#include <deal.II/non_matching/mesh_classifier.h>

Detailed Description

template<int dim>
class NonMatching::MeshClassifier< dim >

Class responsible for determining how the active cells and faces of a triangulation relate to the sign of a level set function. When calling the reclassify() function each of the active cells and faces are categorized as one of the values of LocationToLevelSet: inside, outside, intersected or aligned, depending on the sign of the level set function over the cell/face. This information is typically required in immersed/cut finite element methods, both when distributing degrees of freedom over the triangulation and when the system is assembled. The given class would then be used in the following way:

Vector<double> &level_set = ...
 
MeshClassifier<dim> classifier(dof_handler, level_set);
classifier.reclassify();
 
LocationToLevelSet location = classifier.location_to_level_set(cell);

The level set function can either be described as a discrete function by a (DoFHandler, Vector)-pair or as a general Function. In the case of a discrete function, LocationToLevelSet for a given face is determined by looking at the signs of the local degrees of freedom on the face. Since the Lagrange basis functions are not positive definite, positive/negative definite dof values do not imply that the interpolated function is positive/negative definite. Thus, to classify a face this class internally transforms the local dofs to a basis spanning the same polynomial space over the face but where definite dof values imply a definite function. Currently, only the case of FE_Q-elements is implemented, where we internally change basis to FE_Bernstein.

For cells, the LocationToLevelSet is determined from the faces of the cell. Specifically:

If all faces are inside or outside, the LocationToLevelSet of the cell is set to inside or outside, respectively.
If at least one face is intersected the LocationToLevelSet of the cell is set to intersected.
If one face is aligned and the remaining inside, the LocationToLevelSet of the cell is set to intersected.
If one face is aligned and the remaining outside, the LocationToLevelSet of the cell is set to outside.
If all faces are aligned, the LocationToLevelSet of the cell is set to aligned, indicating that the level set function is zero over the whole cell.
If some faces are inside and some are outside, the LocationToLevelSet of the cell is set to intersected.

Bullets 3 and 4 handles the rare case where one face is perfectly aligned with the zero contour of the level set function. The cells are classified as in the following figure:

        aligned face
+-------------+-------------+
|             |             |
| intersected |   outside   |
|             |             |
|   cell 1    |    cell 2   |
+-------------+-------------+

That is, the cell where the level set function is negative (except for the face) is classified as intersected and the cell where the level set function is positive as outside. The reasoning behind this is the following. When this class is used, we typically iterate over all the cells in the triangulation and check which LocationToLevelSet they have. On the cells that are intersected, we typically integrate over the zero contour of the level set function (see e.g. step-85). If we had defined both cells as intersected, we would have integrated over the zero contour twice. Conversely if we would have defined cell 1 as inside and cell 2 as outside, we would have missed to integrate over the zero contour. With the definition in the figure, we only integrate over the zero contour once.

Bullet 6 above handles another corner case: In 2D, the zero contour can cut the cell diagonally, exactly through the vertices, so that two of the faces are inside and two are outside. Here, none of the faces are intersected even though the cell clearly is.

Note that, the procedure above, where we classify the cell based on the faces, will incorrectly classify the cell as inside/outside, if the mesh refinement is so low that the whole zero contour is contained in a single cell (so that none of its faces are intersected).

When the level set function is described as a Function, the level set function is locally interpolated to an FE_Q element and we proceed in the same way as for the discrete level set function.

Definition at line 162 of file mesh_classifier.h.

Inheritance diagram for NonMatching::MeshClassifier< dim >:

[legend]

Public Member Functions
template<typename VectorType >
	MeshClassifier (const DoFHandler< dim > &level_set_dof_handler, const VectorType &level_set)

	MeshClassifier (const Triangulation< dim > &triangulation, const Function< dim > &level_set, const FiniteElement< dim > &element)

void	reclassify ()

LocationToLevelSet	location_to_level_set (const typename Triangulation< dim >::cell_iterator &cell) const

LocationToLevelSet	location_to_level_set (const typename Triangulation< dim >::cell_iterator &cell, const unsigned int face_index) const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Querying the observer pointers an object has.
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 Member Functions
void	initialize ()

LocationToLevelSet	determine_face_location_to_levelset (const typename Triangulation< dim >::active_cell_iterator &cell, const unsigned int face_index)

EnableObserverPointer functionality
Classes derived from EnableObserverPointer provide a facility to subscribe to this object. This is mostly used by the ObserverPointer 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

void	check_no_subscribers () const noexcept

Private Attributes
const ObserverPointer< const Triangulation< dim > >	triangulation

const std::unique_ptr< internal::MeshClassifierImplementation::LevelSetDescription< dim > >	level_set_description

std::vector< LocationToLevelSet >	cell_locations

std::vector< LocationToLevelSet >	face_locations

std::vector< std::array< LAPACKFullMatrix< double >, GeometryInfo< dim >::faces_per_cell > >	lagrange_to_bernstein_face

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

Constructor & Destructor Documentation

◆ MeshClassifier() [1/2]

template<int dim>

template<typename VectorType >

NonMatching::MeshClassifier< dim >::MeshClassifier	(	const DoFHandler< dim > &	level_set_dof_handler,
		const VectorType &	level_set
	)

Constructor. Takes a level set function described as a DoFHandler and a Vector. The triangulation attached to DoFHandler is the one that will be classified.

Definition at line 313 of file mesh_classifier.cc.

◆ MeshClassifier() [2/2]

template<int dim>

NonMatching::MeshClassifier< dim >::MeshClassifier	(	const Triangulation< dim > &	triangulation,
		const Function< dim > &	level_set,
		const FiniteElement< dim > &	element
	)

Constructor. Takes the triangulation that should be classified, a level set function described as a Function, and a scalar element that we interpolate the Function to in order to classify each cell/face.

Note: The Function and the FiniteElement must both have a single component.

Definition at line 343 of file mesh_classifier.cc.

Member Function Documentation

◆ reclassify()

template<int dim>

void NonMatching::MeshClassifier< dim >::reclassify ( )

Perform the classification of the non artificial cells and faces in the triangulation.

Definition at line 361 of file mesh_classifier.cc.

◆ location_to_level_set() [1/2]

template<int dim>

LocationToLevelSet NonMatching::MeshClassifier< dim >::location_to_level_set ( const typename Triangulation< dim >::cell_iterator & cell ) const

Return how the incoming cell is located relative to the level set function.

Definition at line 487 of file mesh_classifier.cc.

◆ location_to_level_set() [2/2]

template<int dim>

LocationToLevelSet NonMatching::MeshClassifier< dim >::location_to_level_set	(	const typename Triangulation< dim >::cell_iterator &	cell,
		const unsigned int	face_index
	)		const

Return how a face of the incoming cell is located relative to the level set function.

Definition at line 502 of file mesh_classifier.cc.

◆ initialize()

template<int dim>

void NonMatching::MeshClassifier< dim >::initialize ( )

private

For each element in the hp::FECollection returned by level_set_description, sets up the local transformation matrices.

Definition at line 519 of file mesh_classifier.cc.

◆ determine_face_location_to_levelset()

template<int dim>

LocationToLevelSet NonMatching::MeshClassifier< dim >::determine_face_location_to_levelset	(	const typename Triangulation< dim >::active_cell_iterator &	cell,
		const unsigned int	face_index
	)

private

Computes how the face with the given index on the incoming cell is located relative to the level set function.

Definition at line 436 of file mesh_classifier.cc.

◆ n_subscriptions()

unsigned int EnableObserverPointer::n_subscriptions ( ) const

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 318 of file enable_observer_pointer.h.

◆ list_subscribers() [1/2]

template<typename StreamType >

void EnableObserverPointer::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 335 of file enable_observer_pointer.h.

◆ list_subscribers() [2/2]

void EnableObserverPointer::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 200 of file enable_observer_pointer.cc.

◆ serialize()

template<class Archive >

void EnableObserverPointer::serialize	(	Archive &	ar,
		const unsigned int	version
	)

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 327 of file enable_observer_pointer.h.

◆ subscribe()

void EnableObserverPointer::subscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = `""`
	)		const

privateinherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file enable_observer_pointer.cc.

◆ unsubscribe()

void EnableObserverPointer::unsubscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = `""`
	)		const

privateinherited

Unsubscribes a user from the object.

Note: The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 154 of file enable_observer_pointer.cc.

◆ check_no_subscribers()

void EnableObserverPointer::check_no_subscribers ( ) const

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.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

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 212 of file enable_observer_pointer.h.

◆ counter_map

std::map<std::string, unsigned int> EnableObserverPointer::counter_map

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 218 of file enable_observer_pointer.h.

◆ validity_pointers

std::vector<std::atomic<bool> *> EnableObserverPointer::validity_pointers

mutableprivateinherited

In this vector, we store pointers to the validity bool in the ObserverPointer objects that subscribe to this class.

Definition at line 224 of file enable_observer_pointer.h.

◆ object_info

const std::type_info* EnableObserverPointer::object_info

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 232 of file enable_observer_pointer.h.

◆ mutex

std::mutex EnableObserverPointer::mutex

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 239 of file enable_observer_pointer.h.

The documentation for this class was generated from the following files:

include/deal.II/non_matching/mesh_classifier.h
source/non_matching/mesh_classifier.cc

Detailed Description

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Constructor & Destructor Documentation

◆ MeshClassifier() [1/2]

◆ MeshClassifier() [2/2]

Member Function Documentation

◆ reclassify()

◆ location_to_level_set() [1/2]

◆ location_to_level_set() [2/2]

◆ initialize()

◆ determine_face_location_to_levelset()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ serialize()

◆ subscribe()

◆ unsubscribe()

◆ check_no_subscribers()

Member Data Documentation

◆ triangulation

◆ level_set_description

◆ cell_locations

◆ face_locations

◆ lagrange_to_bernstein_face

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex