- *
- * In the two dimensional implementation, we use the pull_back and
- * push_forward mechanism. For three dimensions, this does not work well, so
- * we overload the get_new_point function directly.
- */
- virtual Point<spacedim>
- get_new_point(const Quadrature<spacedim> &quad) const;
-
/**
* The center of the spherical coordinate system.
*/
};
+/**
+ * Manifold description for a spherical space coordinate system.
+ *
+ * You can use this Manifold object to describe any sphere, circle,
+ * hypersphere or hyperdisc in two or three dimensions, both as a co-dimension
+ * one manifold descriptor or as co-dimension zero manifold descriptor.
+ *
+ * The two template arguments match the meaning of the two template arguments
+ * in Triangulation<dim, spacedim>, however this Manifold can be used to
+ * describe both thin and thick objects, and the behavior is identical when
+ * dim <= spacedim, i.e., the functionality of SphericalManifold<2,3> is
+ * identical to SphericalManifold<3,3>.
+ *
+ * While PolarManifold reflects the usual notion of polar coordinates,
+ * it may not be suitable for domains that contain either the north or
+ * south poles.
+ * Consider for istance the pair of points \f$x_1=(1,\pi/3,0)\f$ and
+ * \f$x_2=(1,\pi/3,\pi)\f$.
+ * These two points would be connented (using a PolarManifold) by the curve
+ * \$[
+ * \begin{align}
+ * s: [0,1] & \rightarrow & \mathbb S^3 \\
+ * t & \mapsto & (1,\pi/3,0) + (0,0,t\pi)
+ * \$]
+ * This curve is not a geodesic on the sphere, and it is not how we
+ * would choose a curve on the sphere. A better one would be the one
+ * passing through the North pole:
+ * \[
+ * s(t) = x_1 \cos(\alpha(t)) + \kappa \times x_1 \sin(\alpha(t)) +
+ * \kappa ( \kappa \cdot x_1) (1-\cos(\alpha(t))).
+ * \]
+ * where $\kappa = \frac{x_1 \times \x_2}{\Vert x_1 \times \x_2 \Vert}$
+ * and $\alpha(t) = t * \arccos(x_1 * x_2) $ for $t\in[0,1]$.
+ * Indeed, this is a geodesic, and it is the natural choice when
+ * connecting points on the surface of the sphere.
+ *
+ * This class implements a Manifold that joins any two points in space
+ * by first projecting them on the surface of a sphere with unit
+ * radius, then connecting them with a geodesic, and finally rescaling
+ * the final radius so that the resulting one is the weighted average
+ * of the starting radii. This Manifold is identical to PolarManifold
+ * in dimension two, while for dimension three it returns points that
+ * are more uniformly distributed on the sphere, and it is invariant
+ * with respect to rotations of the coordinate system, therefore
+ * avoiding the problems that PolarManifold has at the poles.
+ *
+ * For mathematical reasons, it is impossible to construct a unique
+ * map of a sphere using only geodesic curves, and therefore, using
+ * this class with MappingManifold is discouraged. If you use this
+ * Manifold to describe the geometry of a sphere, you should use
+ * MappingQ as the underlying mapping, and not MappingManifold.
+ *
+ * @ingroup manifold
+ *
+ * @author Mauro Bardelloni, Luca Heltai, 2016
+ */
+template <int dim, int spacedim = dim>
+class SphericalManifold : public Manifold<dim, spacedim>
+{
+public:
+ /**
+ * The Constructor takes the center of the spherical coordinates.
+ */
+ SphericalManifold(const Point<spacedim> center = Point<spacedim>());
+
+ /**
+ * Given any two points in space, first project them on the surface
+ * of a sphere with unit radius, then connect them with a geodesic
+ * and find the intermediate point, and finally rescale the final
+ * radius so that the resulting one is the convex combination of the
+ * starting radii.
+ */
+ virtual
+ Point<spacedim>
+ get_new_point(const Point<spacedim> &p1,
+ const Point<spacedim> &p2,
+ const double w) const;
+
+ /**
+ * Compute the derivative of the get_new_point function with
+ * parameter w equal to zero.
+ */
+ virtual
+ Tensor<1,spacedim>
+ get_tangent_vector (const Point<spacedim> &x1,
+ const Point<spacedim> &x2) const;
+
+
+ /**
+ * Return a point on the spherical manifold which is intermediate
+ * with respect to the surrounding points.
+ */
+ virtual
+ Point<spacedim>
+ project_to_manifold (const std::vector<Point<spacedim> > &vertices,
+ const Point<spacedim> &candidate) const;
+
+ /**
+ * The center of the spherical coordinate system.
+ */
+ const Point<spacedim> center;
+};
+
+
/**
* Cylindrical Manifold description. In three dimensions, points are
* transformed using a cylindrical coordinate system along the <tt>x-</tt>,
DEAL_II_NAMESPACE_OPEN
+// ============================================================
+// PolarManifold
+// ============================================================
+
template <int dim, int spacedim>
-SphericalManifold<dim,spacedim>::SphericalManifold(const Point<spacedim> center):
- ChartManifold<dim,spacedim,spacedim>(SphericalManifold<dim,spacedim>::get_periodicity()),
+PolarManifold<dim,spacedim>::PolarManifold(const Point<spacedim> center):
+ ChartManifold<dim,spacedim,spacedim>(PolarManifold<dim,spacedim>::get_periodicity()),
center(center)
{}
-
-
template <int dim, int spacedim>
Tensor<1,spacedim>
-SphericalManifold<dim,spacedim>::get_periodicity()
+PolarManifold<dim,spacedim>::get_periodicity()
{
Tensor<1,spacedim> periodicity;
// In two dimensions, theta is periodic.
return periodicity;
}
-
-template <int dim, int spacedim>
-Point<spacedim>
-SphericalManifold<dim,spacedim>::get_new_point(const Quadrature<spacedim> &quad) const
-{
- if (spacedim == 2)
- return ChartManifold<dim,spacedim,spacedim>::get_new_point(quad);
- else
- {
- double rho_average = 0;
- Point<spacedim> mid_point;
- for (unsigned int i=0; i<quad.size(); ++i)
- {
- rho_average += quad.weight(i)*(quad.point(i)-center).norm();
- mid_point += quad.weight(i)*quad.point(i);
- }
- // Project the mid_point back to the right location
- Tensor<1,spacedim> R = mid_point-center;
- // Scale it to have radius rho_average
- R *= rho_average/R.norm();
- // And return it.
- return center+R;
- }
-}
-
-
-
template <int dim, int spacedim>
Point<spacedim>
-SphericalManifold<dim,spacedim>::push_forward(const Point<spacedim> &spherical_point) const
+PolarManifold<dim,spacedim>::push_forward(const Point<spacedim> &spherical_point) const
{
Assert(spherical_point[0] >=0.0,
ExcMessage("Negative radius for given point."));
template <int dim, int spacedim>
Point<spacedim>
-SphericalManifold<dim,spacedim>::pull_back(const Point<spacedim> &space_point) const
+PolarManifold<dim,spacedim>::pull_back(const Point<spacedim> &space_point) const
{
const Tensor<1,spacedim> R = space_point-center;
const double rho = R.norm();
return p;
}
-
template <int dim, int spacedim>
DerivativeForm<1,spacedim,spacedim>
-SphericalManifold<dim,spacedim>::push_forward_gradient(const Point<spacedim> &spherical_point) const
+PolarManifold<dim,spacedim>::push_forward_gradient(const Point<spacedim> &spherical_point) const
{
Assert(spherical_point[0] >= 0.0,
ExcMessage("Negative radius for given point."));
return DX;
}
+// ============================================================
+// SphericalManifold
+// ============================================================
+
+template <int dim, int spacedim>
+SphericalManifold<dim,spacedim>::SphericalManifold(const Point<spacedim> center):
+ center(center)
+{}
+
+template <int dim, int spacedim>
+Point<spacedim>
+SphericalManifold<dim,spacedim>::
+get_new_point (const Point<spacedim> &p1,
+ const Point<spacedim> &p2,
+ const double w) const
+{
+ Assert(w >=0.0 && w <= 1.0,
+ ExcMessage("w should be in the range [0.0,1.0]."));
+
+ if ( p1 == p2 ) return p1;
+
+ const Tensor<1,spacedim> v1 = p1 - center;
+ const Tensor<1,spacedim> v2 = p2 - center;
+ const double r1 = v1.norm();
+ const double r2 = v2.norm();
+
+ // Find the angle gamma described by v1 and v2:
+ const double gamma = std::acos((v1*v2)/(r1*r2));
+
+ // Find the angle sigma that correspont to archlengh equal to w
+ const double sigma = (1-w) * gamma;
+
+ // Versor with the same direction of v1
+ const Tensor<1,spacedim> t = v1/r1;
+ // Normal to v1 in the plane described by v1,v2,and the origin.
+ Tensor<1,spacedim> n = v2 - (v2*t)*t;
+ n = n/n.norm();
+
+ // Find the point Q along O,v1 such that
+ // P1,V,P2 has measure sigma.
+ const Tensor<1,spacedim> P = std::cos(sigma) * t + std::sin(sigma) * n;
+
+ // Project this point on the manifold.
+ return Point<spacedim>(center + (w*r1+(1-w)*r2)*P);
+}
+
+template <int dim, int spacedim>
+Tensor<1,spacedim>
+SphericalManifold<dim,spacedim>::
+get_tangent_vector (const Point<spacedim> &p1,
+ const Point<spacedim> &p2) const
+{
+ Assert(p1 != p2,
+ ExcMessage("p1 and p2 should not concide."));
+
+ const double r1 = (p1 - center).norm();
+ const double r2 = (p2 - center).norm();
+ const Tensor<1,spacedim> e1 = (p1 - center)/r1;
+ const Tensor<1,spacedim> e2 = (p2 - center)/r2;
+
+ // Tangent vector to the unit sphere along the geodesic given by e1 and e2.
+ Tensor<1,spacedim> tg = (e2-(e2*e1)*e1);
+ tg = tg / tg.norm();
+
+ const double gamma = std::acos(e1*e2);
+
+ return (r1-r2)*e1 + r1*gamma*tg;
+}
+
+template <int dim, int spacedim>
+Point<spacedim>
+SphericalManifold<dim,spacedim>::
+project_to_manifold (const std::vector<Point<spacedim> > &vertices,
+ const Point<spacedim> &candidate) const
+{
+ double rho = 0.0;
+ for (unsigned int i = 0; i<vertices.size(); i++)
+ rho += (vertices[i]-center).norm();
+ rho /= (1.0*vertices.size());
+ return center+(rho/(candidate-center).norm())*(candidate-center);
+}
+
// ============================================================
// CylindricalManifold
// ============================================================
for (deal_II_dimension : DIMENSIONS; deal_II_space_dimension : SPACE_DIMENSIONS)
{
#if deal_II_dimension <= deal_II_space_dimension
+ template class PolarManifold<deal_II_dimension, deal_II_space_dimension>;
template class SphericalManifold<deal_II_dimension, deal_II_space_dimension>;
template class CylindricalManifold<deal_II_dimension, deal_II_space_dimension>;
template class FunctionManifold<deal_II_dimension, deal_II_space_dimension, 1>;
-//---------------------------- function_manifold_chart ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+//-------------------------------------------------------------------
+// Copyright (C) 2016 by the deal.II authors.
//
// This file is subject to LGPL 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.
//
-//---------------------------- composition_manifold ---------------------------
+//-------------------------------------------------------------------
// Test the combination of simple ChartManifolds: parabolic + translation
-//---------------------------- function_manifold_chart ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+//-------------------------------------------------------------------
+// Copyright (C) 2016 by the deal.II authors.
//
// This file is subject to LGPL 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.
//
-//---------------------------- composition_manifold ---------------------------
+//-------------------------------------------------------------------
-// Test the combination of simple ChartManifolds: SphericalManifold +
+// Test the combination of simple ChartManifolds: PolarManifold +
// Translation
#include "../tests.h"
const int dim=2, spacedim=2;
- SphericalManifold<1,2> F;
+ PolarManifold<1,2> F;
FunctionManifold<2,2,2> G("x;y+1", "x;y-1");
CompositionManifold<2,2,2,2,1> manifold(F,G);
-//---------------------------- function_manifold_chart ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+//-------------------------------------------------------------------
+// Copyright (C) 2016 by the deal.II authors.
//
// This file is subject to LGPL 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.
//
-//---------------------------- composition_manifold ---------------------------
+//-------------------------------------------------------------------
-// Test the combination of simple ChartManifolds: SphericalManifold +
+// Test the combination of simple ChartManifolds: PolarManifold +
// Rotation
#include "../tests.h"
const int dim=2, spacedim=2;
- SphericalManifold<1,2> F;
+ PolarManifold<1,2> F;
std::map<std::string, double> constants;
constants["k"] = numbers::PI/3;
FunctionManifold<2,2,2> G("cos( k)*x -sin( k)*y; sin( k)*x+cos( k)*y",
-//---------------------------- function_manifold_chart ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+//-------------------------------------------------------------------
+// Copyright (C) 2016 by the deal.II authors.
//
// This file is subject to LGPL 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.
//
-//---------------------------- composition_manifold ---------------------------
+//-------------------------------------------------------------------
-// Stress periodicity in CompositionManifold. Compose SphericalManifold with
+// Stress periodicity in CompositionManifold. Compose PolarManifold with
// the identity, and make sure periodicity is respected.
#include "../tests.h"
Point<spacedim> center;
- SphericalManifold<dim,spacedim> S(center);
+ PolarManifold<dim,spacedim> S(center);
FunctionManifold<dim,spacedim,spacedim> F("x;y", "x;y");
CompositionManifold<dim> manifold(S,F);
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// 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 spherical manifold on hyper shells.
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref=1)
+{
+ deallog << "Testing dim " << dim
+ << ", spacedim " << spacedim << std::endl;
+
+ PolarManifold<dim,spacedim> manifold;
+
+ Triangulation<dim,spacedim> tria;
+ GridGenerator::hyper_shell (tria, Point<spacedim>(), .3, .6, 12);
+
+ for (typename Triangulation<dim,spacedim>::active_cell_iterator cell = tria.begin_active(); cell != tria.end(); ++cell)
+ {
+ cell->set_all_manifold_ids(1);
+ }
+
+ tria.set_manifold(1, manifold);
+ tria.refine_global(1);
+
+ GridOut gridout;
+ gridout.write_msh(tria, deallog.get_file_stream());
+
+ // char fname[50];
+ // sprintf(fname, "mesh_%d_%d.msh", dim, spacedim);
+ // std::ofstream of(fname);
+ // gridout.write_msh(tria, of);
+}
+
+int main ()
+{
+ std::ofstream logfile("output");
+ deallog.attach(logfile);
+ deallog.threshold_double(1.e-10);
+
+ test<2,2>();
+ test<3,3>();
+
+ return 0;
+}
+
--- /dev/null
+
+DEAL::Testing dim 2, spacedim 2
+$NOD
+72
+1 0.600000 0.00000 0
+2 0.519615 0.300000 0
+3 0.300000 0.519615 0
+4 3.67394e-17 0.600000 0
+5 -0.300000 0.519615 0
+6 -0.519615 0.300000 0
+7 -0.600000 7.34788e-17 0
+8 -0.519615 -0.300000 0
+9 -0.300000 -0.519615 0
+10 -1.10218e-16 -0.600000 0
+11 0.300000 -0.519615 0
+12 0.519615 -0.300000 0
+13 0.300000 0.00000 0
+14 0.259808 0.150000 0
+15 0.150000 0.259808 0
+16 1.83697e-17 0.300000 0
+17 -0.150000 0.259808 0
+18 -0.259808 0.150000 0
+19 -0.300000 3.67394e-17 0
+20 -0.259808 -0.150000 0
+21 -0.150000 -0.259808 0
+22 -5.51091e-17 -0.300000 0
+23 0.150000 -0.259808 0
+24 0.259808 -0.150000 0
+25 0.579555 0.155291 0
+26 0.450000 0.00000 0
+27 0.424264 0.424264 0
+28 0.389711 0.225000 0
+29 0.155291 0.579555 0
+30 0.225000 0.389711 0
+31 -0.155291 0.579555 0
+32 2.75546e-17 0.450000 0
+33 -0.424264 0.424264 0
+34 -0.225000 0.389711 0
+35 -0.579555 0.155291 0
+36 -0.389711 0.225000 0
+37 -0.579555 -0.155291 0
+38 -0.450000 5.51091e-17 0
+39 -0.424264 -0.424264 0
+40 -0.389711 -0.225000 0
+41 -0.155291 -0.579555 0
+42 -0.225000 -0.389711 0
+43 0.155291 -0.579555 0
+44 -8.26637e-17 -0.450000 0
+45 0.424264 -0.424264 0
+46 0.225000 -0.389711 0
+47 0.579555 -0.155291 0
+48 0.389711 -0.225000 0
+49 0.289778 0.0776457 0
+50 0.212132 0.212132 0
+51 0.0776457 0.289778 0
+52 -0.0776457 0.289778 0
+53 -0.212132 0.212132 0
+54 -0.289778 0.0776457 0
+55 -0.289778 -0.0776457 0
+56 -0.212132 -0.212132 0
+57 -0.0776457 -0.289778 0
+58 0.0776457 -0.289778 0
+59 0.212132 -0.212132 0
+60 0.289778 -0.0776457 0
+61 0.434667 0.116469 0
+62 0.318198 0.318198 0
+63 0.116469 0.434667 0
+64 -0.116469 0.434667 0
+65 -0.318198 0.318198 0
+66 -0.434667 0.116469 0
+67 -0.434667 -0.116469 0
+68 -0.318198 -0.318198 0
+69 -0.116469 -0.434667 0
+70 0.116469 -0.434667 0
+71 0.318198 -0.318198 0
+72 0.434667 -0.116469 0
+$ENDNOD
+$ELM
+48
+1 3 0 0 4 1 25 61 26
+2 3 0 0 4 25 2 28 61
+3 3 0 0 4 26 61 49 13
+4 3 0 0 4 61 28 14 49
+5 3 0 0 4 2 27 62 28
+6 3 0 0 4 27 3 30 62
+7 3 0 0 4 28 62 50 14
+8 3 0 0 4 62 30 15 50
+9 3 0 0 4 3 29 63 30
+10 3 0 0 4 29 4 32 63
+11 3 0 0 4 30 63 51 15
+12 3 0 0 4 63 32 16 51
+13 3 0 0 4 4 31 64 32
+14 3 0 0 4 31 5 34 64
+15 3 0 0 4 32 64 52 16
+16 3 0 0 4 64 34 17 52
+17 3 0 0 4 5 33 65 34
+18 3 0 0 4 33 6 36 65
+19 3 0 0 4 34 65 53 17
+20 3 0 0 4 65 36 18 53
+21 3 0 0 4 6 35 66 36
+22 3 0 0 4 35 7 38 66
+23 3 0 0 4 36 66 54 18
+24 3 0 0 4 66 38 19 54
+25 3 0 0 4 7 37 67 38
+26 3 0 0 4 37 8 40 67
+27 3 0 0 4 38 67 55 19
+28 3 0 0 4 67 40 20 55
+29 3 0 0 4 8 39 68 40
+30 3 0 0 4 39 9 42 68
+31 3 0 0 4 40 68 56 20
+32 3 0 0 4 68 42 21 56
+33 3 0 0 4 9 41 69 42
+34 3 0 0 4 41 10 44 69
+35 3 0 0 4 42 69 57 21
+36 3 0 0 4 69 44 22 57
+37 3 0 0 4 10 43 70 44
+38 3 0 0 4 43 11 46 70
+39 3 0 0 4 44 70 58 22
+40 3 0 0 4 70 46 23 58
+41 3 0 0 4 11 45 71 46
+42 3 0 0 4 45 12 48 71
+43 3 0 0 4 46 71 59 23
+44 3 0 0 4 71 48 24 59
+45 3 0 0 4 12 47 72 48
+46 3 0 0 4 47 1 26 72
+47 3 0 0 4 48 72 60 24
+48 3 0 0 4 72 26 13 60
+$ENDELM
+DEAL::Testing dim 3, spacedim 3
+$NOD
+150
+1 -0.173205 -0.173205 -0.173205
+2 0.173205 -0.173205 -0.173205
+3 -0.173205 0.173205 -0.173205
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+$ENDNOD
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--- /dev/null
+// ---------------------------------------------------------------------
+//
+// 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 that the flat manifold does what it should on a sphere.
+
+#include "../tests.h"
+
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref=1)
+{
+ PolarManifold<dim,spacedim> manifold;
+
+ Triangulation<dim,spacedim> tria;
+ GridGenerator::hyper_ball (tria);
+
+ typename Triangulation<dim,spacedim>::active_cell_iterator cell;
+
+ for (cell = tria.begin_active(); cell != tria.end(); ++cell)
+ cell->set_all_manifold_ids(1);
+
+ for (cell = tria.begin_active(); cell != tria.end(); ++cell)
+ {
+ if (cell->center().distance(Point<spacedim>()) < 1e-10)
+ cell->set_all_manifold_ids(0);
+ }
+
+ tria.set_manifold(1, manifold);
+ tria.refine_global(2);
+
+ GridOut gridout;
+ gridout.write_msh(tria, deallog.get_file_stream());
+}
+
+int main ()
+{
+ std::ofstream logfile("output");
+ deallog.attach(logfile);
+ deallog.threshold_double(1.e-10);
+
+ test<2,2>();
+ test<3,3>();
+
+ return 0;
+}
+
--- /dev/null
+
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--- /dev/null
+// ---------------------------------------------------------------------
+//
+// 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 the push_forward and pull_back mechanisms
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref=1)
+{
+ deallog << "Testing dim " << dim
+ << ", spacedim " << spacedim << std::endl;
+
+ PolarManifold<dim,spacedim> manifold;
+
+ Triangulation<dim,spacedim> tria;
+ Point<spacedim> p0;
+ Point<spacedim> p1;
+ p0[0] = .2;
+ p1[0] = 1;
+ p0[1] = .1;
+
+ if (spacedim == 2)
+ {
+ p1[1] = 2*numbers::PI-.1; // theta
+ }
+ else if (spacedim == 3)
+ {
+ p1[1] = numbers::PI-.1;
+ p1[2] = 2*numbers::PI-.1;
+ }
+
+ GridGenerator::hyper_rectangle (tria, p0, p1);
+ tria.refine_global(3);
+
+ const std::vector<Point<spacedim> > &vertices = tria.get_vertices();
+
+ for (unsigned int i=0; i<vertices.size(); ++i)
+ {
+ Point<spacedim> p0 = manifold.push_forward(vertices[i]);
+ Point<spacedim> p1 = manifold.pull_back(p0);
+
+ if (p1.distance(vertices[i]) > 1e-10)
+ deallog << "ERROR! d: " << p1.distance(vertices[i])
+ << " - " << p1 << " != " << vertices[i] << std::endl;
+ }
+
+
+
+}
+
+int main ()
+{
+ std::ofstream logfile("output");
+ deallog.attach(logfile);
+ deallog.threshold_double(1.e-10);
+
+ test<2,2>();
+ test<3,3>();
+
+ return 0;
+}
+
--- /dev/null
+
+DEAL::Testing dim 2, spacedim 2
+DEAL::Testing dim 3, spacedim 3
-//---------------------------- spherical_manifold_01.cc ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+// ---------------------------------------------------------------------
//
-// This file is subject to LGPL 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.
+// Copyright (C) 2016 by the deal.II authors
//
-//---------------------------- spherical_manifold_04.cc ---------------------------
+// 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 that the flat manifold does what it should on a sphere surface.
template <int dim, int spacedim>
void test(unsigned int ref=1)
{
- SphericalManifold<dim,spacedim> manifold;
+ PolarManifold<dim,spacedim> manifold;
Triangulation<spacedim, spacedim> volume_tria;
Triangulation<dim, spacedim> tria;
-//---------------------------- spherical_manifold_01.cc ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+// ---------------------------------------------------------------------
//
-// This file is subject to LGPL 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.
+// Copyright (C) 2016 by the deal.II authors
//
-//---------------------------- spherical_manifold_04.cc ---------------------------
+// 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 that the flat manifold does what it should on a sphere surface.
deallog << "Testing dim=" << dim <<", degree="
<< degree << std::endl;
- SphericalManifold<dim> manifold;
+ PolarManifold<dim> manifold;
Triangulation<dim> tria;
GridGenerator::hyper_shell(tria, Point<dim>(), .4, .6, 6);
typename Triangulation<dim>::active_cell_iterator cell;
deallog << "dim=" << dim << ", spacedim=" << spacedim << std::endl;
Point<spacedim> center;
- static const SphericalManifold<dim,spacedim> manifold(center);
+ static const PolarManifold<dim,spacedim> manifold(center);
// Go from 0,1 to 1,0
Point<spacedim> p0,p1;
//
// ---------------------------------------------------------------------
-// test get_normals_at_vertices for a SphericalManifold.
+// test get_normals_at_vertices for a PolarManifold.
#include "../tests.h"
#include <deal.II/base/logstream.h>
GridGenerator::hyper_ball(triangulation);
- static const SphericalManifold<dim, spacedim> manifold;
+ static const PolarManifold<dim, spacedim> manifold;
triangulation.set_all_manifold_ids_on_boundary(0);
triangulation.set_manifold (0, manifold);
//
// ---------------------------------------------------------------------
-// Check SphericalManifold for periodicity issues: check that the
+// Check PolarManifold for periodicity issues: check that the
// spherical manifold finds the right intermediate points independent
// on the number of surrounding points
Point<2> center(.5, .5);
double radius = center.norm();
- const SphericalManifold<2,2> manifold(center);
+ const PolarManifold<2,2> manifold(center);
// Some points on the circle, that would cross the periodicity
// boundary
points.push_back(Point<2>(0.0, 0.0));
points.push_back(Point<2>(1.0, 0.0));
+
// And the weights
std::vector<double> weights(2);
//
// ---------------------------------------------------------------------
-// Check SphericalManifold on faces.
+// Check PolarManifold on faces.
#include "../tests.h"
Point<spacedim> center = cell->center();
double radius = center.distance(cell->vertex(0));
- static const SphericalManifold<dim,spacedim> manifold(cell->center());
+ static const PolarManifold<dim,spacedim> manifold(cell->center());
triangulation.set_all_manifold_ids(0);
triangulation.set_manifold (0, manifold);
-//---------------------------- spherical_manifold_01.cc ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+// ---------------------------------------------------------------------
//
-// This file is subject to LGPL 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.
+// Copyright (C) 2016 by the deal.II authors
//
-//---------------------------- spherical_manifold_01.cc ---------------------------
-
+// 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 spherical manifold on hyper shells.
+// Check SphericalManifold for get_new_point and get_tangent_vector issues.
#include "../tests.h"
-#include <fstream>
-#include <deal.II/base/logstream.h>
-
-// all include files you need here
-#include <deal.II/grid/tria.h>
-#include <deal.II/grid/tria_accessor.h>
-#include <deal.II/grid/tria_iterator.h>
-#include <deal.II/grid/grid_generator.h>
-#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/base/utilities.h>
#include <deal.II/grid/manifold_lib.h>
-#include <deal.II/grid/grid_out.h>
+#include <deal.II/base/quadrature.h>
-// Helper function
-template <int dim, int spacedim>
-void test(unsigned int ref=1)
+int
+main()
{
- deallog << "Testing dim " << dim
- << ", spacedim " << spacedim << std::endl;
-
- SphericalManifold<dim,spacedim> manifold;
-
- Triangulation<dim,spacedim> tria;
- GridGenerator::hyper_shell (tria, Point<spacedim>(), .3, .6, 12);
-
- for (typename Triangulation<dim,spacedim>::active_cell_iterator cell = tria.begin_active(); cell != tria.end(); ++cell)
- {
- cell->set_all_manifold_ids(1);
- }
-
- tria.set_manifold(1, manifold);
- tria.refine_global(1);
-
- GridOut gridout;
- gridout.write_msh(tria, deallog.get_file_stream());
-
- // char fname[50];
- // sprintf(fname, "mesh_%d_%d.msh", dim, spacedim);
- // std::ofstream of(fname);
- // gridout.write_msh(tria, of);
+ initlog();
+
+ // // Center and radius of the Ball
+ // double radius = center.norm();
+
+ {
+ Point<2> center(0.0, 0.0);
+ const SphericalManifold<2,2> manifold(center);
+
+ Point<2> P1(1.0, 0.0);
+ Point<2> P2(0.0, 1.0);
+
+ Point<2> Q = manifold.get_new_point(P1, P2, .5);
+
+ deallog << "=================================" << std::endl;;
+ deallog << manifold.get_new_point(P1, P2, .125) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .25) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .375) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .5) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .625) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .75) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .875) << std::endl;
+ deallog << "=================================" << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .25) << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .5) << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .75) << std::endl;
+ deallog << manifold.get_new_point(P1, P2,.5) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .25) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .5) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .75) << std::endl;
+ deallog << "=================================" << std::endl;
+ }
+
+ {
+ Point<2> center(0.0, 0.0);
+ const SphericalManifold<1,2> manifold(center);
+
+ Point<2> P1(1.0, 0.0);
+ Point<2> P2(0.0, 1.0);
+
+ Point<2> Q = manifold.get_new_point(P1, P2, .5);
+
+ deallog << "=================================" << std::endl;;
+ deallog << manifold.get_new_point(P1, P2, .125) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .25) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .375) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .5) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .625) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .75) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .875) << std::endl;
+ deallog << "=================================" << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .25) << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .5) << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .75) << std::endl;
+ deallog << manifold.get_new_point(P1, P2,.5) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .25) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .5) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .75) << std::endl;
+ deallog << "=================================" << std::endl;
+ }
+
+ {
+ Point<3> center(0.0, 0.0, 0.0);
+ const SphericalManifold<2,3> manifold(center);
+
+ Point<3> P1(1.0, 0.0, 0.0);
+ Point<3> P2(0.0, 0.0, 1.0);
+
+ Point<3> Q = manifold.get_new_point(P1, P2, .5);
+
+ deallog << "=================================" << std::endl;;
+ deallog << manifold.get_new_point(P1, P2, .125) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .25) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .375) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .5) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .625) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .75) << std::endl;
+ deallog << manifold.get_new_point(P1, P2, .875) << std::endl;
+ deallog << "=================================" << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .25) << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .5) << std::endl;
+ deallog << manifold.get_new_point(P1, Q, .75) << std::endl;
+ deallog << manifold.get_new_point(P1, P2,.5) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .25) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .5) << std::endl;
+ deallog << manifold.get_new_point(Q, P2, .75) << std::endl;
+ deallog << "=================================" << std::endl;
+ }
+
+ {
+ Point<3> center(0.0, 0.0, 0.0);
+ const SphericalManifold<3,3> manifold(center);
+
+ Point<3> P1(2.0, 0.0, 0.0);
+ Point<3> P2(0.0, std::sqrt(2), std::sqrt(2) );
+
+ Point<3> Q = manifold.get_new_point(P1, P2, .5);
+
+ const unsigned int num_points = 20;
+ deallog << "=================================" << std::endl;;
+ for (unsigned int i = 0; i<num_points; i++)
+ deallog << manifold.get_new_point(P1, P2, (1.0*i)/(num_points-1)) << std::endl;
+ deallog << "=================================" << std::endl;
+ }
+
+ {
+ Point<3> center(0.0, 0.0, 0.0);
+ const SphericalManifold<3,3> manifold(center);
+
+ Point<3> P1(1.0, 0.0, 0.0);
+ Point<3> P2(0.0, 1.0, 0.0);
+ Point<3> P3(0.0, 0.0, 1.0);
+
+ std::vector<Point<3> > points1(3);
+ std::vector<Point<3> > points2(3);
+ std::vector<Point<3> > points3(3);
+ std::vector<double > weights(3);
+
+ points1[0] = P1;
+ points1[1] = P2;
+ points1[2] = P3;
+
+ points2[0] = P2;
+ points2[1] = P1;
+ points2[2] = P3;
+
+ points3[0] = P2;
+ points3[1] = P3;
+ points3[2] = P1;
+
+ weights[0] = 1.0/3.0;
+ weights[1] = 1.0/3.0;
+ weights[2] = 1.0/3.0;
+
+ Quadrature<3> quad1(points1, weights);
+ Quadrature<3> quad2(points2, weights);
+ Quadrature<3> quad3(points3, weights);
+
+ Point<3> Q = manifold.get_new_point(quad1);
+ Point<3> S = manifold.get_new_point(quad2);
+ Point<3> T = manifold.get_new_point(quad3);
+
+ Point<3> P5(0.707107, 0.707107, 0.0);
+ Point<3> P4(0.0, 0.0, 1.0);
+ Point<3> R = manifold.get_new_point(P5, P4, 2.0/3.0);
+
+ deallog << "=================================" << std::endl;;
+ deallog << Q << std::endl;
+ deallog << S << std::endl;
+ deallog << T << std::endl;
+ deallog << R << std::endl;
+ deallog << "=================================" << std::endl;
+ }
+
+ // Quadrature (const std::vector< Point< dim > > &points, const std::vector< double > &weights);
+ return 0;
}
-int main ()
-{
- std::ofstream logfile("output");
- deallog.attach(logfile);
- deallog.threshold_double(1.e-10);
- test<2,2>();
- test<3,3>();
-
- return 0;
-}
-DEAL::Testing dim 2, spacedim 2
-$NOD
-72
-1 0.600000 0.00000 0
-2 0.519615 0.300000 0
-3 0.300000 0.519615 0
-4 3.67394e-17 0.600000 0
-5 -0.300000 0.519615 0
-6 -0.519615 0.300000 0
-7 -0.600000 7.34788e-17 0
-8 -0.519615 -0.300000 0
-9 -0.300000 -0.519615 0
-10 -1.10218e-16 -0.600000 0
-11 0.300000 -0.519615 0
-12 0.519615 -0.300000 0
-13 0.300000 0.00000 0
-14 0.259808 0.150000 0
-15 0.150000 0.259808 0
-16 1.83697e-17 0.300000 0
-17 -0.150000 0.259808 0
-18 -0.259808 0.150000 0
-19 -0.300000 3.67394e-17 0
-20 -0.259808 -0.150000 0
-21 -0.150000 -0.259808 0
-22 -5.51091e-17 -0.300000 0
-23 0.150000 -0.259808 0
-24 0.259808 -0.150000 0
-25 0.579555 0.155291 0
-26 0.450000 0.00000 0
-27 0.424264 0.424264 0
-28 0.389711 0.225000 0
-29 0.155291 0.579555 0
-30 0.225000 0.389711 0
-31 -0.155291 0.579555 0
-32 2.75546e-17 0.450000 0
-33 -0.424264 0.424264 0
-34 -0.225000 0.389711 0
-35 -0.579555 0.155291 0
-36 -0.389711 0.225000 0
-37 -0.579555 -0.155291 0
-38 -0.450000 5.51091e-17 0
-39 -0.424264 -0.424264 0
-40 -0.389711 -0.225000 0
-41 -0.155291 -0.579555 0
-42 -0.225000 -0.389711 0
-43 0.155291 -0.579555 0
-44 -8.26637e-17 -0.450000 0
-45 0.424264 -0.424264 0
-46 0.225000 -0.389711 0
-47 0.579555 -0.155291 0
-48 0.389711 -0.225000 0
-49 0.289778 0.0776457 0
-50 0.212132 0.212132 0
-51 0.0776457 0.289778 0
-52 -0.0776457 0.289778 0
-53 -0.212132 0.212132 0
-54 -0.289778 0.0776457 0
-55 -0.289778 -0.0776457 0
-56 -0.212132 -0.212132 0
-57 -0.0776457 -0.289778 0
-58 0.0776457 -0.289778 0
-59 0.212132 -0.212132 0
-60 0.289778 -0.0776457 0
-61 0.434667 0.116469 0
-62 0.318198 0.318198 0
-63 0.116469 0.434667 0
-64 -0.116469 0.434667 0
-65 -0.318198 0.318198 0
-66 -0.434667 0.116469 0
-67 -0.434667 -0.116469 0
-68 -0.318198 -0.318198 0
-69 -0.116469 -0.434667 0
-70 0.116469 -0.434667 0
-71 0.318198 -0.318198 0
-72 0.434667 -0.116469 0
-$ENDNOD
-$ELM
-48
-1 3 0 0 4 1 25 61 26
-2 3 0 0 4 25 2 28 61
-3 3 0 0 4 26 61 49 13
-4 3 0 0 4 61 28 14 49
-5 3 0 0 4 2 27 62 28
-6 3 0 0 4 27 3 30 62
-7 3 0 0 4 28 62 50 14
-8 3 0 0 4 62 30 15 50
-9 3 0 0 4 3 29 63 30
-10 3 0 0 4 29 4 32 63
-11 3 0 0 4 30 63 51 15
-12 3 0 0 4 63 32 16 51
-13 3 0 0 4 4 31 64 32
-14 3 0 0 4 31 5 34 64
-15 3 0 0 4 32 64 52 16
-16 3 0 0 4 64 34 17 52
-17 3 0 0 4 5 33 65 34
-18 3 0 0 4 33 6 36 65
-19 3 0 0 4 34 65 53 17
-20 3 0 0 4 65 36 18 53
-21 3 0 0 4 6 35 66 36
-22 3 0 0 4 35 7 38 66
-23 3 0 0 4 36 66 54 18
-24 3 0 0 4 66 38 19 54
-25 3 0 0 4 7 37 67 38
-26 3 0 0 4 37 8 40 67
-27 3 0 0 4 38 67 55 19
-28 3 0 0 4 67 40 20 55
-29 3 0 0 4 8 39 68 40
-30 3 0 0 4 39 9 42 68
-31 3 0 0 4 40 68 56 20
-32 3 0 0 4 68 42 21 56
-33 3 0 0 4 9 41 69 42
-34 3 0 0 4 41 10 44 69
-35 3 0 0 4 42 69 57 21
-36 3 0 0 4 69 44 22 57
-37 3 0 0 4 10 43 70 44
-38 3 0 0 4 43 11 46 70
-39 3 0 0 4 44 70 58 22
-40 3 0 0 4 70 46 23 58
-41 3 0 0 4 11 45 71 46
-42 3 0 0 4 45 12 48 71
-43 3 0 0 4 46 71 59 23
-44 3 0 0 4 71 48 24 59
-45 3 0 0 4 12 47 72 48
-46 3 0 0 4 47 1 26 72
-47 3 0 0 4 48 72 60 24
-48 3 0 0 4 72 26 13 60
-$ENDELM
-DEAL::Testing dim 3, spacedim 3
-$NOD
-150
-1 -0.173205 -0.173205 -0.173205
-2 0.173205 -0.173205 -0.173205
-3 -0.173205 0.173205 -0.173205
-4 0.173205 0.173205 -0.173205
-5 -0.173205 -0.173205 0.173205
-6 0.173205 -0.173205 0.173205
-7 -0.173205 0.173205 0.173205
-8 0.173205 0.173205 0.173205
-9 -0.300000 0.00000 0.00000
-10 0.300000 0.00000 0.00000
-11 0.00000 -0.300000 0.00000
-12 0.00000 0.300000 0.00000
-13 0.00000 0.00000 -0.300000
-14 0.00000 0.00000 0.300000
-15 -0.346410 -0.346410 -0.346410
-16 0.346410 -0.346410 -0.346410
-17 -0.346410 0.346410 -0.346410
-18 0.346410 0.346410 -0.346410
-19 -0.346410 -0.346410 0.346410
-20 0.346410 -0.346410 0.346410
-21 -0.346410 0.346410 0.346410
-22 0.346410 0.346410 0.346410
-23 -0.600000 0.00000 0.00000
-24 0.600000 0.00000 0.00000
-25 0.00000 -0.600000 0.00000
-26 0.00000 0.600000 0.00000
-27 0.00000 0.00000 -0.600000
-28 0.00000 0.00000 0.600000
-29 -0.266422 -0.0975173 -0.0975173
-30 -0.259808 -0.259808 -0.259808
-31 0.266422 -0.0975173 -0.0975173
-32 0.0975173 -0.266422 -0.0975173
-33 0.0975173 -0.0975173 -0.266422
-34 0.259808 -0.259808 -0.259808
-35 -0.266422 0.0975173 -0.0975173
-36 -0.0975173 0.266422 -0.0975173
-37 -0.259808 0.259808 -0.259808
-38 0.0975173 0.266422 -0.0975173
-39 0.259808 0.259808 -0.259808
-40 -0.266422 -0.0975173 0.0975173
-41 -0.0975173 -0.0975173 0.266422
-42 -0.259808 -0.259808 0.259808
-43 0.0975173 -0.0975173 0.266422
-44 0.259808 -0.259808 0.259808
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-95 0.00000 -0.212132 -0.212132
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-98 -0.399633 0.146276 -0.146276
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-126 -0.146276 0.146276 0.399633
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-135 -0.424264 -0.424264 0.00000
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-137 -0.424264 0.00000 -0.424264
-138 0.00000 0.424264 -0.424264
-139 -0.318198 -0.318198 0.00000
-140 -0.318198 0.00000 0.318198
-141 0.00000 -0.318198 0.318198
-142 0.318198 -0.318198 0.00000
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-146 0.318198 0.00000 -0.318198
-147 0.00000 0.318198 -0.318198
-148 -0.318198 0.318198 0.00000
-149 -0.318198 0.00000 -0.318198
-150 0.00000 -0.318198 -0.318198
-$ENDNOD
-$ELM
-96
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-96 5 0 0 8 150 119 83 129 121 30 15 87
-$ENDELM
+DEAL::=================================
+DEAL::0.195090 0.980785
+DEAL::0.382683 0.923880
+DEAL::0.555570 0.831470
+DEAL::0.707107 0.707107
+DEAL::0.831470 0.555570
+DEAL::0.923880 0.382683
+DEAL::0.980785 0.195090
+DEAL::=================================
+DEAL::0.831470 0.555570
+DEAL::0.923880 0.382683
+DEAL::0.980785 0.195090
+DEAL::0.707107 0.707107
+DEAL::0.195090 0.980785
+DEAL::0.382683 0.923880
+DEAL::0.555570 0.831470
+DEAL::=================================
+DEAL::=================================
+DEAL::0.195090 0.980785
+DEAL::0.382683 0.923880
+DEAL::0.555570 0.831470
+DEAL::0.707107 0.707107
+DEAL::0.831470 0.555570
+DEAL::0.923880 0.382683
+DEAL::0.980785 0.195090
+DEAL::=================================
+DEAL::0.831470 0.555570
+DEAL::0.923880 0.382683
+DEAL::0.980785 0.195090
+DEAL::0.707107 0.707107
+DEAL::0.195090 0.980785
+DEAL::0.382683 0.923880
+DEAL::0.555570 0.831470
+DEAL::=================================
+DEAL::=================================
+DEAL::0.195090 0.00000 0.980785
+DEAL::0.382683 0.00000 0.923880
+DEAL::0.555570 0.00000 0.831470
+DEAL::0.707107 0.00000 0.707107
+DEAL::0.831470 0.00000 0.555570
+DEAL::0.923880 0.00000 0.382683
+DEAL::0.980785 0.00000 0.195090
+DEAL::=================================
+DEAL::0.831470 0.00000 0.555570
+DEAL::0.923880 0.00000 0.382683
+DEAL::0.980785 0.00000 0.195090
+DEAL::0.707107 0.00000 0.707107
+DEAL::0.195090 0.00000 0.980785
+DEAL::0.382683 0.00000 0.923880
+DEAL::0.555570 0.00000 0.831470
+DEAL::=================================
+DEAL::=================================
+DEAL::1.22465e-16 1.41421 1.41421
+DEAL::0.165159 1.40938 1.40938
+DEAL::0.329189 1.39493 1.39493
+DEAL::0.490971 1.37094 1.37094
+DEAL::0.649399 1.33759 1.33759
+DEAL::0.803391 1.29510 1.29510
+DEAL::0.951895 1.24376 1.24376
+DEAL::1.09390 1.18393 1.18393
+DEAL::1.22843 1.11601 1.11601
+DEAL::1.35456 1.04047 1.04047
+DEAL::1.47145 0.957821 0.957821
+DEAL::1.57828 0.868628 0.868628
+DEAL::1.67433 0.773502 0.773502
+DEAL::1.75895 0.673091 0.673091
+DEAL::1.83155 0.568083 0.568083
+DEAL::1.89163 0.459194 0.459194
+DEAL::1.93880 0.347169 0.347169
+DEAL::1.97272 0.232772 0.232772
+DEAL::1.99317 0.116785 0.116785
+DEAL::2.00000 0.00000 0.00000
+DEAL::=================================
+DEAL::=================================
+DEAL::0.612372 0.612372 0.500000
+DEAL::0.612372 0.612372 0.500000
+DEAL::0.500000 0.612372 0.612372
+DEAL::0.612373 0.612373 0.500000
+DEAL::=================================
-//---------------------------- spherical_manifold_01.cc ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+// ---------------------------------------------------------------------
//
-// This file is subject to LGPL 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.
+// Copyright (C) 2016 by the deal.II authors
//
-//---------------------------- spherical_manifold_02.cc ---------------------------
-
+// 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 that the flat manifold does what it should on a sphere.
+// Check SphericalManifold for get_new_point and get_tangent_vector issues.
#include "../tests.h"
-#include <fstream>
-#include <deal.II/base/logstream.h>
-
+#include <deal.II/base/utilities.h>
+#include <deal.II/grid/manifold_lib.h>
-// all include files you need here
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/function.h>
#include <deal.II/grid/tria.h>
-#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>
-#include <deal.II/grid/grid_generator.h>
-#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
#include <deal.II/grid/grid_out.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q.h>
+#include <deal.II/fe/mapping_manifold.h>
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+#include <iostream>
-// Helper function
-template <int dim, int spacedim>
-void test(unsigned int ref=1)
+#include <deal.II/grid/manifold.h>
+
+using namespace dealii;
+
+struct MappingEnum
+{
+ enum type
+ {
+ MappingManifold,
+ MappingQ
+ };
+};
+
+void test (MappingEnum::type mapping_name, unsigned int refinements=1)
{
- SphericalManifold<dim,spacedim> manifold;
+ using namespace dealii;
- Triangulation<dim,spacedim> tria;
- GridGenerator::hyper_ball (tria);
+ deallog.depth_console (0);
- typename Triangulation<dim,spacedim>::active_cell_iterator cell;
+ const unsigned int degree = 2; // Degree of shape functions
- for (cell = tria.begin_active(); cell != tria.end(); ++cell)
- cell->set_all_manifold_ids(1);
+ Triangulation<2,3> triangulation;
- for (cell = tria.begin_active(); cell != tria.end(); ++cell)
+ FE_Q<2,3> fe(degree);
+ DoFHandler<2,3> dof_handler(triangulation);
+ QGaussLobatto<2> cell_quadrature(degree+1);
+
+
+
+ const double radius = 1.0;
+ Point<3> center(0.0, 0.0, 0.0);
+ GridGenerator::hyper_sphere(triangulation, center, radius);
+
+ static const SphericalManifold<2,3> sphere;
+ triangulation.set_manifold (0, sphere);
+ // static const RotatedSphericalManifold rotated_sphere;
+ // triangulation.set_manifold (1, rotated_sphere);
+
+ for (typename Triangulation<2,3>::active_cell_iterator
+ cell=triangulation.begin_active();
+ cell!=triangulation.end(); ++cell)
+ {
+ cell->set_all_manifold_ids(0);
+ // deallog << "Setting SphericalManifold\n";
+ }
+
+ triangulation.refine_global(refinements);
+ dof_handler.distribute_dofs (fe);
+
+ {
+ // Save mesh to file for visualization
+ GridOut grid_out;
+ std::ofstream grid_file("grid.vtk");
+ grid_out.write_vtk(triangulation, grid_file);
+ // deallog << "Grid has been saved into grid.vtk" << std::endl;
+ }
+
+ // deallog << "Surface mesh has " << triangulation.n_active_cells()
+ // << " cells."
+ // << std::endl;
+ // deallog << "Surface mesh has " << dof_handler.n_dofs()
+ // << " degrees of freedom."
+ // << std::endl;
+
+ std::shared_ptr<Mapping<2,3> > mapping;
+ switch (mapping_name)
+ {
+ case MappingEnum::MappingManifold:
+ // deallog << " MappingManifold" << std::endl;
+ mapping = std::unique_ptr<Mapping<2,3> >(
+ new MappingManifold<2,3 >());
+ break;
+ case MappingEnum::MappingQ:
+ // deallog << " MappingQ" << std::endl;
+ mapping = std::unique_ptr<Mapping<2,3> >(
+ new MappingQ<2,3>(fe.degree));
+ break;
+ }
+
+ FEValues<2,3> fe_values (*mapping, fe, cell_quadrature,
+ update_values |
+ update_gradients |
+ update_quadrature_points |
+ update_JxW_values);
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;
+ const unsigned int n_q_points = cell_quadrature.size();
+
+ double surface_area = 0;
+ for (typename DoFHandler<2,3>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ cell!=endc; ++cell)
{
- if (cell->center().distance(Point<spacedim>()) < 1e-10)
- cell->set_all_manifold_ids(0);
+ double patch_surface = 0;
+ fe_values.reinit (cell);
+ const auto &qp = fe_values.get_quadrature_points();
+
+
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+ {
+ patch_surface += fe_values.JxW(q_point);
+ // deallog << "--> " << qp[q_point] << std::endl;
+ }
+ // deallog << " Patch area = "
+ // << patch_surface << std::endl;
+ surface_area += patch_surface;
}
- tria.set_manifold(1, manifold);
- tria.refine_global(2);
+ deallog << " Ref = " << std::setw(5) << refinements;
+ // deallog << " Surface area = "
+ // << surface_area << std::endl;
+ deallog << " RelErr = "
+ << (surface_area - 4 * numbers::PI * radius * radius) /
+ (4 * numbers::PI * radius * radius)
+ << std::endl;
- GridOut gridout;
- gridout.write_msh(tria, deallog.get_file_stream());
+ return;
}
-int main ()
+int main()
{
- std::ofstream logfile("output");
- deallog.attach(logfile);
- deallog.threshold_double(1.e-10);
+ initlog();
- test<2,2>();
- test<3,3>();
+ std::string bar(35,'-');
+
+ deallog << bar << std::endl;
+ for (unsigned int i = 1; i<8; ++i)
+ test(MappingEnum::MappingManifold, i);
+ deallog << bar << std::endl;
+ for (unsigned int i = 1; i<8; ++i)
+ test(MappingEnum::MappingQ, i);
+ deallog << bar << std::endl;
return 0;
}
+
+
-$NOD
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-321 5 0 0 8 9 106 318 108 104 314 502 306
-322 5 0 0 8 106 30 182 318 314 178 401 502
-323 5 0 0 8 104 314 502 306 29 176 397 170
-324 5 0 0 8 314 178 401 502 176 57 247 397
-325 5 0 0 8 108 318 180 31 306 502 393 168
-326 5 0 0 8 318 182 58 180 502 401 251 393
-327 5 0 0 8 306 502 393 168 170 397 249 55
-328 5 0 0 8 502 401 251 393 397 247 78 249
-329 5 0 0 8 30 107 320 182 178 316 503 401
-330 5 0 0 8 107 10 114 320 316 112 334 503
-331 5 0 0 8 178 316 503 401 57 177 395 247
-332 5 0 0 8 316 112 334 503 177 33 196 395
-333 5 0 0 8 182 320 181 58 401 503 392 251
-334 5 0 0 8 320 114 34 181 503 334 198 392
-335 5 0 0 8 401 503 392 251 247 395 248 78
-336 5 0 0 8 503 334 198 392 395 196 62 248
-337 5 0 0 8 29 176 397 170 105 315 504 308
-338 5 0 0 8 176 57 247 397 315 179 400 504
-339 5 0 0 8 105 315 504 308 1 80 282 82
-340 5 0 0 8 315 179 400 504 80 17 146 282
-341 5 0 0 8 170 397 249 55 308 504 391 169
-342 5 0 0 8 397 247 78 249 504 400 250 391
-343 5 0 0 8 308 504 391 169 82 282 144 18
-344 5 0 0 8 504 400 250 391 282 146 49 144
-345 5 0 0 8 57 177 395 247 179 317 505 400
-346 5 0 0 8 177 33 196 395 317 113 335 505
-347 5 0 0 8 179 317 505 400 17 81 284 146
-348 5 0 0 8 317 113 335 505 81 2 86 284
-349 5 0 0 8 247 395 248 78 400 505 390 250
-350 5 0 0 8 395 196 62 248 505 335 199 390
-351 5 0 0 8 400 505 390 250 146 284 145 49
-352 5 0 0 8 505 335 199 390 284 86 20 145
-353 5 0 0 8 31 180 319 109 168 393 506 307
-354 5 0 0 8 180 58 183 319 393 251 399 506
-355 5 0 0 8 168 393 506 307 55 249 396 171
-356 5 0 0 8 393 251 399 506 249 78 246 396
-357 5 0 0 8 109 319 124 12 307 506 346 122
-358 5 0 0 8 319 183 39 124 506 399 208 346
-359 5 0 0 8 307 506 346 122 171 396 210 38
-360 5 0 0 8 506 399 208 346 396 246 65 210
-361 5 0 0 8 58 181 321 183 251 392 507 399
-362 5 0 0 8 181 34 115 321 392 198 336 507
-363 5 0 0 8 251 392 507 399 78 248 394 246
-364 5 0 0 8 392 198 336 507 248 62 197 394
-365 5 0 0 8 183 321 125 39 399 507 347 208
-366 5 0 0 8 321 115 11 125 507 336 118 347
-367 5 0 0 8 399 507 347 208 246 394 211 65
-368 5 0 0 8 507 336 118 347 394 197 36 211
-369 5 0 0 8 55 249 396 171 169 391 508 309
-370 5 0 0 8 249 78 246 396 391 250 398 508
-371 5 0 0 8 169 391 508 309 18 144 283 83
-372 5 0 0 8 391 250 398 508 144 49 147 283
-373 5 0 0 8 171 396 210 38 309 508 348 123
-374 5 0 0 8 396 246 65 210 508 398 209 348
-375 5 0 0 8 309 508 348 123 83 283 92 4
-376 5 0 0 8 508 398 209 348 283 147 23 92
-377 5 0 0 8 78 248 394 246 250 390 509 398
-378 5 0 0 8 248 62 197 394 390 199 337 509
-379 5 0 0 8 250 390 509 398 49 145 285 147
-380 5 0 0 8 390 199 337 509 145 20 87 285
-381 5 0 0 8 246 394 211 65 398 509 349 209
-382 5 0 0 8 394 197 36 211 509 337 119 349
-383 5 0 0 8 398 509 349 209 147 285 93 23
-384 5 0 0 8 509 337 119 349 285 87 3 93
-385 5 0 0 8 13 128 358 132 130 362 510 366
-386 5 0 0 8 128 41 222 358 362 224 389 510
-387 5 0 0 8 130 362 510 366 42 226 385 228
-388 5 0 0 8 362 224 389 510 226 69 241 385
-389 5 0 0 8 132 358 220 43 366 510 381 230
-390 5 0 0 8 358 222 68 220 510 389 245 381
-391 5 0 0 8 366 510 381 230 228 385 243 70
-392 5 0 0 8 510 389 245 381 385 241 79 243
-393 5 0 0 8 41 129 360 222 224 363 511 389
-394 5 0 0 8 129 5 98 360 363 96 302 511
-395 5 0 0 8 224 363 511 389 69 227 383 241
-396 5 0 0 8 363 96 302 511 227 25 166 383
-397 5 0 0 8 222 360 221 68 389 511 380 245
-398 5 0 0 8 360 98 26 221 511 302 164 380
-399 5 0 0 8 389 511 380 245 241 383 242 79
-400 5 0 0 8 511 302 164 380 383 166 54 242
-401 5 0 0 8 42 226 385 228 131 364 512 367
-402 5 0 0 8 226 69 241 385 364 225 388 512
-403 5 0 0 8 131 364 512 367 14 134 370 136
-404 5 0 0 8 364 225 388 512 134 44 232 370
-405 5 0 0 8 228 385 243 70 367 512 379 231
-406 5 0 0 8 385 241 79 243 512 388 244 379
-407 5 0 0 8 367 512 379 231 136 370 234 45
-408 5 0 0 8 512 388 244 379 370 232 71 234
-409 5 0 0 8 69 227 383 241 225 365 513 388
-410 5 0 0 8 227 25 166 383 365 97 304 513
-411 5 0 0 8 225 365 513 388 44 135 371 232
-412 5 0 0 8 365 97 304 513 135 6 100 371
-413 5 0 0 8 241 383 242 79 388 513 378 244
-414 5 0 0 8 383 166 54 242 513 304 165 378
-415 5 0 0 8 388 513 378 244 232 371 235 71
-416 5 0 0 8 513 304 165 378 371 100 27 235
-417 5 0 0 8 43 220 359 133 230 381 514 368
-418 5 0 0 8 220 68 223 359 381 245 387 514
-419 5 0 0 8 230 381 514 368 70 243 384 229
-420 5 0 0 8 381 245 387 514 243 79 240 384
-421 5 0 0 8 133 359 140 16 368 514 374 142
-422 5 0 0 8 359 223 47 140 514 387 238 374
-423 5 0 0 8 368 514 374 142 229 384 236 48
-424 5 0 0 8 514 387 238 374 384 240 72 236
-425 5 0 0 8 68 221 361 223 245 380 515 387
-426 5 0 0 8 221 26 99 361 380 164 303 515
-427 5 0 0 8 245 380 515 387 79 242 382 240
-428 5 0 0 8 380 164 303 515 242 54 167 382
-429 5 0 0 8 223 361 141 47 387 515 376 238
-430 5 0 0 8 361 99 8 141 515 303 102 376
-431 5 0 0 8 387 515 376 238 240 382 237 72
-432 5 0 0 8 515 303 102 376 382 167 28 237
-433 5 0 0 8 70 243 384 229 231 379 516 369
-434 5 0 0 8 243 79 240 384 379 244 386 516
-435 5 0 0 8 231 379 516 369 45 234 372 137
-436 5 0 0 8 379 244 386 516 234 71 233 372
-437 5 0 0 8 229 384 236 48 369 516 375 143
-438 5 0 0 8 384 240 72 236 516 386 239 375
-439 5 0 0 8 369 516 375 143 137 372 138 15
-440 5 0 0 8 516 386 239 375 372 233 46 138
-441 5 0 0 8 79 242 382 240 244 378 517 386
-442 5 0 0 8 242 54 167 382 378 165 305 517
-443 5 0 0 8 244 378 517 386 71 235 373 233
-444 5 0 0 8 378 165 305 517 235 27 101 373
-445 5 0 0 8 240 382 237 72 386 517 377 239
-446 5 0 0 8 382 167 28 237 517 305 103 377
-447 5 0 0 8 386 517 377 239 233 373 139 46
-448 5 0 0 8 517 305 103 377 373 101 7 139
-$ENDELM
+DEAL::-----------------------------------
+DEAL::Grid has been saved into grid.vtk
+DEAL:: MappingManifold
+DEAL:: Surface area = 12.5058
+DEAL:: Relative error = -0.00481934
+DEAL::-----------------------------------
+DEAL::Grid has been saved into grid.vtk
+DEAL:: MappingQ
+DEAL:: Surface area = 12.5664
+DEAL:: Relative error = 4.23599e-09
+DEAL::-----------------------------------
-//---------------------------- spherical_manifold_03.cc ---------------------------
-// Copyright (C) 2011 - 2015 by the mathLab team.
+// ---------------------------------------------------------------------
//
-// This file is subject to LGPL 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.
+// Copyright (C) 2016 by the deal.II authors
//
-//---------------------------- spherical_manifold_03.cc ---------------------------
-
+// 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 the push_forward and pull_back mechanisms
+// test tangent vectors to SphericalManifold at the poles
#include "../tests.h"
-#include <fstream>
-#include <deal.II/base/logstream.h>
-
-// all include files you need here
-#include <deal.II/grid/tria.h>
-#include <deal.II/grid/tria_accessor.h>
-#include <deal.II/grid/tria_iterator.h>
-#include <deal.II/grid/grid_generator.h>
-#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/base/utilities.h>
#include <deal.II/grid/manifold_lib.h>
-#include <deal.II/grid/grid_out.h>
-// Helper function
-template <int dim, int spacedim>
-void test(unsigned int ref=1)
+int
+main()
{
- deallog << "Testing dim " << dim
- << ", spacedim " << spacedim << std::endl;
-
- SphericalManifold<dim,spacedim> manifold;
-
- Triangulation<dim,spacedim> tria;
- Point<spacedim> p0;
- Point<spacedim> p1;
- p0[0] = .2;
- p1[0] = 1;
- p0[1] = .1;
-
- if (spacedim == 2)
- {
- p1[1] = 2*numbers::PI-.1; // theta
- }
- else if (spacedim == 3)
- {
- p1[1] = numbers::PI-.1;
- p1[2] = 2*numbers::PI-.1;
- }
-
- GridGenerator::hyper_rectangle (tria, p0, p1);
- tria.refine_global(3);
-
- const std::vector<Point<spacedim> > &vertices = tria.get_vertices();
-
- for (unsigned int i=0; i<vertices.size(); ++i)
- {
- Point<spacedim> p0 = manifold.push_forward(vertices[i]);
- Point<spacedim> p1 = manifold.pull_back(p0);
-
- if (p1.distance(vertices[i]) > 1e-10)
- deallog << "ERROR! d: " << p1.distance(vertices[i])
- << " - " << p1 << " != " << vertices[i] << std::endl;
- }
-
-
-
-}
-
-int main ()
-{
- std::ofstream logfile("output");
- deallog.attach(logfile);
- deallog.threshold_double(1.e-10);
-
- test<2,2>();
- test<3,3>();
-
- return 0;
-}
-
+ initlog();
+
+ const SphericalManifold<3> manifold;
+
+ // get tangent vectors at the south pole of the sphere in direction
+ // of the meridional equator point and a point 90 degrees to the
+ // east or west of that point. this should yield two tangent vectors
+ // that are orthogonal to each other
+ deallog << manifold.get_tangent_vector (Point<3>(0, 0, -1),
+ Point<3>(1, 0, 0)) << std::endl
+ << manifold.get_tangent_vector (Point<3>(0, 0, -1),
+ Point<3>(0, 1, 0)) << std::endl;
+}
\ No newline at end of file
-DEAL::Testing dim 2, spacedim 2
-DEAL::Testing dim 3, spacedim 3
+DEAL::1.57080 0.00000 0.00000
+DEAL::0.00000 1.57080 0.00000
std::ostream &out = deallog.get_file_stream();
FunctionManifold<1,1> F("x","x");
- SphericalManifold<2,2> G;
+ PolarManifold<2,2> G;
TensorProductManifold<2, 1,1,1, 2,2,2> manifold(F, G);
deallog << "Testing dim " << dim
<< ", spacedim " << spacedim << std::endl;
- SphericalManifold<dim,spacedim> manifold;
+ PolarManifold<dim,spacedim> manifold;
Triangulation<dim,spacedim> tria;
GridGenerator::hyper_shell (tria, Point<spacedim>(), .3, .6, 12);
deallog << "Testing dim " << dim
<< ", spacedim " << spacedim << std::endl;
- SphericalManifold<dim,spacedim> manifold;
+ PolarManifold<dim,spacedim> manifold;
Triangulation<dim,spacedim> tria;
GridGenerator::hyper_shell (tria, Point<spacedim>(), .3, .6, 12);
deallog << "Testing dim " << dim
<< ", spacedim " << spacedim << std::endl;
- SphericalManifold<dim,spacedim> manifold;
+ PolarManifold<dim,spacedim> manifold;
Triangulation<dim,spacedim> tria;
GridGenerator::hyper_shell (tria, Point<spacedim>(), .3, .6, 12);