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Reference documentation for deal.II version 9.6.0
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Reference documentation for deal.II version 9.6.0
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#include <deal.II/grid/manifold_lib.h>
Public Types | |
| using | FaceVertexNormals |
Public Member Functions | |
| EllipticalManifold (const Point< spacedim > ¢er, const Tensor< 1, spacedim > &major_axis_direction, const double eccentricity) | |
| virtual std::unique_ptr< Manifold< dim, spacedim > > | clone () const override |
| virtual Point< spacedim > | pull_back (const Point< spacedim > &space_point) const override |
| virtual Point< spacedim > | push_forward (const Point< spacedim > &chart_point) const override |
| virtual DerivativeForm< 1, spacedim, spacedim > | push_forward_gradient (const Point< spacedim > &chart_point) const override |
| const Tensor< 1, spacedim > & | get_major_axis_direction () const |
| const Point< spacedim > & | get_center () const |
| double | get_eccentricity () const |
| Point< 2 > | push_forward (const Point< 2 > &chart_point) const |
| Point< 2 > | pull_back (const Point< 2 > &space_point) const |
| DerivativeForm< 1, 2, 2 > | push_forward_gradient (const Point< 2 > &chart_point) const |
| virtual Point< spacedim > | get_intermediate_point (const Point< spacedim > &p1, const Point< spacedim > &p2, const double w) const override |
| virtual Point< spacedim > | get_new_point (const ArrayView< const Point< spacedim > > &surrounding_points, const ArrayView< const double > &weights) const override |
| virtual void | get_new_points (const ArrayView< const Point< spacedim > > &surrounding_points, const Table< 2, double > &weights, ArrayView< Point< spacedim > > new_points) const override |
| virtual Point< spacedim > | push_forward (const Point< chartdim > &chart_point) const=0 |
| virtual DerivativeForm< 1, chartdim, spacedim > | push_forward_gradient (const Point< chartdim > &chart_point) const |
| virtual Tensor< 1, spacedim > | get_tangent_vector (const Point< spacedim > &x1, const Point< spacedim > &x2) const override |
| const Tensor< 1, chartdim > & | get_periodicity () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Computing the location of points. | |
| virtual Point< spacedim > | project_to_manifold (const ArrayView< const Point< spacedim > > &surrounding_points, const Point< spacedim > &candidate) const |
| virtual Point< spacedim > | get_new_point_on_line (const typename Triangulation< dim, spacedim >::line_iterator &line) const |
| virtual Point< spacedim > | get_new_point_on_quad (const typename Triangulation< dim, spacedim >::quad_iterator &quad) const |
| virtual Point< spacedim > | get_new_point_on_hex (const typename Triangulation< dim, spacedim >::hex_iterator &hex) const |
| Point< spacedim > | get_new_point_on_face (const typename Triangulation< dim, spacedim >::face_iterator &face) const |
| Point< spacedim > | get_new_point_on_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const |
Computing normal vectors | |
| virtual Tensor< 1, spacedim > | normal_vector (const typename Triangulation< dim, spacedim >::face_iterator &face, const Point< spacedim > &p) const |
| virtual void | get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, FaceVertexNormals &face_vertex_normals) const |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
| void | subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
| void | unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
| unsigned int | n_subscriptions () const |
| template<typename StreamType > | |
| void | list_subscribers (StreamType &stream) const |
| void | list_subscribers () const |
Static Public Member Functions | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Private Types | |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
| void | check_no_subscribers () const noexcept |
Static Private Member Functions | |
| static Tensor< 1, spacedim > | get_periodicity () |
Private Attributes | |
| const Tensor< 1, spacedim > | direction |
| const Point< spacedim > | center |
| const double | eccentricity |
| const double | cosh_u |
| const double | sinh_u |
| const FlatManifold< chartdim, chartdim > | sub_manifold |
| std::atomic< unsigned int > | counter |
| std::map< std::string, unsigned int > | counter_map |
| std::vector< std::atomic< bool > * > | validity_pointers |
| const std::type_info * | object_info |
Static Private Attributes | |
| static std::mutex | mutex |
Elliptical manifold description derived from ChartManifold. More information on the elliptical coordinate system can be found at Wikipedia .
This is based on the definition of elliptic coordinates \((u,v)\)
\[ \left\lbrace\begin{aligned} x &= x_0 + c \cosh(u) \cos(v) \\ y &= y_0 + c \sinh(u) \sin(v) \end{aligned}\right. \]
in which \((x_0,y_0)\) are coordinates of the center of the cartesian system.
The current implementation uses coordinates \((c,v)\), instead of \((u,v)\), and fixes \(u\) according to a given eccentricity. Therefore, this choice of coordinates generates an elliptical manifold characterized by a constant eccentricity: \(e=\frac{1}{\cosh(u)}\), with \(e\in\left]0,1\right[\).
The constructor of this class will throw an exception if both dim and spacedim are different from two.
This manifold can be used to produce hyper_shells with elliptical curvature. As an example, the test elliptical_manifold_01 produces the following triangulation:
Definition at line 563 of file manifold_lib.h.
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inherited |
Type keeping information about the normals at the vertices of a face of a cell. Thus, there are GeometryInfo<dim>::vertices_per_face normal vectors, that define the tangent spaces of the boundary at the vertices. Note that the vectors stored in this object are not required to be normalized, nor to actually point outward, as one often will only want to check for orthogonality to define the tangent plane; if a function requires the normals to be normalized, then it must do so itself.
For obvious reasons, this type is not useful in 1d.
Definition at line 305 of file manifold.h.
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privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
| EllipticalManifold< dim, spacedim >::EllipticalManifold | ( | const Point< spacedim > & | center, |
| const Tensor< 1, spacedim > & | major_axis_direction, | ||
| const double | eccentricity ) |
Constructor that takes the center of the manifold system, the direction of the major axis, and the manifold eccentricity. The default major axis is the x-axis. The manifold is rotated in order to align the major axis to the direction specified in input.
| center | Center of the manifold. |
| major_axis_direction | Direction of the major axis of the manifold. |
| eccentricity | Eccentricity of the manifold \(e\in\left]0,1\right[\). |
Definition at line 1188 of file manifold_lib.cc.
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overridevirtual |
Return a copy of this manifold.
Every derived class should implement this operation in a sensible manner.
Implements Manifold< dim, spacedim >.
Definition at line 1212 of file manifold_lib.cc.
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overridevirtual |
Pull back the given point in spacedim to the Euclidean chartdim dimensional space.
Refer to the general documentation of this class for more information.
Implements ChartManifold< dim, dim, dim >.
Definition at line 1262 of file manifold_lib.cc.
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overridevirtual |
Given a point in the chartdim dimensional Euclidean space, this method returns a point on the manifold embedded in the spacedim Euclidean space.
Refer to the general documentation of this class for more information.
Definition at line 1234 of file manifold_lib.cc.
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overridevirtual |
Given a point in the chartdim dimensional Euclidean space, this method returns the derivatives of the function \(F\) that maps from the chartdim-dimensional to the spacedim-dimensional space. In other words, it is a matrix of size \(\text{spacedim}\times\text{chartdim}\).
This function is used in the computations required by the get_tangent_vector() function. Since not all users of the Manifold class interface will require calling that function, the current function is implemented but will trigger an exception whenever called. This allows derived classes to avoid implementing the push_forward_gradient function if this functionality is not needed in the user program.
Refer to the general documentation of this class for more information.
Definition at line 1304 of file manifold_lib.cc.
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inline |
Get the Tensor parallel to the cylinder's major axis.
Definition at line 1302 of file manifold_lib.h.
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inline |
Return the center of the elliptical coordinate system.
Definition at line 1311 of file manifold_lib.h.
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inline |
Return the ellipse's eccentricity.
Definition at line 1320 of file manifold_lib.h.
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staticprivate |
Return the periodicity associated with the submanifold.
For \(\text{dim}=2\) and \(\text{spacedim}=2\), the first coordinate is non-periodic, while the second coordinate has a periodicity of \(2\pi\).
Definition at line 1221 of file manifold_lib.cc.
| Point< 2 > EllipticalManifold< 2, 2 >::push_forward | ( | const Point< 2 > & | chart_point | ) | const |
Definition at line 1244 of file manifold_lib.cc.
| Point< 2 > EllipticalManifold< 2, 2 >::pull_back | ( | const Point< 2 > & | space_point | ) | const |
Definition at line 1272 of file manifold_lib.cc.
| DerivativeForm< 1, 2, 2 > EllipticalManifold< 2, 2 >::push_forward_gradient | ( | const Point< 2 > & | chart_point | ) | const |
Definition at line 1315 of file manifold_lib.cc.
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overridevirtualinherited |
Refer to the general documentation of this class and the documentation of the base class for more information.
Reimplemented from Manifold< dim, spacedim >.
Definition at line 942 of file manifold.cc.
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overridevirtualinherited |
Refer to the general documentation of this class and the documentation of the base class for more information.
Reimplemented from Manifold< dim, spacedim >.
Definition at line 951 of file manifold.cc.
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overridevirtualinherited |
Compute a new set of points that interpolate between the given points surrounding_points. weights is a table with as many columns as surrounding_points.size(). The number of rows in weights must match the length of new_points.
The implementation of this function first transforms the surrounding_points to the chart space by calling pull_back(). Then, new points are computed on the chart by usual interpolation according to the given weights, which are finally transformed to the image space by push_forward().
This implementation can be much more efficient for computing multiple new points from the same surrounding points than separate calls to get_new_point() in case the pull_back() operation is expensive. This is because pull_back() is only called once for the surrounding points and the interpolation is done for all given weights using this set of points. Often, pull_back() is also more expensive than push_forward() because the former might involve some kind of Newton iteration in non-trivial manifolds.
Reimplemented from Manifold< dim, spacedim >.
Definition at line 976 of file manifold.cc.
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pure virtualinherited |
Given a point in the chartdim dimensional Euclidean space, this method returns a point on the manifold embedded in the spacedim Euclidean space.
Refer to the general documentation of this class for more information.
Implemented in CompositionManifold< dim, spacedim, chartdim, intermediate_dim, dim1, dim2 >, and FunctionManifold< dim, spacedim, chartdim >.
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virtualinherited |
Given a point in the chartdim dimensional Euclidean space, this method returns the derivatives of the function \(F\) that maps from the chartdim-dimensional to the spacedim-dimensional space. In other words, it is a matrix of size \(\text{spacedim}\times\text{chartdim}\).
This function is used in the computations required by the get_tangent_vector() function. Since not all users of the Manifold class interface will require calling that function, the current function is implemented but will trigger an exception whenever called. This allows derived classes to avoid implementing the push_forward_gradient function if this functionality is not needed in the user program.
Refer to the general documentation of this class for more information.
Reimplemented in CompositionManifold< dim, spacedim, chartdim, intermediate_dim, dim1, dim2 >, and FunctionManifold< dim, spacedim, chartdim >.
Definition at line 1014 of file manifold.cc.
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overridevirtualinherited |
Return a vector that, at \(\mathbf x_1\), is tangential to the geodesic that connects two points \(\mathbf x_1,\mathbf x_2\). See the documentation of the Manifold class and of Manifold::get_tangent_vector() for a more detailed description.
For the current class, we assume that this geodesic is the image under the push_forward() operation of a straight line of the pre-images of x1 and x2 (where pre-images are computed by pulling back the locations x1 and x2). In other words, if these preimages are \(\xi_1=F^{-1}(\mathbf x_1), \xi_2=F^{-1}(\mathbf x_2)\), then the geodesic in preimage (the chartdim-dimensional Euclidean) space is
\begin{align*} \zeta(t) &= \xi_1 + t (\xi_2-\xi_1) \\ &= F^{-1}(\mathbf x_1) + t\left[F^{-1}(\mathbf x_2) -F^{-1}(\mathbf x_1)\right] \end{align*}
In image space, i.e., in the space in which we operate, this leads to the curve
\begin{align*} \mathbf s(t) &= F(\zeta(t)) \\ &= F(\xi_1 + t (\xi_2-\xi_1)) \\ &= F\left(F^{-1}(\mathbf x_1) + t\left[F^{-1}(\mathbf x_2) -F^{-1}(\mathbf x_1)\right]\right). \end{align*}
What the current function is supposed to return is \(\mathbf s'(0)\). By the chain rule, this is equal to
\begin{align*} \mathbf s'(0) &= \frac{d}{dt}\left. F\left(F^{-1}(\mathbf x_1) + t\left[F^{-1}(\mathbf x_2) -F^{-1}(\mathbf x_1)\right]\right) \right|_{t=0} \\ &= \nabla_\xi F\left(F^{-1}(\mathbf x_1)\right) \left[F^{-1}(\mathbf x_2) -F^{-1}(\mathbf x_1)\right]. \end{align*}
This formula may then have to be slightly modified by considering any periodicity that was assumed in the call to the constructor.
Thus, the computation of tangent vectors also requires the implementation of derivatives \(\nabla_\xi F(\xi)\) of the push-forward mapping. Here, \(F^{-1}(\mathbf x_2)-F^{-1}(\mathbf x_1)\) is a chartdim-dimensional vector, and \(\nabla_\xi F\left(F^{-1}(\mathbf x_1)\right) = \nabla_\xi F\left(\xi_1\right)\) is a spacedim-times-chartdim-dimensional matrix. Consequently, and as desired, the operation results in a spacedim-dimensional vector.
| x1 | The first point that describes the geodesic, and the one at which the "direction" is to be evaluated. |
| x2 | The second point that describes the geodesic. |
Reimplemented from Manifold< dim, spacedim >.
Definition at line 1072 of file manifold.cc.
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inherited |
Return the periodicity associated with the submanifold.
Definition at line 1079 of file manifold.cc.
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virtualinherited |
Given a point which lies close to the given manifold, it modifies it and projects it to manifold itself.
This class is used by the default implementation of the function get_new_point() and should be implemented by derived classes. The default implementation simply throws an exception if called.
If your manifold is simple, you could implement this function only, and the default behavior should work out of the box.
Reimplemented in FlatManifold< chartdim, chartdim >, FlatManifold< dim, dim >, FlatManifold< dim, spacedim >, OpenCASCADE::DirectionalProjectionManifold< dim, spacedim >, OpenCASCADE::NormalProjectionManifold< dim, spacedim >, and OpenCASCADE::NormalToMeshProjectionManifold< dim, spacedim >.
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virtualinherited |
Backward compatibility interface. Return the point which shall become the new middle vertex of the two children of a regular line. In 2d, this line is a line at the boundary, while in 3d, it is bounding a face at the boundary (the lines therefore is also on the boundary).
The default implementation of this function passes its argument to the Manifolds::get_default_points_and_weights() function, and then calls the Manifold<dim,spacedim>::get_new_point() function. User derived classes can overload Manifold<dim,spacedim>::get_new_point() or Manifold<dim,spacedim>::project_to_manifold(), which is called by the default implementation of Manifold<dim,spacedim>::get_new_point().
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virtualinherited |
Backward compatibility interface. Return the point which shall become the common point of the four children of a quad at the boundary in three or more spatial dimensions. This function therefore is only useful in at least three dimensions and should not be called for lower dimensions.
This function is called after the four lines bounding the given quad are refined, so you may want to use the information provided by quad->line(i)->child(j), i=0...3, j=0,1.
The default implementation of this function passes its argument to the Manifolds::get_default_points_and_weights() function, and then calls the Manifold<dim,spacedim>::get_new_point() function. User derived classes can overload Manifold<dim,spacedim>::get_new_point() or Manifold<dim,spacedim>::project_to_manifold(), which is called by the default implementation of Manifold<dim,spacedim>::get_new_point().
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virtualinherited |
Backward compatibility interface. Return the point which shall become the common point of the eight children of a hex in three or spatial dimensions. This function therefore is only useful in at least three dimensions and should not be called for lower dimensions.
This function is called after the all the bounding objects of the given hex are refined, so you may want to use the information provided by hex->quad(i)->line(j)->child(k), i=0...5, j=0...3, k=0,1.
The default implementation of this function passes its argument to the Manifolds::get_default_points_and_weights() function, and then calls the Manifold<dim,spacedim>::get_new_point() function. User derived classes can overload Manifold<dim,spacedim>::get_new_point() or Manifold<dim,spacedim>::project_to_manifold(), which is called by the default implementation of Manifold<dim,spacedim>::get_new_point().
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inherited |
Backward compatibility interface. Depending on dim=2 or dim=3 this function calls the get_new_point_on_line or the get_new_point_on_quad function. It throws an exception for dim=1. This wrapper allows dimension independent programming.
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inherited |
Backward compatibility interface. Depending on dim=1, dim=2 or dim=3 this function calls the get_new_point_on_line, get_new_point_on_quad or the get_new_point_on_hex function. This wrapper allows dimension independent programming.
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virtualinherited |
Return the normal vector to a face embedded in this manifold, at the point p. It is not required that the normals actually point outward from the domain even if the face iterator given points to a face on the boundary of the domain. If p is not in fact on the surface, but only close-by, try to return something reasonable, for example the normal vector at the surface point closest to p. (The point p will in fact not normally lie on the actual surface, but rather be a quadrature point mapped by some polynomial mapping; the mapped surface, however, will not usually coincide with the actual surface.)
This function only makes sense if dim==spacedim because otherwise there is no unique normal vector but in fact a (spacedim-dim+1)-dimensional tangent space of vectors that are all both normal to the face and normal to the dim-dimensional surface that lives in spacedim-dimensional space. For example, think of a two-dimensional mesh that covers a two-dimensional surface in three-dimensional space. In that case, each face (edge) is one-dimensional, and there are two linearly independent vectors that are both normal to the edge: one is normal to the edge and tangent to the surface (intuitively, that would be the one that points from the current cell to the neighboring one, if the surface was locally flat), and the other one is rooted in the edge but points perpendicular to the surface (which is also perpendicular to the edge that lives within the surface). Thus, because there are no obviously correct semantics for this function if spacedim is greater than dim, the function will simply throw an error in that situation.
The face iterator gives an indication which face this function is supposed to compute the normal vector for. This is useful if the boundary of the domain is composed of different nondifferential pieces (for example when using the FlatManifold class to approximate a geometry that is completely described by the coarse mesh, with piecewise (bi-)linear components between the vertices, but where the boundary may have a kink at the vertices itself).
Reimplemented in FlatManifold< chartdim, chartdim >, FlatManifold< dim, dim >, FlatManifold< dim, spacedim >, and PolarManifold< dim, spacedim >.
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virtualinherited |
Compute the normal vectors to the boundary at each vertex of the given face embedded in the Manifold. It is not required that the normal vectors be normed somehow. Neither is it required that the normals actually point outward.
This function is needed to compute data for C1 mappings. The default implementation calls normal_vector() on each vertex.
Note that when computing normal vectors at a vertex where the boundary is not differentiable, you have to make sure that you compute the one-sided limits, i.e. limit with respect to points inside the given face.
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inherited |
Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.
Definition at line 135 of file subscriptor.cc.
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inherited |
Unsubscribes a user from the object.
identifier and the validity pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.
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inlineinherited |
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 300 of file subscriptor.h.
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inlineinherited |
List the subscribers to the input stream.
Definition at line 317 of file subscriptor.h.
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inherited |
List the subscribers to deallog.
Definition at line 203 of file subscriptor.cc.
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inlineinherited |
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.
Definition at line 309 of file subscriptor.h.
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privatenoexceptinherited |
Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 52 of file subscriptor.cc.
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private |
The direction vector of the major axis.
Definition at line 624 of file manifold_lib.h.
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private |
The center of the manifold.
Definition at line 629 of file manifold_lib.h.
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private |
The eccentricity.
Definition at line 634 of file manifold_lib.h.
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private |
Parameters deriving from the eccentricity of the manifold.
Definition at line 639 of file manifold_lib.h.
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private |
Definition at line 640 of file manifold_lib.h.
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privateinherited |
The sub_manifold object is used to compute the average of the points in the chart coordinates system.
In an ideal world, it would have type FlatManifold<dim,chartdim>. However, this would instantiate cases where dim>spacedim, which leads to invalid situations. We instead use <chartdim,chartdim>, which is (i) always valid, and (ii) does not matter at all since the first (dim) argument of manifolds is, in fact, ignored as far as manifold functionality is concerned.
Definition at line 1093 of file manifold.h.
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mutableprivateinherited |
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.
Definition at line 218 of file subscriptor.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.
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mutableprivateinherited |
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 248 of file subscriptor.h.
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staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().
Definition at line 271 of file subscriptor.h.
1.11.0